AN ABSTRACT OF THE DISSERTATION OF
Christopher John Stapels for the degree of Doctor of Philosophy in Physics presented
on September 20. 2004.
Title: Level Structure of '52Gd Populated in 152Th flDecay
Abstract Approved:
Redacted for Privacy
As part of a research program to study the transitional region of N= 88
isotones, l52
was produced by the reaction '51Eu(a,3n)152Th in the 88" cyclotron
located at LBNL. Gamma-ray spectroscopy of the radiation emitted from excited
152Gd following the
j3f
decay of '52Th has been performed using an array of 20
germanium detectors. The large Q-value (3990 keV) of the '52Th 2 decay allows for
the population of many levels; study of coincidence and single events resulted in the
establishment of 54 new levels and 266 new transitions. Angular correlation of the
coincidences has determined spin and parity of many levels with several seen as key to
the band structure, including two new 0 levels. One new rotational band including
the new 1475.2 keV 0 level and the 1771.7 keV 2 level is proposed. The overall
band structure compared to collective excitation models demonstrates the position of
'52Gd in the transition from a spherical to deformed shape, also seen in other N =88
isotones. Monopole transition strength among bands indicates the possibility of
mixing of both shapes among the excited states. The remarkable similarity of the band
structure among these isotones is discussed.
Level Structure of '52Gd Populated in '52Th fiDecay
by
Christopher John Stapels
A DISSERTATION
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Doctor of Philosophy
Presented September 20, 2004
Commencement June 2005
Doctor of Philosophy dissertation of Christopher John Stapels
presented on September 20. 2004.
APPROVED:
Redacted for Privacy
Majoi Professor, representing Physics
Redacted for Privacy
Chair of theDka4Itment of Physics
Redacted for Privacy
Dean of th 4IadIjate School
I understand that my dissertation will become part of the permanent collection of
Oregon State University libraries. My signature below authorizes release of my
dissertation to any reader upon request.
Redacted for privacy
ACKNOWLEDGMENTS
There are many individuals who have been crucial to the development or this
work. The most influential of these include the following: My advisor, Dr. Ken
Krane. Without the hundreds of hours of tutoring, explaining, editing, and reexplaining, I would have only have dreams of a completed thesis. My wife, Martha,
who has continually encouraged me with love, supported me financially for the last
several months, and gave me a goal to drive for by fmishing her PhD last year. Jeff
Loats and Paul Schmelzenbach, my group members, provided a whole lot of the
computer code I used, many critical discussions, and encouragement by proving that it
is possible to graduate with these data sets. They also helped in the original
experiment. John Wood of Georgia Tech. helped me understand much of the nuclear
structure theory, and was vital to developing the band structure of' 52Gd, not to
mention the fact that he made several trips to Corvallis to help with the interpretation
of the data set for this work. David Kuip originally interpreted the data stream, and
was the key person involved in gathering the data during the experiment. Dr. Corinne
Manogue provided extra encouragement when I was thhildng of giving up. My
committee members, Dr. Henri Jansen, Dr. Al Stetz, Dr. William Warren, and Dr.
Mary Flahive have provided the academic guidance that I needed to complete my
program at Oregon State University, including the wisdom to make sure I had a
second try at my oral exam. Last, I thank my son Jonah for many smiles over the last
ten months. Thank you to all of you for helping me achieve my goal.
TABLE OF CONTENTS
Chapter1
Introduction ............................................................................................ 1
Chapter 2
Emission and Correlation of EM Radiation ............................................. 4
2.1
Radiation field ................................................................................................ 4
2.1.1
Quantum mechanical description of the radiation field ........................ 6
2.1.2
Transition rates ................................................................................... 7
2.1.3
Weisskopf estimates .......................................................................... 10
2.1.4
Angular momentum and parity selection rules ................................... 11
2.1.5
Internal conversion ........................................................................... 13
2.2
y y coincidence rates .................................................................................. 15
2.3
Angular correlation ....................................................................................... 16
2.3.1
Angular correlation example ............................................................. 17
2.3.2
Angular correlation formalism .......................................................... 18
2.3.3
Multipole mixing .............................................................................. 19
2.3.4
Solid angle correction factors ............................................................ 22
2.3.5
Unobserved intermediate transitions ................................................. 23
2.3.6
Elucidation of spin and parity values ................................................. 24
Chapter 3
3.1
Nuclear Models .................................................................................... 27
Shell model .................................................................................................. 27
Shell model potential ........................................................................ 27
'52Gd in the shell model .................................................................... 29
Pairing and the spin predictions ......................................................... 30
3.1.1
3.1.2
3.1.3
3.2
Collective nuclear vibrations ........................................................................ 30
Theoretical description ...................................................................... 30
Spherical vibrator band structure ....................................................... 32
3.2.1
3.2.2
3.3
Deformation ................................................................................................. 33
Vibrations of deformed nuclei ........................................................... 35
3.3.2
Nuclear rotations in deformed nuclei ................................................. 35
3.3.3
Deformed rotational structure............................................................ 37
3.3.1
TABLE OF CONTENTS (Continued)
Chapter4 Previous Work ...................................................................................... 39
4.1
Particle transfer studies ................................................................................. 40
4.2
Spectroscopy ................................................................................................ 41
4.3
Internal conversion (ICC) ............................................................................. 43
4.4
152Eu and I52mTb decay ................................................................................. 44
4.5
Angular correlations ..................................................................................... 44
4.6
Computational models .................................................................................. 45
Chapter 5
Experimental Description ..................................................................... 47
5.1
Source preparation ........................................................................................ 47
5.2
Detectors ...................................................................................................... 48
5.3
Angle relationships ....................................................................................... 50
5.4
Electronics ................................................................................................... 51
Timing .............................................................................................. 53
Coincidence pile up .......................................................................... 54
5.4.1
5.4.2
5.5
Data stream .................................................................................................. 54
5.5.2
Format .............................................................................................. 54
Errors in the data stream ................................................................... 56
Chapter 6
Analysis and Results ............................................................................. 58
5.5.1
6.1
Data sorting and calibration .......................................................................... 58
Timing .............................................................................................. 58
Scale down correction to singles ....................................................... 60
Efficiencies ....................................................................................... 61
6.1.4
Energy and width calibrations ........................................................... 65
6.1.1
6.1.2
6.1.3
TABLE OF CONTENTS (Continued)
6.2
Level scheme ................................................................................................ 66
6.2.1
Singles analysis ................................................................................. 66
6.2.2
Coincidence analysis ......................................................................... 67
6.2.3
Level placement ................................................................................ 71
6.2.4
Transition and level results ............................................................... 72
6.3
Comparison to previous results ..................................................................... 90
6.3.1
New levels ........................................................................................ 90
6.3.2
Newtransitions ................................................................................. 91
6.3.3
Upper limits on unseen transitions .................................................. 119
6.4
Angular correlation ..................................................................................... 120
6.4.1
Determination of correlation coefficients ........................................ 120
6.4.2
Matrix solution of distribution coefficients ...................................... 121
6.5
Mixing ratio (ö) calculation ........................................................................ 129
Previous mixing ratio measurements ............................................... 130
6.5.1
6.6
Determination of level spin ......................................................................... 132
1475.2keV0leve1 ......................................................................... 132
1681.1 keV0level ......................................................................... 134
1839.9keV34level ......................................................................... 134
6.6.4
1915.5keV3level ......................................................................... 134
6.6.5
Other spin assignments ................................................................... 135
6.6.1
6.6.2
6.6.3
6.7
E0 transition strength calculation ................................................................ 135
Chapter 7
Band Structure .................................................................................... 138
7.1
Nuclear structure model applications to '52Gd ............................................. 139
7.1.1
Quasirotational bands ...................................................................... 139
7.1.2
Ground state band ........................................................................... 141
7.1.3
Variable moment of inertia model ................................................... 143
7.1.4
Soft rotor ........................................................................................ 144
7.1.5
Anharmonic vibrator ....................................................................... 145
7.1.6
Interacting boson model (IBM) ...................................................... 147
7.2
Multipole transition strengths ..................................................................... 149
7.2.1
Monopole transition intensity .......................................................... 149
TABLE OF CONTENTS (Continued)
Page
7.2.2
Relative B(E2) values in positive parity bands ................................. 151
7.3
Other bands and excited states ..........................................................
Octupole states ..................................................................................
Broken pair states ..............................................................................
Shell model excitations .....................................................................
7.3.1
7.3.2
7.3.3
Band structure systematics ................................................................ 156
7.4
7.5
7.5.1
7.5.2
8.
154
154
154
155
Conclusions ....................................................................................... 158
Summary ........................................................................................... 158
Further work ...................................................................................... 160
Appendix ........................................................................................... 161
Appendix I Energy sorted 7-ray list.......................................................................... 162
LIST OF FIGURES
Figure
2-1 Spin 0-1-0 cascade showing possible rn-projections of the intermediate state ..... 17
2-2 Diagram for angular correlation with an unobserved intermediate transition ...... 23
2-3 Possible combinations of correlation coefficients A22 and A for correlations
with 2 to 0 transitions for selected spin values of the initial level .................. 25
3-1 Two-neutron binding energy difference for some Gd isotopes ............................ 28
3-2 Band diagram for a theoretical spherical vibrator............................................... 33
3-3 Theoretical rotor band spacing........................................................................... 36
3-4 Theoretical deformed vibrational structure with quasi-rotational bands .............. 37
4-1 Low lying excited states for selected Z = 64 isotopes ......................................... 39
4-2 Comparison of ground-state and ybands of selected even Z, N= 88 isotones ..... 43
5-1 Inside the 8it detector ......................................................................................... 49
5-2 A schematic rendering of the relative placements of the crystals for the HPGe
detectors inside the 8it detector........................................................................ 50
5-3 Angle relationships in the 8m detector array ....................................................... 51
5-4 Sample data stream from the 8m ......................................................................... 55
6-1 Sample time spectrum ........................................................................................ 59
6-2 Sample time difference spectrum ....................................................................... 60
6-3 '54Gd ground state rotational band ...................................................................... 62
6-4 Summed detector efficiency for singles and coincidences in the 8it .................... 64
6-5 Typical peak fit of singles data ........................................................................... 67
LIST OF FIGURES (Continued)
Figure
6-6 Comparison of singles and coincidence spectra .................................................. 69
6-7 Coincidence intensity method ............................................................................ 70
6-8 Sample angular distribution fit ......................................................................... 122
6-9 Sample of X2 reduction method ........................................................................ 130
6-10 1130 keV gated coincidence spectrum showing 344 keV coincidence and
feeding transitions ......................................................................................... 133
7-1 Positive parity band structure diagram for some low-lying states in '52Gd ........ 138
7-2 Energy levels for selected bands showing deviation from rotational spacing .... 140
7-3 The moment of inertia implied by a pure rotor for selected bands..................... 141
7-4 Low-lying members of the ground-state band of' 52Gd..................................... 142
7-5 Change in ground state band spacing due to VMI ............................................ 144
7-6 Partial level diagram showing B(E2) values that differ from the anharmonic
vibrator ......................................................................................................... 147
7-7 Band structure diagram showing B(E2) values ................................................. 152
7-8 Selected B(E2) values for additional bands in '52Gd ......................................... 153
7-9 Negative parity bands in '52Gd ......................................................................... 155
7-10 Example of a single nucleon excitation across the Z = 64 subshell gap ........... 156
7-11 Comparison offlquasirotational bands for some N 88 isotones ................... 157
7-12 Comparison of ybands for some N 88 isotones .......................................... 158
7-13 Comparison of the "i" rotational bands in some N 88 isotones .................... 159
LIST OF TABLES
ig
Table
2-1 Approximate relative probability for emission of pure multipole transitions ....... 11
2-2 Selection rules for common multipoles .............................................................. 12
2-3 Q-factor calculation parameters.......................................................................... 22
5-1 Run numbers, scale-down factors, and time information for each data set
created for this experiment .............................................................................. 53
6-1 Efficiency parameters describing the fits shown in Figure 6-4 ............................ 64
6-2 Level sorted transition list .................................................................................. 73
6-3 Comparison of published levels to those proposed in this work.......................... 92
6-4 Transition comparison........................................................................................ 97
6-5 Upper limits on transitions seen in Adam et
al.
but not seen in this work ......... 119
6-6 Angular correlation results ............................................................................... 123
6-7 Previously measured Svalues compared to this work ....................................... 131
6-8 Calculation of Uk factors using ratios of angular correlation factors .................. 137
7-1 Lifetimes and absolute B(E2) values, as reported by Johnson et
al ...................
142
7-2 Electric monopole intensities JO for selected transitions and relevant
conversion coefficients .................................................................................. 149
PREFACE
Ernest Rutherford once wrote the following in a letter to A. S. Eve from his
country cottage. He reported of his garden what he had also done for physics,
vigorous and generous work: "I have made a still further clearance of the blackberry
patch and the view is now quite attractive."
I hope that statement can be applied at least in part to the subject of this work.
From Richard Rhodes, The Making of the Atomic Bomb (New York. Simon
and Schuster, 1986)
Chapter 1 Introduction
The composition and structure of nuclei is well developed but not fully
understood. The profile of a three-dimensional plot of nuclear binding energy
differences for nuclei of different numbers of protons (Z) and neutrons (N) reveals
hints to the gross structure and makeup of the nucleus. Both peaks and valleys in such
a diagram indicate significant bounds to nuclear properties and indicate points of
interest for probing those properties. A valley in this diagram occurs for the N = 88
isotones those nuclei having 88 neutrons. '52Gd is one of these isotones, making it
of interest to study. The nuclear structure determined by the energies of excited states
can help elucidate these properties.
Though the energy levels of an excited nucleus are determined by quantum
mechanics, the many-body problem of 152 nucleons orbited by 64 electrons is beyond
analytical solution. Some computational models have had varying degrees of success,
yet the energies of excited states must be found experimentally by measuring the
energy of radiation emitted during the decay of these levels. Study of the energies
and relationships between levels nuclear structure provides an indication of the
nuclear forces that determine the properties of all nuclei.
Because nuclear excited states have definite angular momentum and parity
properties, selection rules prohibit certain transitions between levels and enhance
others. A heavy nucleus might have over 500 detectable yrays, thus the level scheme
for such a nucleus can be a complicated maze of levels and transitions. Observing
2
emitted radiation with a single detector will indicate only the energy and intensity of
radiations. Coincidence spectroscopy observing multiple radiations within a given
time window indicates the relationships of different transitions in the level scheme.
Many models have been developed to explain the observed level schemes.
Further development and testing of these models requires the study of nuclei at the
extremes of the model parameters. Often, these nuclei must be created artificially.
Many of the artificially producible isotopes were originally studied during the rapid
expansion of nuclear structure investigations in the 1950's to the 1970's. Since then
great developments in detector resolution and efficiency have been made. Along with
these changes has come a proliferation of multiple-detector arrays for coincidence y
detection. Large improvements can now be made above and beyond on the data
previously collected on artificial isotopes. Specifically, the detector array used in the
present work has this ability.
'52Tb decays by
decay - the emission of a positron during the conversion of
a proton into a neutron. The daughter nucleus that is the result of this decay is '52Gd.
Since the total energy of' 52Tb minus the byproducts of the beta radiation is greater
than the ground state energy of'52Gd, the daughter is left in an excited state. In
recording the relationships of the energies emitted as
decays to the ground state,
some patterns emerge.
The onset of nuclear deformation above A = 150 makes the study of '52Gd
especially interesting. Doubly-even nuclei with 80-86 neutrons are generally thought
to have spherically shaped ground states and excited states with a spherical
equilibrium. At N = 90, the excited states of nuclei begin to exhibit properties
consistent with a deformed shape. Thus the N = 88 isotones are often deemed
transitional. Study of the patterns of excited states in these nuclei can help develop
models for both spherical and deformed nuclei.
This thesis involves '-ray energies and coincidence information recorded by a
20 detector array observing a '52Tb sample decaying to '52Gd. The data have
suggested many new transitions and excited states in the 152Gd level scheme. Angular
correlations of coincident yrays have determined or restricted angular momentum and
parity assignments for many of these excited states. Nuclear structure models are
applied to the results to infer the character of the '52Gd nucleus.
Chapter 2 of this thesis describes the emission of electromagnetic radiation by
nuclei and describes the angular correlation formalism. Some aspects of applicable
nuclear models are described in Chapter 3. An overview of previously published work
relating to the structure of '52Gd and similar nuclei, along with some pertinent
conclusions of these authors, is contained in Chapter 4.
Chapter 5 describes the details of the experimental apparatus and the format of
the collected data. Methods of analysis are presented in Chapter 6. Lists of the
excited states determined and all the observed transitions between those levels are
included. The levels and yrays are also compared to the most recently published
results. Chapter 7 deals with patterns seen in the low-energy levels or band structure
in comparison to specific models and to the surrounding nuclei.
4
Chapter 2 Emission and Correlation of EM Radiation
2.1
Radiation field
The electromagnetic radiation emitted from a nucleus is the basis of this study.
In order to extract the maximum amount of information from the radiation, it is
necessary to understand the nature of the radiation. Nuclear levels in general have
well defined angular momentum and defmite parity. Electromagnetic radiation
connecting levels also is seen to have these properties.
Maxwell's equations provide a fundamental description of the electric and
magnetic components of the radiation field.
V XE +
=0,
V.E=4ffp,
at
2-1
VxB=4j,
V.B=0.
Far from the nucleus, p and j are zero. The vector potential and a scalar
potential are required to link the electric and magnetic fields:
B=VxA,
2-2
E=VcI.
2-3
at
Combining Maxwell's equations with these potentials produces the
inhomogeneous wave equation that describes electromagnetic radiation fields (in
Coulomb gauge):
5
2-4
it
V A =0 (Coulomb gauge).
The scalar potential version of 2-4
2-5
is:
V2(r,9,q5,t)_r0øt)
=0.
2-6
t2
The solutions to the scalar wave equation are building blocks for the
corresponding vector equation. The solutions are obtained by separation of variables.
The radial parts can be solved by spherical Bessel functions and the angular parts by
the spherical harmonics.
L,M (r,9,Ø,t)
=
L,M(r,O,ø)e
L has positive integer values L
terms of the EM field, L
is
0, 1, 2,
3,... and M=
0, ±1, ±2,
k is
±L.
In
the angular momentum carried by the field, while Mis its
projection on some chosen z-axis. The value w is the frequency of the
The value
2-7
= jL(kr)YL,M(9,ø)e°t.
EM radiation.
used to match the radial solution to the boundary conditions. It has
units of inverse distance.
Using the proper vector and differential operators, the scalar solution can be
transformed into a solution of the vector wave equation. These vector wave equations
have defmite parity. The two possible parities give rise to two different types of
electromagnetic radiation fields: magnetic (M) and electric (E). The gradient operator
alone changes the parity of a vector field, but does not produce a solution to the vector
wave equation. Since the parity depends on the angular momentum, the angular
momentum operator produces solutions with the proper vector and parity properties.'
In natural units (h = m = c = 1), the vector potential can be written as
1
A(M)
L,M
LLM(r),
2-8
L(L + 1)
1
L,M
k..jL(L+1)
(VxL)GLM(r),
2-9
L=ihrxV.
2-10
An EL (ML) transition refers to radiation with electric (magnetic) type parity
and L units of angular momentum. A 7-ray transition connecting two states can be a
pure multipole or consist of a combination of several multipolarities.
2.1.1
Quantum mechanical description of the radiation field
The vector field description of the electromagnetic field allows transition
probabilities for EM radiation to be written th terms of quantum mechanical matrix
elements. The matrix element that describes the transition probability for emission of
multipole2
radiation is (J1m j(r ')A
I
Jm1) from an initial state of total angular
momentum (spin) .1, and projection m, to the state .Jj with projection mj. The symbol
j (r') is the nuclear current density operator
2-il
7
It is often simpler to write the matrix elements in terms of the multipole
operators1,
1
(2L+1)!!
7si(ML,M)
L
(L+1)[I+1)I1
(2L+1)!!
1(EL,M)
(OL(L+1)
[L(L+1)]
Jj(r')A(r')
Jj(r')A(r
2-12
2-13
The transition matrix elements can be written in terms of the multipole matrix
elements:
(Jfmf
j(r')A(r')Jm1)
=
1
i
(Jfmf
(2L + 1)!!
The value of
2-14
kL
U
0 for .ir= E, and 1 for r=
i1(L, M) Jm1)
M
Transition rates
2.1.2
The Wigner-Eckart theorem allows the transition matrix elements to be written
in a simplified form that separates the element into a geometrical factor due to the
angular momentum change of the transition, and a reduced matrix element due to the
remaining nuclear force moderated parts of the transition probability.2
(Jfmflj(r1)AJjmj)=(_1)3mf( Jf
L
J(Jjj(r1)AJj),
m1 _Mm)
The Wigner
3]
symbol is defmed by'
2-15
(i 12
(_1)i2
13
m1m2m3
(j1m,j2m2 j3-rn3).
2-16
(2j3+1)
or, in terms of the 3] symbol in 2-15,
LJ
[Jm1Mm.
(1Y'm'
(Jj,m1,L,M
J,_m1)
2-17
(2J1+1)
It is frequently useful to compare transition strengths without the energy
dependence. The reduced matrix elements defined in 2-15 allow such a
simplification. The commonly used reduced transition probability is
B(L,JJ1)=
The B (,rL, .1, -i
II(2L)IIJ
2-18
(2+1)
is important in determining structure since it depends only on
the nuclear parts of the transition matrix element. The total transition probability'
contains the energy and angular momentum dependant factors:
8,21 (L + 1)
[(2L+1)!!)]2 L
B(irL,J
J1).
2-19
Since electric quadrupole transitions are the most common in transitions
between nuclear collective states at low excitation energy, the B(E2) reduced
transition probabilities are often an aid to determination of the nuclear structure. The
average time for a decay to take place is directly related to the strength of the
transition matrix element so the reduced transition probabilities can be determined if
the half life is known. Using 2-19 and noting that the transition rate is related to the
half-life, the B(,rL) can be written as3
h(hcj
B(2rL;JJf)= L[(2L+l),
2L+1
ln(2)
2-20
rpartic
82T(L+1)
7
For a half-life in seconds and energy in keV, the B(E2) in units of e2b2 has a
simplified4
form:
B(E2)=
56.4
1/2
2-21
E5
The partial half-life is the total half-life of an excited state divided by the
fraction of the decays that occur by the tray process of interest. In the B(E2), the
process of interest would be transitions ofE2 multipolarity. For example, for a level
that decays only by one transition that consists of E0, Ml and E2 multipolarities, the
total half-life can be written as
TMl.ub0l
TEoPct
1/2
+
1/2
TE2,Phic
+
1/2
,
2-22
fE2
where f is the intensity of a transition that involves a given multipolarity divided by
the total intensity of transitions from the same level.
Due to the difficulty of measuring times in the picosecond and shorter range
and the problem of isolating yrays from a particular level, few lifetimes of excited
states have been measured. Table 7-1 lists the all the measured absolute B(E2) values
for transitions in '52Gd.
The reduced transition probabilities for transitions from a common level can be
compared. The normalized B(E2) values from a given level are an indication of the
reduced nuclear matrix element in 2-18. The relative B(E2) is calculated using the
10
intensity I7of the transition of interest, the percentage of that transition that involves
the E2 multipolarity %E2, and the energy E in any convenient units:
B(E2)1
(%E2)Ir
C.
2-23
The value C is a normalization factor determined by making the strongest B(E2) from
a level equal to 100.
2.1.3
Weisskopf estimates
Since the wavefunctions of nuclear states are generally not known, it is not
generally possible to get the transition rates directly from 2-19. If the assumption that
the radiation is due to one nucleon moving from one shell-model orbit to another is
made, an estimation of some transition rates for certain types of radiation is possible
(for a description of the shell model, see
3.1).
These estimates are known as the
Weisskopf or single-particle estimates. Using the transition rate
2-19,
a simplified
form for the radial dependence, and estimating the spin and angular parts of the
integral to be unity the transition probabilities can be estimated for the lower
multipolarities5
B(EL)W =
4,r
A2''3,
L+3)
B(ML)W =(l.2)22(
2-24
2-25
Table 2-1 shows the most common type of multipole radiations and
approximate strengths determined by Weisskopf estimates6. The many simplifying
11
assumptions made to develop these estimates make them useful only as a rough
guideline to multipole strength. The af' energy dependence in 2-19 has been
included in these estimates to highlight the differences in strengths.
2.1.4
Angular momentum and parity selection rules
The total angular momentum of a nuclear state is the sum of orbital angular
momentum and the nucleon spin. The combination is commonly referred to as simply
the spin Jof the nuclear state. Since similar nucleons pair to form states of total
angular momentum zero, the spin is generally due to only the unpaired nucleons. The
angular momentum quantum numbers Jand
m3
of a nuclear state and of the multipole
radiation are considered definite and determine the allowed transitions from levels of
spin-parity J to J.
The change in spin is constrained by the multipolarity of the 'y-ray emission.
Table 2-1 Approximate relative probability for emission of pure multipole transitions6
Multipolarity
Description
El
Electric Dipole
Electric Quadrupole
Electric Octupole
Magnetic Dipole
Magnetic Quadrupole
E2
E3
Mi
M2
Approximate relative
emission probability
(in s1 for E in MeV)
1 .Ox 1 014A213E3
7.3x1O7A413E5
34A2E7
5.6x10'3E3
3.5 xl
7 A213E5
12
2-26
M=m1mf.
2-27
The multipole fields also have well defmed parity. This determines the parity
change of a given multipole transition.
(_1)t
;ir1.
= (-1)'
(magnetic multipoles),
2-28
(electric multipoles).
2-29
A summary of the possible change in spin (J) and parity (sr) for the most
common multipole transitions is depicted in Table
The selection rules in Table
2-2
2-2.
and the rapid decline of multipole strength
with increasing L seen in Table 2-1 allow coincidence information to be an aid to the
determination of the spin and parity of a level. For example, transitions with L
infrequently observed. If L
= 2 is
feeds a O level can at most be a
2
are
taken as the highest multipole order, a level that
state (2
is
unlikely since the parity change would
Table 2-2 Selection rules for common multipoles
Multipolarity
> 2
Possible
Ar
EO
0
0
El
0,1
1
E2
0,1,2
0
MI
0,1
0
M2
0,1,2
1
j
13
require an M2 transition). If a transition from that same level to a 4 level is found,
the spin and parity of the original level is almost certainly 2. Even where the spin
and parity cannot be unambiguously determined by this method, it is often able to
limit the choices to only a few spin and parity combinations.
2.1.5
Internal conversion
Overlap of the electronic wavefunctions with the nucleus can provide other
channels for the excited nucleus to release energy. The transfer of energy directly to
the electrons in various shells is known as internal conversion. For transition
probability
T(e, n/c)
for electron emission and T() for remission, the conversion
coefficient is defmed as'
T(e, nic)
T(v)
'
2-30
where n is the principal quantum number and K indicates the angular momentum
quantum number of the electron shells. The total conversion coefficient is the sum of
the coefficient for each shell:
a=
2-31
Since the K-shell orbitals have the most overlap with the nucleus, these electrons have
the largest conversion coefficients; the conversion coefficients decrease approximately
as
1/n3
for higher electron shells.6
The internal conversion process can involve any multipolarity and uniquely
uses E0 (there are no E0 'y-ray transitions). The E0 transition refers to zero change in
14
angular momentum for an electric (K) type transition. The diagonal elements of the
multipole operator 2-13 for the EO process are directly related to the mean square
radii.7
Since EO transitions indicate a change in the mean-square radius of the nucleus
and not the spin, nuclear levels with large EO components indicate the possibility of
largely different shapes. Such transitions can be an important determinant of different
coexisting shapes in the nuclear structure.
The EO multipolarity intensity of a transition that involves EO + E2 + MI can
be calculated if the experimental
(XJ(
and the mixing ratio for E2/M1 are known. The
aK designation isolates the effects of electronic transitions from the K shell. The
experimental (rK can be expanded into terms specific to each multipole8:
1E0
1
82
2-32
The
aMI
and
aE2
are the ratios of internal conversion by MI or E2 to the total
v-ray intensity. The term 1° in 2-32 describes the intensity of electron emissions that
involve EO. The a's depend on the multipole operators and the electron
wavefunctions; they can be calculated since the electronic wavefunctions are well
known. Online computer codes9 can be used to generate these coefficients for input Z
and E1 values.
In cases where the half-life of the level has been measured, it is possible to
calculate the EO transition strength. The EO electron intensity is used to calculate the
partial half-life
15
I+I01a1
Tb'o
rbotal
1/2
x
,EO
2-33
'
which depends also on the total gamma ray intensity I, and the total internal
conversion intensity
L1, L11, L111,
jbotal
which includes the intensity due to all the electron shells K,
M etc. The EO transition strength p2(EO) depends on the partial half-life of
the level with respect to EO.
1
p2(EO)
1/2
The
K
2-34
K
are due to the electron wavefunctions and are available from Bell et
al)° The EO electron intensities for selected yrays from the present experiments are
shown in Table 7-2.
2.2
'y
y coincidence rates
In general, determination of the level structure of the nucleus requires the
simultaneous (within a small time window) detection of two 'yrays. Inmost nuclei,
including '52Gd, the lifetimes of nuclear excited states are generally in the
femtosecond range, although some are as long as a few nanoseconds. In a relatively
strong source of 1 jiCi, the average time between decays is on the order of tens of
microseconds. Two yrays from this source that are detected within a time window of
a few nanoseconds are much more likely to be from the same nucleus than two
different nuclei. A level scheme for a nucleus can thus be created by detecting
multiple simultaneous radiations with only a small correction for accidental
16
coincidences.
The rate of collection of individual coincidence events can be calculated based
on the source strength. The efficiencies for detecting i and
b
are e, and
describes the ratio of the number of i events to total decay events
ratio of y, and
'Y2
(b
e2.
The value
describes the
coincidence events to total events). The rate R depends on the
activity A:
Rsng
=e,Ab,
2-35
=e,e2Ab.
The accidental coincidence rate depends on the activity squared:
Racnc
in a time window of width
2.3
=
e2A2t,
2-36
t.
Angular correlation
The probability of emission of radiation depends on the angle between the
quantization axis and the direction of propagation of the radiation. Therefore,
observing the direction of radiation as a function of angle indicates the spins of states
that are connected by that transition. Such a measurement is defmed as a directional
distribution.'3
To measure the distribution requires some orientation, or a preferred axis,
which produces an unequal distribution of rn-state orientations of the nuclear spins.
The direction of one radiation in a cascade of coincident transitions from a single
nucleus can be used to fix the orientation of the nucleus, as in this experiment. In this
17
case, the angle between two radiations is measured and the measurement is defined as
an angular correlation.
2.3.1
Angular correlation example
The defmite angular momentum and parity properties of pure multipole transitions
give a characteristic angular dependence to the radiation (due to the spherical
harmonics) depending on L and its projection M For dipole radiation, M= 0 radiation
varies as sin29, and M= ±1 radiation varies as 2(1+cos29). For example, a ray
transition from a state of J = F to
= 0 is pure electric dipole (El), with an
angular distribution that varies depending on z.m. Figure 2-1 shows the three possible
projections (m) for the spin(J) of the initial state: -1, 0, and 1. With no preferred
jr
J1
p
7
=
=1
=0
Figure 2-1 Spin 0-1-0 cascade showing possible rn-projections of the intermediate
state
18
orientation, each m state is equally populated, and the intensity of emitted radiation
W(G) is independent of a
W(0)oc 2[ W i]+Wm
= 2[I(1+cos2 O)]+sin2 0 = 2.
If another transition from a J
O
state to the
2-37
= 1 state is observed
first, the emitted radiation determines a preferred axis for quantization. The angle 0 is
defmed as the angle between the two observed yrays, with the 0= O direction
defmed by the first yray.
The
distribution is the same as the original distribution for m = 0 and Am =
1, with respect to 0 = 0. The sin20 dependence of the Am = 0 transition forces the
observed Y2 transitions to have Am = ±1. And, therefore, the distribution of the
radiation with respect to the direction of 21 (angular correlation) is now the sum of two
Am = 1 distributions that depends on Oas:
W(0) oc
2.3.2
2[WAm
I]
= 2[(1+cos2
0)] = 1+cos2 0.
2-38
Angular correlation formalism
The previous example indicates how rotating the quantization axis from the
direction of one radiation to the other produces a correlation between 21 and
that
depends on the angle between them. The general case of two successively detected y
rays can be written in terms of independently weighted Legendre polynomials. The
resulting angular distribution equation is
19
W(0)=N
APk(cosO),
2-39
k=even
where N is a normalization constant and the
Akk
are weighting factors known as the
angular correlation coefficients.
The circular polarization angular distribution contains a sum over the emitted
photon's helicity states r= +1,-i of the form
ik.
In this experiment the circular
polarization is not measured, so the angular correlation is a sum over the helicity
states, which leaves oniy even terms.'3
(2 fork
even'\
rk__l+(_l)k=0fOrkOddJ.
2-40
When no polarization measurement is made, the angular intensity is independent
of the parity of the transition. The highest term in
2-39
is determined by the angular
momentum selection rule"
kmax =Min(2J,,2L1,2L2).
L,
2-41
and L2 refer to the angular momentum of the largest observed multipoles in the first
and second transition, respectively. For the majority of nuclear transitions, the highest
possible order is quadrupole, thus the angular correlation contains terms in P2 and P4
only. In transitions where the selection rules demand pure or relatively pure
multipolarity, the An and A44 have distinctive values. For example, the correlation
between the transitions of a spin 4+ - 2 + - 0+cascade involves almost pure E2
multipolarity. The expected A22 value is nearly 0.1 and the A44 is approximately 0.
2.3.3
Multipole mixing
20
In cases where the selection rules allow more than one multipolarity, there are
generally only two major competing components. For example, in a spin 0 - 2
2
cascade, the first transition (0+2) is pure E2, but the second (2*2) can be a
combination of E2 and MI radiation (see table 2-1). The experimentally measured A22
and A44 will then depend on the amount of each multipolarity present, which is defined
by the mixing ratio
The mixing ratio is written so that the numerator is always the
multipolarity with the larger L. For parity iv and iv' = E or Mand wave number k,
(+1 (IMOTL ')II)
k :L!L
i
2-42
(J+1Hi1(7r'L)IIJ)
Forexample,E2,M1 mixinghas L' =2,L= 1, ir=E, and iv' = M Themixingratio
is a function of both the multipolarities of the transition and the initial and final spins
of the states connected by a given transition. The analysis of mixed multipole
transitions is simplified by recasting the angular distribution function into products of
factors depending on each transition in a cascade separately. In the case of
coincidence with
in direct
in a cascade from JjJ2J3:
W(9) =
B(y)A(y2)PjcosO).
2-43
The Bk and Ak can be written using the reduced matrix elements2:
Bk (ri)
L,rL,t
F(L1IJ1J2)(1)h1' (2 IJNALJIJI X2
iNAL1
JI)
2-44
(J2 IIJNAII
L1,r1
ll'
21
Fk(L2L2J3J2)(J II.
311JN
Ak(72)
L2r2L2,r2
AJ2)(J A°J)
311JN
L2
L2
2-45
.
2
L2 V
Ar2J2)311JN
The Akk is the product of the two factors:
A=Ak(y2)Bk(yI).
2-46
The F-coefficients determine the angular momentum dependence of the
angular distribution. The F-coefficients have been tabulated and are available in
convienient tables.'2 The have the following
form'3,
in terms of the 3] symbol, which
is defmed in 2-16:
Fk(LL 'J2J,) = (_1)J2' [(2k+1)(2L +1)(2L +1) (2J, +i)]2
(L
xl
'
k IL L'
k
1 1 O)J,
.J,
2-47
k
J2
The symbol in braces{}is a 6fsymbol, as defined in
Edmonds.'4
The effect of
the 6fsymbol is to recouple the possible angular momenta in terms of different
orderings of the J.
The single-transition angular correlation factors Ak and Bk can be simplified in
terms of the F coefficients and the mixing ratio ö:
Ak
B
(LLJfJ)+28(y)F(LLJfJ)+ö2((L?LhJfJ)
1+82(y
2-48
F(LLJJ)-28(7)F(LL'J1J1)+ S2(y)F(L'LJ1J,)
1+2(y)
2-49
The form for Ak and Bk as a function of 8provides limits on the initial and final
22
fof the transitions j'j and
determine the mixing ratio
.
If thef are known, then the Ak and Bk can be used to
In this experiment E2, Mi and M2,
El
mixing ratios
were measured, the most common case being E2, Mi multipole mixing.
2.3.4
Solid angle correction factors
The angular correlation formalism described in 2.3 assumes that each detector
is small enough so that the angle between two detectors is an exact number. The
experimental situation deviates from the theory due to the fmite sizes of the detectors
and the relatively small source to detector separation. The solid angle correction
factors Qk correct for this deviation. When Qk (Yi) and
correction factors for
and
Qk (72)
are the respective
in a distribution measurement, 2-43 can then be written
as:
W(9)NQk(y)Qk(y2)Bk(y)Ak(y2)F(cos9).
2-50
The Qk used in this experiment were calculated using the computer method of
Krane.15'16
The estimated average values used in the program are shown in Table 2-3.
Table 2-3 Q-factor calculation parameters
IDescription
Radius
Length
Dead layer thickness
Value (cm2J
2.45
5.7
0.3
23
The calculated correction factors vary slowly with energy so the
Q2
and
Q4
factors were only calculated for every 100 keV. The resulting product
Qk (
) Q (12) =
approximately
2.3.5
Q had similar values over a large range of energy. The values were
Q22
= 0.985 and Q = 0.95 1.
Unobserved intermediate transitions
When the lifetimes of the intermediate states are relatively short, correlations
between 7rays not immediately in succession can be used to calculate multipole
mixing. Figure 2-2 shows a sample case where the angular distribution of j ang
could be measured without observing
.
Ji
Ji
(Vu)
J2
72
Jf
Figure 2-2 Diagram for angular correlation with an unobserved intermediate
transition.
24
The deorientation coefficient Uk accounts for the effects on the correlation due
to unobserved transitions. In such a measurement the correlation function 2-50 is
written as
W(0)= NUkQkkBk(yI)Ak(y2)Pk(cos6).
2-51
The deorientation factors are
Uk(J!,J2,L)
(_1)u12
1.i,
[(2..,, +1)(2J2 +i)]
J, L
2
They have been tabulated for common
tables.'2
J1 ,
,
kj>
2-52
L and are available in published
In cases where the unobserved transition has a mixture of multipoles, the 8
value must be measured by a direct correlation measurement or previous experiment.
The adjusted U coefficient for such a case is a weighted average of the Uk (J1, j2 , L)
for both dominant multipoles L and L' in the mixed transition:
Uk(JI,J2)=
2.3.6
Uk (J,, J2 , L) + 52Uk
(J, ,
__ ,
L')
1+82
2-53
Elucidation of spin and parity values
In certain cases, the angular correlation coefficients can be used to deduce the
spin of an excited level. When one of the transitions in a correlation is a pure
transition, the process is somewhat simplified. Figure 2-3 shows the allowed
25
combinations of A22 and A44 for transitions with spin 1, 2, and 3 feeding a 2 to 0
transition. In these plots oranges from -5 to 5. Two experimental pairs of correlation
coefficients are shown: the 2365-344 keV correlation and the 1441-1109 keV
correlation. The 2365-344 keV correlation clearly indicates spin 2 of the initial level.
The experimental data falls very near 5 = 0, so nothing can be said about the parity.
Correlation coefficients for selected spin cascades
- - -2-2-0
0.2
3-2-0
0.15
*
-1-2-0
S
t
1441-1109
4.
01
I
-e-- 2365-344
I
i
4-2-0
IT
-0.8
0.4
I
-0.2
0.6
0.8
A22
Figure 2-3 Possible combinations of correlation coefficients An and A for
correlations with 2 to 01 transitions for selected spin values of the initial level.
Moving along a given curve represents a change in 8, the curves are approximately
symmetric about 8= 0.
Although the angular correlation measurement is independent of the parities of
the levels involved, a measurement of Scan often indicate the change in parity. For a
transition where there is a parity change from the initial to the final level, the dominant
multipolarities are El and M2. The Weisskopf estimates in Table 2-1 show that El
is
favored over M2 by about a factor of 100, thus S(M2/El) should be small if there is
a parity change. A large measured mixing ratio indicates a Sof the form S (E2
I Mi)
where the multipoles involved are E2 and Mi. Since E2 and Mi transitions cannot
change the parity of a state, a large Sgenerally indicates no change of parity from the
initial to the final state connected by that transition. For example, the
transition from the 2539 keV to the 344 keV level has 5
-1.4.
2195
keV
Since the 344 level
has positive parity, the large absolute value of the mixing ratio indicates that the 2539
keV level also has positive parity. Table 6-2 shows the resulting 3 assignment.
27
Chapter 3 Nuclear Models
3.1
Shell model
The observation of sudden discontmuities in nuclear properties suggests a
description of nucleon orbitals in terms of discrete shells, similar to the atomic orbitals
of electrons. For example, the nucleon separation energies and nuclear radii exhibit
sudden changes at particular numbers of protons or neutrons.6 This is clearly shown in
plots of two-nucleon separation energies (S2, S2) which are directly related to binding
energy differences. The changes observed in two-nucleon separation energies at
closed shells are strong indications of an underlying shell structure in the nucleus.
Figure 3-1 shows the closed shell at 82 neutrons, occurring near the 88 neutron
nucleus '52Gd, as a drop in the S2. The slight increase in energy after N = 88 is due to
the onset of deformation. The position near the onset of deformation is a major
motivation for interest in the '52Gd nuclear structure.
Nuclear excitations in the shell model can be explained as individual nucleons
being promoted to higher shell model orbitals. This version of the shell model is called
the single-particle model.
3.1.1
Shell model potential
The nucleus can be modeled to first order as a finite square well. However, the
S2 of some Gd isotopes
21000
19000
17000
15000
13000
11000
76
78
80
82
84
86
88
90
92
94
96
98
100
N
Figure 3-1 Two-neutron binding energy difference for some Gd isotopes.17 The value
S2 = BE(N,Z) - BE(N-2,Z).
nuclear mass distribution at the surface is not as sharp as a square well. More detailed
forms of the nuclear potential can do a better job of modeling the actual nucleus, but
require numerical solution methods. The harmonic oscillator potential has a similar
basic shape, but has less sharp edges and also has analytical solutions. A coupling
between the spin of the nucleon and the angular momentum of its orbit is apparent and
adding such a term gives energy gaps at numbers that match the discontinuities (such
as seen in Figure 3-1). A negative term proportional to
12
counters growth in the
potential for high values of angular momentum 1. The shell model potential can be
written as:
29
V(r)=Mw2r2 +ClL+D12
2
3-1
Shell model orbitals are indicated by the oscillator quantum number N and the
orbital angular momentum 1, the total spinj (j
1 ± s), and the directional component
of total spin in. The angular momentum is denoted by a letter sequence s, p, d, f, g,
h,... corresponding respectively to 1= 0, 1, 2,
3, 4, 5...
Since the Pauli exclusion applies only to identical particles, protons and
neutrons fill shells independently. Each level is 2j+1 degenerate, corresponding to the
different projections of the total spinj (mi). The calculated energy levels of the shell
model potential closely match the actual energy discontinuities at
and
126.
2, 8, 20, 28, 50, 82,
These numbers indicate the number of protons or neutrons required to create
a closed shell; they are known as 'magic numbers'. Nuclei with numbers of protons or
neutrons far from magic numbers exhibit properties that diverge markedly from those
near magic numbers.
3.1.2
152Gd in the shell model
The nucleus '52Gd has 64 protons, thus contains full g7/2 and d512 subshells. A
small energy gap occurs at 64 protons. While the gap at 64 is not as large as the
energy gaps at the magic numbers,
64
is a relatively stable number of protons. The
88
neutrons, however, give just over a half full h912 subshell, and 6 neutrons away from
the closed shell at
82.
The properties seen outside closed shells are consistent with
extra nucleons polarizing a spherical core. The nuclear deformation increases as more
30
nucleons beyond a closed shell are added.
3.1.3
Pairing and the spin predictions
Pairing of spin (s =
'/2
particles) to achieve a total angular momentumJ= 0 is
seen in many systems such as in Cooper pairs in a superconductor. Protons and
neutrons are fermions with intrinsic spin
'/2,
and they also tend to pair and form quasi-
boson pairs with J = 0. It is safe to assume that nuclei with even numbers of protons
or neutrons have their angular momentum paired. Thus, the ground state spin of all
even-even nuclei such as '52Gd is zero. Even-odd nuclei have ground state spins
determined by the unpaired nucleon. Doubly odd nuclei can couple the two unpairedj
values with values from 1
j2J tojj, +J2.
While the shell model is successful at predicting the magic numbers and spins
of excitations in nuclei near closed shells, the single-particle theory breaks down in
regions away from magic numbers. For example, many nuclei in the region above A =
150 have first excited 2 states at energies below the single-particle excitation
energies. Collective nuclear models have been postulated to explain this discrepancy.
3.2
Collective nuclear vibrations
3.2.1
Theoretical description
Nuclear vibrations are one type of collective nuclear motion. The vibrating
nuclear surface can be represented as a sum over spherical harmonics with time-
31
varying amplitude:
r
p=2
a(t)Y(G,çb)
R(9,Ø)=R01 1+
L
2=2 fl-2
1
3-2
I
A change in oo corresponds to a change in the nuclear volume, which is a
much higher energy process than the shape vibration. Placing the center of mass at the
origin forces a = 0. Thus, the lowest low-energy mode is the quadrupole vibration
which involves changes in a2. The Hamiltoman for a vibrating nucleus can be
quantized in the form:
3-3
HVIb =
+ .).
The product /I counts the number of vibrational phonons N in a nuclear
state. The energy of the vibrator is then:
EN =h(D(N+.)
3-4
For a single phonon excitation, the spin of the excited state equals 2, which is
the
spin
of the vibrational phonon. Multiple phonon excitations have total spins that
range over the different possible ways to couple spin 2 bosons symmetrically. For N =
2, for example, the spins of the excited states can be 0, 2, or 4. Comparing the
energies of low lying states can often indicate a particular model. The ratio of the
energy of the lowest 4 state to the lowest 2 state for a vibrating nucleus is thus
expected to be:
R
E(41)
= 2.00
E(21)
3-5
32
where the subscript 1 of 4 refers to the lowest energy 4 level, and so on.
3.2.2
Spherical vibrator band structure
The possible coupling of vibrational phonons leads to only certain possible
spin values with a distinct pattern. The right side of Figure
3-2
provides a basic
diagram of some of the expected levels of a purely quadrupole vibrational nucleus.
The electric quadrupole operator1 contains only one-phonon annihilation and creation
operators:
1(E2)=_ZeRo)2(t+),
36
where C is the restoring force constant for quadrupole vibrations of the nucleus, Z is
the number of protons, e is the electron charge and R0 - 1.5 fin is the average nuclear
radius for A = 1. Since the operators in 3-6 appear only singly, E2 transitions in the
vibrational model will have LN = 1. Due to this restriction, the possible levels shown
on the left of Figure
3-2
can be loosely organized into the bands seen on the right.
Nuclei exhibiting exact vibrational behavior do not exist, although there are
many examples that resemble this pattern. The triplet of O, 2, and 4 states at twice
the energy of the first
2
state is a strong indication of vibrational structure.
Furthermore, the B(E2; N*N-1) values predicted by the vibrational model are
proportional to N. Thus,
B(E2;4
2)= 2xB(E2;2
Or),
3-7
33
4
3+
______
64+
2k-'_____
o+J
4+
2
0
______
0
0k-'
2
2-
2
0
Figure 3-2 Band diagram for a theoretical spherical vibrator. The groups of states at
higher energies are nearly degenerate.
"4Cd and '°2Ru are often considered to be good examples of vibrational nuclei, they
have values for B(E2;4, *2,)IB(E2;2, *O) of 1.99 and 1.47. Harmonic
vibrational motion is more often not observed. The observed spectra seem to indicate
that it takes only a few valence nuclei to soften the nucleus to deformation enough that
the simple spherical vibrator loses applicability.'9
3.3
Deformation
As described in 3.1, adding protons or neutrons beyond the "magic" numbers,
tends to change the nuclear shape. This deformation changes the types of collective
modes allowed. Deformation can be modeled in terms of a change in the (static)
34
amplitude of a spherical harmonic. Based on empirical evidence, the deformation is
generally taken to be primarily of quadrupole type, thus the nuclear surface is written
in the form:
Ro[1+a2flY(6'øt)].
R
3-8
The primes indicate a rotation from the space-fixed to the body-fixed axis.
After performing this transformation, the a20 and a22 can be parameterized'8 in terms
of/land I
a20
=flcosy,
3-9
1
a22
=.-=flsiny.
3-10
Choosing the body-fixed frame to be the principalaxes forces
and
a22
a21
a21
=0
a2,_2.
The parameter flis related to the deformation of the nucleus:
fl2a2
The parameter yspecifies the axial asymmetry: y =
3-11
,
,
and 0, are prolate
(cigar-shaped) ellipsoids with the 1, 2, and 3-axes as symmetry axes respectively.
When '
57i.
r, and
r
the shapes are oblate (pancake) shapes with the same
symmetry axes respectively.
35
3.3.1
Vibrations of deformed nuclei
Vibrations of deformed nuclei are described in terms of time-dependant
variations of/i and yabout non-zero equilibrium values. A /3 vibration preserves the
axial symmetry of the nucleus; this change can be modeled by compressing the ends
of a football-shaped object. The yvibration breaks the axial symmetry; compressing
the top and bottom of the football approximates a yvibration. The /3 vibration carries
zero units of angular momentum, the yvibration carries two units of angular
momentum. The structure seen for a deformed nucleus is often a rotating structure
built on vibrational states.
3.3.2 Nuclear rotations in deformed nuclei
A second class of collective motion is rotations of the nucleus. The increasing
static deformation of nuclei with A? 150 makes such rotations observable. If the
nucleus has a moment of inertia 3, then the Hamiltonian for an axially symmetric
rotor has analytic solutions with the energy
eigenvalues'9
E=--[J(J+1)K(K+1)],
3-12
where K is the projection of J onto the body-fixed axis. Within a rotational band, K
constant, and
K(K-i-1)
23
can be combined with the mtnnsic energy of the band E0.
The energies within a band are
is
36
E =E0+J(J+1).
3-13
23
With the energy spacing of 3-13, the ratio of the
4
state to the
2
state in a
rotational band is distinctly different from the vibrational spacing seen in 3-5:
E(41)
R4
3-14
E(21)
Higher levels in this pattern will have a spacing based on the first excited state
in the band. For A = --, the
2
level is expected at 6A, the 4 at
20A,
and so forth, as
illustrated in Figure 3-3.
Ground-state rotational bands of strongly-deformed nuclei have excited states
that fit the spacing implied by 3-13 to very high values of total spin (J). Once again
we fmd no nucleus that is a pure rotor, but the match here is significantly better than
6
+
42A
20A
2
0
Figure 3-3 Theoretical rotor band spacing.
6A
0
37
the pure vibrator.
3.3.3
Deformed rotational structure
If the ground state of the nucleus or an excited state has a permanent
deformation, patterns of nuclear levels increasing in spin connected by a change of
rotation built on the deformed vibrating structure are common. For an axial
symmetric nucleus, bands with a spin o band head, such as the ground state band,
have only even spins. Thus the ground state rotational band has spins O, 2, 4 etc.
The bands of deformed nuclei exhibit patterns consistent with rotational bands built on
vibrational phonons. Experimentally, the level spacing in these bands usually does not
2
4+
4+
0
6
4,
0
g.s.
f3
y
13J3
Figure 3-4 Theoretical deformed vibrational structure with quasi-rotational bands.
match the expected J (J+ 1) rotor spacing as well. The quality of K as a quantum
number and the potential for mixtures of configurations from different band structures
are thought to be the cause. Vibrational levels built on a O fl-vibration have a
similar spin pattern as the ground state band: 0 2, 4, etc. A band of rotations built
on a yvibration can have any integer spin larger than two: 2, 3 4 etc.
The deformed rotational model fits the data qualitatively well, though once
again, there is no perfect match. Vibrational modes will mix so that the bands are not
truly as separated as indicated in Figure 3-4. The mixing causes closely spaced levels
to repel, leading to non-rotational spacing in energy.
The actual band structures of many nuclei generally have features of both
vibrations and rotations. The nucleus '52Gd which lies at the onset of deformation
displays clear characteristics of both collective models.
39
Chapter 4 Previous Work
As described previously, the primary motivation for the study of '52Gd comes
from its placement in the midst of a transformation from spherical to deformed
structure. Data compiled34 from studies o.f several gadolinium isotopes, for example,
demonstrate this trend. As pairs of neutrons are added to gadolinium isotopes, the
nearly vibrational spacing seen in '48Gd becomes the clearly rotational pattern of the
low-lying levels in '56Gd and beyond. The change is evident moving from left to right
in Figure 4-1.
4-,-2500-
2000 2
1500-
6-
6
4-,--
6 +
(keV)
22
ftTrs
500
6k-
6 +
+
4+
+
+
6 -
4 - 4__+
-
0 ' 0 O 0 0 O 02+_O+_Ø+
Gd
148
Gd
150
Gd
152
Gd
154
Gd
156
Gd
Gd
160
Gd
Figure 4-1 Low lying excited states for selected Z = 64 isotopes.
The progression from vibrational to rotational structure is apparent from left to right.
40
The majority of the published work on the nuclear structure of '52Gd describes
its structure in relation to the onset of deformation.
4.1
Particle transfer studies
Resonances in particle transfer reactions are often seen as indications of
collectivity. Flemming et al. measured (p,t) reactions on even gadolinium nuclei.20
The 0 excited states at 615 keV and 1048 keV are strongly populated in the reaction
'54Gd(p,t)'52Gd. The population of these excited states indicates a shape transition in
gadolinium isotopes at N = 88 as seen in Figure 4-1. An earlier paper by the same
group21
describes the lack of 0 states in '54'58Gd from (p,t) reactions leading to a
similar conclusion (that '52Gd has collective attributes). The population of the 615
keV state in '52Gd was observed with nearly the same strength as the ground state, and
this is evidence for the transition into "quasirotational" nuclei. The quasirotational or
"soft" nature of what is called the flvibration in '52Gd can explain the enhanced
population of the 615 keV state. They also describe that the second excited 0 state at
1048 keV is enhanced due to overlap with the '54Gd ground state. The enhancement
indicates the presence of both a spherical and a deformed shape in the '52Gd excited
states. EIze et al. also measured the results of(p,t) reactions in gadolinium
isotopes.22
Both Flemming and Elze indicate the similarity of the dual excited 0 states in 152Gd to
'50Sm which is also anN= 88 isotone.
Deuteron scattering
(d, d')
on gadolinium isotopes is also used to investigate
rii
collective states. All the excited states seen in the deuteron experiments have a
corollary in '50Sm except the 1047 keV level. Several spin and parity assignments
consistent with collectivity and with previous measurements result from the
(d,d')
scattering performed by Bloch et al.23
4.2
Spectroscopy
Many studies have described the nuclear structure of 152Gd from the decay of
'52Tb, including Gromov et al. ,24 Kormiciki et al. ,25 Harmatz et al. ,26 Strigachev et
al.,27
Basina et al.,28 Frana et al.,29 Toth
etal.,3°
Flerov etal.,31 and Adam et al.32 The
defmitive spectroscopy work, published by Zolnowski et al.
placed over 290
transitions in the level scheme. They describe a band structure (including previously
published bands) of nine bands, two with negative parity. The low-spin members of
the ground-state band are observed, along with a quasi-fl band based on the 0 615
keV level. Large observed E0 transitions are given as evidence for the K
= 0
assignment for this band. The 1047 keV level is described as the head of a quasi-2fl
band. They note the difference in the observed B(E2) values of this 2fl band compared
to 2/1 band B(E2) values in '54Gd; the difference is due to the spherical nature of 52Gd
(compared to the deformed '54Gd). The quasi- yband described begins with the 1109
keV level, the lack of substantial E0 admixture in the 765 keV transition from this
level leads to a K = 2 designation. A two-phonon flyband made of the 1605 keV and
1839 keV levels is chosen based on preferential decay to members of the one phonon
bands. The 1862 keV level is tentatively described as the second member of a 3/1
42
band with the 1484 0 state observed by
Adam.32
Observation of this level has yet to
be confirmed. The 1941 keV level is postulated as a
flfl
coupling to produce a K = 2
band.
Two negative parity bands are described in the Zolnowski paper. A band built
on the 3 level at 1123 keV is assigned K= 0 while the 1643 keV level at 2 starts a K
= 1 band. The expected separation of the octupole vibration into K = 0, 1, 2 , and 3
components is not fully realized, but the first two negative parity bands fit this
prescription well.
Zolnowski
et al.
describe the striking similarity of the structure in this region
that is the motivation for the present study. This similarity can be seen in the
comparison of severalN= 88 isotones in Figure 4-2. All data in the figure are from
the Nuclear Data Sheets (NDS) as reported online by the Table of Radioactive
Isotopes34. Note the almost identical ground state bands even over a change of 8
protons.
The Zolnowski compilation remained the most complete report until a newer
paper35
by Adam et
al.
was published in 2003. Adam reports over 131 new transitions
between the excited states of 152Gd and introduces 46 new levels
into
the decay
scheme. The NDS36 compilation of the '52Gd spectroscopy is based primarily on
Zolnowski's data, and predates the recent Adam paper. The NDS compilation
provides energy, spin, level placement, mixing ratio, and conversion electron data
evaluated from all available sources.
The more recent paper by Adam et
al.
does not propose any new band
43
_
(10
10
1
±
(6
-
8
(5
-
_
(8
4f
(2
-
(6
+
y
-
4+
4
4_
0
'
Ce gs.
148 Nd g.s.
150 Sm g.s.
152 Gd gs.
Dy g.s.
Figure 4-2 Comparison of ground-state and ybands of selected even Z,
isotones.
N = 88
structure. They do use several different models to predict the ratios of the energies of
excited states. Their conclusion is that the quadrupole phonon model has the best
predictive value for '52Gd, and that this nucleus is either at or very near to a phase
transition from a spherical to deformed shape.
4.3
Internal conversion (ICC)
The conversion electrons were first measured by Antoneva et aL37 Conversion
44
coefficients are generally taken from the earlier Adam paper32, though Gromov also
published internal conversion data. 24 The more recent Adam paper has reanalyzed the
older data using newer v-ray intensities. Gono et
al.
also measured conversion
electrons and T-rays with a focus on the 931 keV level.38 All calculations using
experimental conversion coefficients in this document use the values in the more
recent Adam et
4.4
al.
152Eu and
paper.35
lszmTb
decay
Many papers have reported on the '52Gd decay populated by 152Eu39'40'41'42'43'44
and from lS2mEU4S46,47 decays. Zolnowski and Hughes et al.48 measured the
spectroscopy of l52mTb. The lS2mTb has a 4.2 minute half life and f=8. Bowman et
al.
also measured this decay much earlier, and included some quasirotational band
assignments.49
4.5
Angular correlations
Angular correlation and distribution measurements have been published by six
groups. Kalfas and Hamilton50 used yyangular correlations, low temperature nuclear
orientation (LTNO), and '.ray conversion electron angular correlation experiments to
determine the angular correlation parameters and mixing ratios for five transitions.
Ferencei51 used LTNO to measure 8for 34 transitions. Additionally they conclude
that the variations in measured values cannot be completely described by the rotation-
vibration model. Lipas
et
al.52 measured six mixing ratios using LTNO. The most
45
recent and comprehensive work is that of Tagziria et
al.53
who also used LTNO to
measure anisotropies with two detectors. They reported mixing ratios for 45
transitions and upper or lower limits for 14 more transitions. Asai and Kawade54
describe a method for using five detectors and the resulting -ycorrelation to
determine angular correlation parameters. They provide a sample
ofA22 and A
for
three transitions. A comparison of the results is provided in Table 6-7. The major
disagreements in the chart arise most often due to a difference in the spin and parity
assignments in the initial or fmal levels when compared to other experimental results.
4.6
Computational models
Published results of model predictions of energy levels, mixing ratios, reduced
matrix elements and other nuclear parameters are extensive for 152Gd. There have
been many attempts to describe the character of 152Gd using models based on
refmements of the rotational and vibrational models described in chapter 3
One set of models is referred to as the interacting boson approximation (IBA)
or the interacting boson model (IBM). The nucleus treated as if it were composed of
nucleon pairs, or bosons. The bosons can be of two types, either s bosons, with spin 0
or d bosons with spin 2. An interaction Hamiltonian is postulated, and then solved to
fmd the level energies. More details of the model are presented in 7.1.6. The IBA-1
model treats protons and neutrons exactly the same, where the IBA-2 accounts for
them separately.
The Lipas
et al.53
paper concludes that the IBA- 1 model is overextended for
46
152Gd. Another Lipas
et
al. paper calculates mixing ratios for a few transitions, though
no general comments about the structure are
made.55 Chu et
al. 56 apply the IBA-
1
to
the N = 88 isotones, they find improved results when including higher spin levels to
determine the model parameters. They also note the similarity of the '52Gd level
structure to 150Sm almost every level with assigned spin and parity has a matching
partner within
150
keV. Several other studies57'58'59'6° apply IBA-1 across a range of
nuclei including '52Gd. One interesting result of Kern et al. is the prediction of a 0
state at
1425,
near the new 0 level at
1475
seen in this work.6' Han et
62
al.
applied
the same model to the negative parity states in N = 88 isotones. The IBA-2 model has
also been applied to calculate systematics across this
region.63'64'65
These models have
had widely varying levels of success; none approach a close fit of different parameters
across a broad range.
47
Chapter 5 Experimental Description
5.1
Source preparation
The original target used to produce the excited states
'52Gd was enriched
'51Eu powder. The powder has an isotopic purity of 98.6%. The powder was slurried
with a few drops of water and then dried with a heat lamp onto a 5 cmx5 cmx 0.1 cm
Al foil. The first foil was then covered by a second foil and the ends folded to create a
package containing the
'51EU
The package was irradiated in a beam of a particles
produced by the Lawrence Berkeley 88" cyclotron. Several Al degrader foils were
placed in the beam upstream of the target to produce the optimal beam energy at the
target. The optimal energy was chosen for producing '52Tb by the reaction 151Eu(a,
3n) '52Tb while minimizing 151Eu (a, 2n) 153Tb and '51Eu (a, 4n) '51Tb. The final
parameters chosen were an abeam energy of-42 MeV with three aluminum degrader
foils in front of the target.
The resulting '52Tb has a 17.5 hour half-life and decays by fl emission. The
activity was allowed to cool for a period of time determined by the total beam current
that the packet received. This time was generally a few hours. After cooling, the
radioactive powder was dissolved in HC1 to create a liquid sample. The liquid was
placed in a plastic vial 8 mm in diameter and 5 cm long, and then transferred to the 8rt
detector for counting. Samples were counted for approximately one half-life, after
which fresh activity was added to the sample to keep the counting rate high. This
48
process was repeated for approximately one week (99.5 hours online time), producing
8.68 GB of data, on the order of 108 total single events.
Several competing reactions produce contamination. Substantial amounts of
'51Tb, '53Tb, and 154Tb were created in the sample as well. These also decay to Gd by
fidecay.
5.2
Detectors
Radiations from the source were recorded by 20 HPGe (High Purity
Germanium) detectors with an average resolution (FWHM) of 2.7 keV at 100 keV to
4.5 keV at 2.8 MeV. The detectors have volumes ranging from 95 cm3 to 127 cm3
with front face diameters from 49.4 to 53.5 mm. The efficiencies varied considerably
from one detector to another. The efficiencies of 18 of the detectors normalized to
344 keV have standard deviation at 2.5 MeV of approximately 40%. The efficiencies
for detectors 13 and 18 vary by a factor of 2 from the median value at 2.5 MeV.
The
detectors are numbered in the data stream from 0 to 19.
A major benefit to the 8it detector array is that each detector has a Bismuth
Germinate (BGO) Compton suppression shield. The shields serve to cancel events
that deposit only some of their energy in the detector and scatter into the Compton
shields. The Compton suppression shields cover only the sides and rear of the
germanium detector crystals but result in a large increase iii the peak to background
ratio, especially in the low energy region of the spectrum. The peak to Compton ratio
for the whole array is approximately 28, as measured in several gated spectra for
49
several different energies.
The detectors are positioned so that their surfaces sit approximately on the face of
a common sphere. The source was placed at the center of the sphere so that the source
to detector separation was approximately 20 cm. At this range, the detectors actually
cover only about 10% of the total solid angle. A photograph of the inside of the
detector array can be seen in Figure 5-1. Figure 5-2 shows.a schematic diagram
showing the relative placements of the germanium crystals. Inside the sphere of
HPGe detectors was another spherically shaped shell of BGO scintillator detectors.
Figure 5-1 Inside the 8ic detector. Half the detectors have been removed to show the
detector positioning. The BGO ball has also been removed.
50
These detectors were not used in this experiment.
5.3
Angle relationships
Through there are 190 unique detector pairs in the array of 20 detectors, the
symmetry of the detector positions provides for only 5 unique angle pairs: 41.80,
70.5°, 109.5°, 138.2°, and 180.0°. 30 pairs of detectors form the angle 42°, 30 pairs
have 138° between them, 60 pairs have 71°, 60 pairs have 109°, and 10 pairs have
180° between them. The number of detector pairs that form a particular angle occurs
Figure 5-2 A schematic rendering of the relative placements of the crystals for the
HPGe detectors inside the 8m detector.
51
in the ratio 3:6:6:3:1 with respect to increasing angle. The detector angle relationships
are indicated in a matrix format in Figure 5-3. Note that each detector appears the
same number of times in each angle. Thus in the first order, parameters specific to a
particular detector can be divided out.
5.4
Electronics
The electronics supporting the detectors were originally designed to record the
events from in-beam scattering experiments, and were somewhat modified during the
Detector #
0
1
2
3
4
5
6
7
8
9
10
11
12 13 14 15 16 17 18 19
0
-nnuiinunn
-nanniinn
2
3
4
5
-giniiiign
6
7
8
nncrnñ
IIflNUII1I
0
10
a)
011
12
13
14
15
16
17
18
__EI
-EInnhI1In
UflBEI
-IIIfl
-II
19
Figure 5-3 Angle relationships in the 8ir detector array. The matrix is symmetric; the
bottom half has been removed for readability.
52
present experiment. The supporting electronics recorded the energy of events
recorded by the detectors, and the multiplicity for events that were coincident within a
time window. The time from the start of an event to each yray in a multiplet was also
recorded. It is important to understand the specifics of the data recording method in
order to appreciate the format of the data and the modifications that were required.
Determining the level scheme for a nucleus requires information about the
relationship of different transitions in that scheme. The spectra of single events or
"singles" are necessary only to determine the efficiency for the sum of all detectors in
the array and for each detector separately. Placing a yray in the level scheme requires
information about which events occurred simultaneously. Thus coincidence data is of
higher value than the singles
data.66
Unfortunately, coincidence events are less likely
to be detected than singles data as seen in 2-35. Since
82
is generally on the order of
icr3, the coincidence rate is generally low with respect to singles.
The electronics included a dual triggering device that distinguished events of
multiplicity one (singles) from those events with multiple yrays, in order to enhance
the collection of coincidence data with respect to singles data. A scale-down
component rejected all events for recording as singles data until the scale-down setting
had been reached. Thus a setting of 100 would reject 99 events and record the 100th
Some modification of the data was necessary due to the fact that the scale-down box
incremented for each yray, including those that are part ofa coincidence event. The
entire procedure for modification and sorting of the data is described in 6.1. Since
coincidence events count two yrays from the same decay, the singles as recorded by
53
the 8ir have proportionally more counts for a peak in coincidence than a true single
detector would.
The scale down factor (SDF) was chosen to keep the amount of singles data
from overwhelming the data recording system. Thus the scale down setting for each
run was determined by the source strength. Table 5-1 records the SDF and basic
infonnation about each of the 11 data sets recorded. In almost all analyses, the runs
were combined into a single data set.
5.4.1
Timing
Timing electronics recorded the time from the beginning of an event as seen by
the master trigger device to each individual yray in that event. Events that occur
Table 5-1 Run numbers, scale-down factors, and time information for each data set
created for this experiment.
Run Number
1.1
2.1
2.2
2.3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
I
SDF
Time (br)
62
62
62
62
126
126
8.0
10.5
11.83
11.73
40
256
256
96
32
2.45
10.0
3.5
4.0
14.0
14.0
9.5
I
Date fmished
10/26/99
10/26/99
10/27/99
10/27/99
10/28/99
10/28/99
10/28/99
10/28/99
10/29/99
10/29/99
10/30/99
54
without another v ray within the time window were delayed from zero by 25-40 ns in
order to allow separation of single events from coincidence events by using the timing
information.
5.4.2
Coincidence pile up
The common usage of pile-up in y.ray counting refers to two events close in
time in the same detector. The 8it electronics created another type of pile-up event
which needed to be corrected for. If a single detector detects more than one yray
during the time another detector takes to process a single 7-ray, a coincidence pile up
condition is created. The resulting event will have only a single 7-ray but timing
information similar to a coincidence event. The initial data sorting routing removes
these events due to improper event length. However, the software that generates the
singles spectra uses the count of pile-up events in order to create an accurate
efficiency spectrum.
5.5
Data stream
5.5.1
Format
The data stream was stored in a file buffer on the collection computer and then
written in binary format on 8-mm tape. Each event has the same basic structure. A
representation of a section of the data is shown in Figure 5-4. Each column represents
a two byte binary word converted to base 10. The bold section represents one event.
55
The first numbers contain information about the BGO detectors; in this experiment
those first three numbers written are always zero. The next number is the multiplicity
or number of yrays in the time window, which generally varies from 0 to 4. The bold
event shown in the figure has multiplicity two.
The next section varies in length based upon the multiplicity. For each y ray in
the event, the detector number, the energy of the y ray (in channels), and the time from
the start of the event (in channels) are listed. The list starts with the event that has the
lowest detector number (0-19) not necessarily the first yray to arrive. The length of
this section is three times the multiplicity. The bold text in the figure indicates an
event with detector 8 having energy 688 and time 129 channels in coincidence with an
event in detector
15,
energy of 390, and time 144 channels.
Energy and time channels refer to the channel number on the multi-channel
analyzer connected to a detector or its timing electronics. The energy spectrum is 8 k
0001120
0001140
0001160
0001200
0001220
0001240
0001260
0001300
0001320
104 65535
129
15
0
14
0
16
0
6
2
8
364
688
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
15
0
0
2
6
132 65534
103 65535
0
0
0
0
0
275
1984
0
0
0
390
384
496
438
689
1996
144
103
128
140
105
144
65535
65535
65534
65535
65535
0
0
0
8
2
0
12
Figure 5-4 Sample data stream from the 8it. The leftmost colunm represents the line
numbers in the text file.
or 8192 channels. The energy channel calibration is described later, but is very near
0.5 keV per channel. The time spectrum was 4096 channels in length, but generally
only recorded events within 100 us of each
other.4
It was unnecessary to calibrate the
time channels absolutely; however, the gain was approximately 1 ns per channel. The
fmal number is the end of event (EOE) flag: 65535 or FFFF in hexadecimal.
5.5.2
Errors in the data stream
Previous investigations of the data stream from other data sets gathered with
the same apparatus found several recurring deviations from the standard data
format.4'66
These errors were also found in the data set used for the 152Gd
investigation (this experiment.) For an unknown reason, the data stream exhibited
dropped bits at certain points in the data. Since the data is written in binary, one easily
distinguishable consequence of a dropped bit is that odd numbers are turned to even
numbers.
Since the length of an event is detennined by the multiplicity, if an event were
to have been dropped bit in the multiplicity, the event length would not match properly
(there would be more detector, energy, and timing information than expected.) While
the sort program was written to reject events with the improper length, short events do
not seem to be due to dropped bits in the multiplicity. Less than 0.02% of events were
removed due to improper length.
Dropped bits in the energy resulted in some even-odd staggering in the data,
especially apparent at high energies. To remove this problem, the energy scale was
57
cut in half. The result is that the even and odd channels were summed, which
removed the staggering at the cost of resolution. No similar even-odd staggering was
observed in the detector number or the energy spectra.
The EOE flag was the other major place where dropped bits were observed. In
this case, the EOE flag is written as
65534.
The second to last event in figure 5-2
shows this problem. The sorting program was written to accept 65534 as an EOE flag,
and the frequency was recorded. The frequency of the EOE dropped bit varied
considerably from run to run, though was as high as 34% in some runs.
1:1
Chapter 6 Analysis and Results
6.1
Data sorting and calibration
It was necessary to sort the data for analysis. Utilizing previously written
code4
as
a substantial building block, a program was written in C++ to sort the data. The sorting
program split each data set into two files: one containing singles events (multiplicity
1) and one containing coincidence events (multiplicity 2). Triple and quadruple
coincidence events were written as three and six independent coincidence events (for
all possible-permutations.) Since higher multiplicity events have much lower
statistics, they are a small part of the coincidence data set. 2.1% of all data are triple
events and 0.07% are quadruple events.
6.1.1
Timing
Separating singles and coincidences required adjustment ofthe timing data.
Differing cable lengths and other delays in the timing circuitry caused the singles
timing peak in the data stream to be written in slightly different channels for each
detector. It was necessary to determine an offset for each detector and shift the timing
data accordingly. After adjusting for the offset, events with a time within a sevenchannel-wide gate around the singles timing peak were counted as singles. A sample
time spectrum is shown in Figure 6-1.
59
rj/
2o
Channe's
Figure 6-1 Sample time spectrum. The calibration for the x axis is approximately 1 ns
per channel.
Though the lifetimes of most of the nuclear states in '52Gd are in the range of
picoseconds or smaller, the offsets described above and other delays in the
coincidence electronics separated coincident yrays in time. The time window for the
master trigger (to decide if events were coincident) was about 100 ns long. The
histogram of the time difference between the later and the earlier 7-ray in a
coincidence event is called the time-difference spectrum. These spectra were used to
filter out some of the accidental events. It is clear in the time difference spectrum
(Figure 6-2) that there is a sharp drop-off at approximately 60 channels, followed by a
relatively flat background. The flat background indicates chance coincidences (or
accidentals) while the higher counts below 60 channels are composed of true
coincident events. The two peaks between 35 and 60 channels are from pile up and
other not clearly resolved events. The time cut was taken at a difference of 35
channels to avoid these events. The result is that coincident 7-rays are those that
[
I
C
Chnnes
1-.IC
C
W
Figure 6-2 Sample time difference spectrum. The time cut at 35 channels is shown by
a vertical line. The calibration for the x-axis is approximately 1 ns per channel.
were less than
35
ns apart in the recorded data stream.
It is often the case in coincidence experiments that the flat chance background
is used to subtract a background of accidental coincidences from events with a time
difference indicating coincidence. In the 8it data in the configuration used at LBL, the
time window is too short for the background to truly become flat. Furthermore, the
background lacked the necessary statistics to make this procedure possible. Instead,
an adjusted singles spectrum was scaled and subtracted from each spectrum. This
process is described in 6.2.2.
6.1.2
Scale-down correction to singles
The singles files were used primarily for calibrating the efficiency and energy
of the detectors and of the array as a whole. Due to the method for separation of
multiplicity 1 and multiplicity > I events by the electronics, transitions that were
p
61
commonly in coincidence pairs were more likely to be recorded as single events.
Furthermore, pile-up and dead time rejection is more likely for more intense events.
Therefore, the singles files had to be corrected before they could be used for an
accurate efficiency calibration.
The adjustment to the singles counts was achieved by adding the coincidence
file to a scaled number of the singles events. A scale factor was determined by
modifying the hardware scale-down factor (SDF) for the events it undercounted. The
effective scale-down factor (ESDF) has the following form:
ESDF = SDF
(CNC + PU),
SNG
6-1
where CNC, PU, and SNG refer to the total number of coincidence events, pile up
events and singles events in a particular detector, for a certain data set. The resulting
spectra, referred to as true singles, were created by multiplying the singles spectrum
by the ESDF and then adding coincidence and pile up counts. The fmal spectrum was
then rescaled to match the original singles data. A summed true singles spectra was
created for each detector and for the entire array.
6.1.3
Efficiencies
The true singles spectrum was used to generate efficiency parameters for the
whole detector array. The intensity values of several of the peaks reported by
Zolonowski33
were used to create values of the relative efficiency over the entire range
of energies. Higher intensity peaks were chosen based on their separation from other
62
peaks and their spread across the dynamic range of the detectors.
There are few low-energy transitions in the 152Gd spectrum, and none with
large intensity. Unfortunately, the efficiency changes rapidly with energy at lower
energies. However, the '54Tb contamination decays to a rotational band cascade in
'54Gd with several peaks in the low energy region leading to the 123.1 keV transition.
The cascade is shown in Figure 6-3.
A coincidence gate was taken on the 426.7 keV peak to isolate these
transitions. The relative intensity of peaks in that cascade in the resulting coincidence
spectrum varies from the actual intensities only by the efficiency. Recent data on the
8
1144.4
426.7
6+
717.7
346.7
371 .0
4+
247.9
2
0
123.1
123.1
Figure 6-3 '54Gd ground state rotational band
0.0
63
relative strength of transitions in that cascade was used to produce efficiencies in the
low energy region.67 The number of counts in the 346 keV peak was nonnalized to
equal the efficiency of the 344 keV peak in the '52Gd. Combining the '52Gd peaks and
the '54Gd data produced efficiency values across a wide range of energies. A fourthorder polynomial was fit to the logio (efficiency) vs. logio(energy) plot.
Later in the experiment it was found that the 8ic detector, in the configuration
of this experiment, recorded very different efficiencies for singles events and for
coincidence events as seen in Figure 6-4. Although the exact cause is not understood
part of the difference is due to the effect of the scale down factor explained in 6.1.2.
To develop a proper coincidence efficiency curve, the efficiencies taken from strong
peaks in direct coincidence with the 344 keV and 411 keV y-rays were normalized to
match the '54Gd data taken in the manner described above. The piecewise matched
data were fit with the same procedure as the singles data to produce efficiency
parameters. These parameters were used for adjusting coincidence intensities. The
resulting fits are shown in Figure 6-4. The coefficients for the polynomial fits plotted
in Figure 6-4 are provided in Table 6-1.
The efficiency of each detector was calculated in a similar manner using the
singles data separated by detector. The coincidence matrix generated by the original
sort code removed detector information, so a new projection of the coincidence data
for each detector was necessary. The gated spectrum for the '54Gd efficiency data
consisted of all transitions in a single detector that were coincident with any other
detector recording the 427 transition. The single detector efficiencies were necessary
64
10.00
Singles Vs. CoincIdence Efficiency
ya*Iog(E)4+b*Iog(E)s3+c*log(E )A2+d*log(E)+e
1.00
i 000
'
F
H'-
0.10
sngfit
Cnc fit
Log [Energy] (key)
Figure 6-4 Summed detector efficiency for singles and coincidences in the 8it. A
polynomial fit to log(efficiency) vs. log(energy) for singles data and coincidence data,
normalized at 344 keY is shown.
Table 6-1 Efficiency parameters describing the fits shown in Figure 6-4.
Sng effpann.
Cnc effparm.
a
-1.5518
-2.0566
b
18.4685
23.8070
-81.9544
-102.8205
159.9937
195.5189
-115.6941
-137.7717
65
to adjust the number of counts detected in a particular angle pair (in angular
distribution.)
The standard deviation of the efficiencies calculated for the points chosen for
the singles fit is approximately 3%. This number is taken as a lower limit of the
efficiency error.
6.1.4
Energy and width calibrations
The energy calibrations were determined by comparing the locations of 15
intense peaks to the energies provided by the Table of Online Radioactive
Isotopes68
(TORI). The entire data set was gain-shifted to align the centroids of those peaks with
the accepted values. The average deviation from the accepted values for those strong
peaks in the gain-matched data is less than 0.1 keV. In general, the deviation in
energy calibration is due to higher resolution that allows detection of weaker peaks
that are not separated in previous data.
Width parameters are important for separating closely spaced peaks. Peak
width parameters were developed for each detector, for singles data, and for
coincidence data. The different width parameters were used at various stages of the
analysis. In the fmal analysis, one consistent set of width parameters was required for
consistency. The following equation for full width at half maximum in channels is
derived from a combination of several fits.
FWHM2 = 2.732 + 0.082x + 1.322x2,
6-2
where x
6.2
E
1000
with E7in keY.
Level scheme
6.2.1
Singles analysis
The peak areas in the summed singles spectrum from all runs and all detectors
(about 766,315,264 counts) were determined first. The analysis started at higher
energies (3-4 MeV) and progressively decreased in energy. This strategy was chosen
in order to fit the less complicated parts of the spectra first, and thus develop a robust
method that would help deal with the complexities at lower energies. Figure 6-5
shows an example of this complexity. The relative simplicity at higher energies is due
to the fact that the energy of any decay is limited by the Q -value. The sum of the
ray energy and the energy of the level it decays to must be less than the total energy
available for the decay. Thus the higher-energy y-rays can decay only to the ground
state or low excited states. Deducing the coincidence relationships for these
transitions is somewhat simpler.
In many cases the singles spectrum was too complicated to fit directly. The
coincidence data were often used to determine the exact peak locations to be given as
fixed parameters in the fit of the singles data.
6.2.2
Coincidence analysis
Using the fit results from singles data, gates in the two-dimensional data were
'pulled' for each peak. This process consisted of defming a gate window width, and
choosing background windows above and below the gate window to subtract from the
coincidence spectrum. Software was developed that determined the number of counts
in each background window, calculated a slope, and subtracted a linearly
approximated background from the coincidence gate window proportional to the
summed counts in the background window.
The strong sources used in this experiment produced a relatively high ratio of
74.O
Figure 6-5 Typical peak fit of singles data. The ordinate has a log scale of number of
counts with fit residuals shown between the abscissa and the peaks.
accidental to true coincidences. The ratio was determined to be approximately 0.09.
A singles spectrum scaled to 9.9% of the total counts in a raw coincidence spectrum
was subtracted to account for accidental coincidences.
The power of coincidence gates is especially potent in cases where there are
several closely spaced peaks in the singles spectrum. Some peaks that could not be
seen at all in the singles data could be clearly resolved in the coincidence data. Gates
as small as two channels wide were pulled across a complicated doublet or triplet to
resolve its constituent parts. A sample of the resolving power of coincidence gates is
shown in Figure 6-6.
62.2.1 Measurement of absolute intensities
Absolute intensities for the strongest peaks were determined from the singles
spectrum. The error from summing smaller unresolved peaks is generally much less
than the statistical error for a large peak. In general, weaker peaks are much harder to
resolve in singles data. The majority of the intensities were determined by
coincidence. If several transitions feed the same level, as seen schematically in Figure
6-7, the ratio of intensities in a coincidence gate for a transition that depopulates that
level is the same as the ratio of absolute intensities. If the absolute intensity of one of
those transitions can be determined from the singles data, it can be used to normalize
all the other relative intensities. The normalization is
N
J(sng)
6-3
gate
AB (cnc)
cm
Figure 6-6 Comparison of singles and coincidence spectra. The upper spectrum is the
summed singles and the lower is a composite of the 411 keV gate (dashed) and the
586 keV gate.
where 'B is the singles intensity of
spectrum produced by gating On
in direct coincidence with
coincidence spectrum.
Ygate
Ygate.
and AB is the area of y in the coincidence
The intensity of another yray (such as
depends on
Ngate
in 6-3 and AA, the area of
or lc)
in the
flate
70
6-4
'A = NgaAA(cnc)
In a few cases (approximately 10 out of 620) is was not possible to determine
the absolute intensity of any transitions in any gate appropriate for a given weak
transition. In this case the normalization was determined using
below
flate
a transition
in the level scheme. Assuming there are no other ways to get from the
level depopulated by
flate
to the level it feeds, the intensity of
spectrum will be equal to the measured intensity of
ate
e1ow
in the
2ate
The normalization in this
case is
Nga
'y(gate) (sng)
6-5
AT(beIow) (cnc)
where
'y(gate)
is the singles intensity of 2'gate and
Figure 6-7 Coincidence intensity method.
4(below)
is the area of that yray in the
71
coincidence spectrum produced by gating on
Ygate.
Uncertainties in the intensities result from a cautious 5% uncertainty in the
efficiency (Ueff), the fit uncertainty determined by Radware for the peak of interest
(Uk), and the fit uncertainty for the peak used to determine the normalization
(Unorm). Since the uncertainties are unrelated, the sum of squares is used:
= Ju +
The uncertainty for the method using
+ u.
6-6
described above is increased by
10% to adjust for the possibility of alternate paths from the intermediate level in
Figure 6-7 that do not include
6.2.3
Level placement
The background-subtracted coincidence spectra were used to determine or
verify the placement of yrays in the level scheme. The low-lying excited levels below
approximately 1.3 MeV are generally accepted as complete since the level structure
has been studied and published many times. The high efficiency, improved resolution,
and the clarity gained from Compton suppression make it easier to detect low intensity
transitions not before detected. Previous investigations used one or two detectors, the
8m array has 20. Most earlier publications have used a dedicated gate, meaning that
each coincidence spectrum required a separate experiment. The data recording format
of the 8it allows a coincidence gate to be placed on any channel, after the experiment
is completed. This depth and breadth of coincidence data allows detection and
72
placement of newly-discovered 7-rays and placement of previously unplaced (but
detected) 7-rays. Since important differences in the nuclear structure description can
often hinge on weakly populated levels, such information is crucial to the development
of an accurate explanation of nuclei in the complex transitional region between
spherical in deformed shapes.
A list of all transitions in 152Gd along with all the strong contamination lines
was produced. Coincidence gates were used to determine what lower levels were fed
by a yray. The level sum was tabulated as the sum of the 7-ray energy the energy of
the level directly fed by that transition. Groups of 7-rays with level sums within about
1.5 keV were assigned as coming from a single level. The 7-ray intensity weighted
average of all the energy sums was used to calculate the level energies. An iterative
process was used to check and double-check the established scheme, where level sums
would be checked and possible missed feedings and alternative explanations for a
particular placement were attempted. For levels with energies above 2 MeV, new
levels with only one 7-ray are proposed with a lower level of confidence.
6.2.4
Transition and level results
The data analysis process resulted in the confirmation of the majority of the
known tray placements in '52Gd, and the establishment of at least 266 more
transitions feeding or depopulating known levels or new levels. These yrays are listed
ordered by initial level in Table 6-2. A listing in energy order is available in the
appendix.
73
Table 6-2 Level sorted transition list. Normalized intensity is the strength of a yray
with respect to all the detected yrays that depopulate a given level. Energies are in
keV, LF is the fmal level for a given transition.
EL
J
Ey
LF
Jf
344.3
2+
344.3
100.00 ± 0.00
0.0
0+
615.5
0+
271.2
100.00 ± 5.33
344.3
2+
0.0
0+
615.5
755.5
4+
930.8
2+
1048.1
0+
100.00 ± 5.01
344.3
2+
175.2
0.42 ± 0.02
755.5
4+
315.2
7.38 ± 0.37
615.5
0+
586.7
79.55 ± 3.98
344.3
2+
930.2
12.64 ± 0.25
0.0
0+
117.2
5.70 ± 0.34
930.8
2+
615.5
0+
344.3
2+
0.0
0+
703.9
1048.1
1123.4
2+
3-
1227.1
6+
1282.4
4+
1314.7
1318.6
1-
2+
E0
411.2
432.6
1109.4
Norm. I
E0
94.30 ± 8.08
EQ
178.6
0.24 ± 0.06
930.8
2+
353.7
0.43 ± 0.02
755.5
4+
494.0
2.67 ± 0.14
615.5
0+
765.2
50.82 ± 2.55
344.3
2+
1109.3
45.85 ± 2.31
0.0
0+
367.8
5.88 ± 0.31
755.5
4+
779.1
94.12 ± 4.78
344.3
2+
471.7
100.00 ± 8.15
755.5
4+
158.4
6.44 ± 0.43
1123.4
3-
351.7
48.05 ± 2.45
930.8
2+
527.0
45.51 ± 2.40
755.5
4+
699.6
4.02 ± 0.22
615.5
0+
970.5
35.47 ± 1.81
344.3
2+
1314.7
60.51 ± 3.03
0.0
0+
195.1
8.13 ± 0.43
1123.4
3-
208.9
0.67 ± 0.05
1109.4
2+
270.3
9.95 ± 6.99
1048.1
0+
387.7
7.27 ± 0.37
930.8
2+
563.2
1.04 ± 0.06
755.5
4+
703.3
14.96 ± 1.28
615.5
0+
974.3
53.04 ± 2.67
344.3
2+
1318.6
4.94 ± 0.39
0.0
0+
74
Table 6-2 Level sorted transition list. (Continued)
EL
1434.1
J
3+
1470.7
5(-)
1475.2
0+
1550.2
1605.8
1643.9
4+
2+
2-
Ey
Norm. I
324.7
2.93 ± 0.23
1109.4
2+
503.6
6.07 ± 0.33
930.8
2+
678.8
18.91 ± 1.00
755.5
4+
1089.8
72.09 ± 4.05
344.3
2+
100.00 ± 5.73
755.5
4+
715.3
6+
1681.1
0+
1692.5
3+
1757.1
1-
1771.7
2+
J
160.4
11.48 ± 1.03
1314.7
1-
1131 .0
88.52 ± 5.26
344.3
2+
441.0
11.52 ± 0.86
1109.4
2+
794.9
56.12 ± 2.99
755.5
4+
1205.5
32.36 ± 1.99
344.3
2+
482.5
2.08 ± 0.11
1123.4
3-
496.4
5.31 ± 0.31
1109.4
2+
557.9
3.17 ± 0.17
1048.1
0+
675.2
20.39 ± 1.04
930.8
2+
850.4
0.69 ± 0.04
755.5
4+
990.4
28.53 ± 1.45
615.5
0+
1261.4
32.85 ± 1.67
344.3
2+
1605.8
6.98 ± 0.35
0.0
0+
211.6
0.30 ± 0.09
1434.1
3+
520.4
3.32 ± 0.18
1123.4
3-
534.4
2.41 ± 0.15
1109.4
2+
713.1
1668.2
L1
5.78 ± 0.30
930.8
2+
1299.2
88.19 ± 4.41
344.3
2+
912.7
100.00 ± 36.11
755.5
4+
365.3
3.12 ± 1.26
1314.7
1-
750.5
14.37 ± 0.92
930.8
2+
1336.8
82.50 ± 4.36
344.3
2+
762.0
1.16 ± 0.10
930.8
2+
937.3
15.99 ± 0.86
755.5
4+
1348.2
82.85 ± 4.16
344.3
2+
1412.9
100.00 ± 5.13
344.3
2+
296.1
0.05
1475.2
0+
456.8
11.90 ± 0.94
1314.7
1-
648.5
28.59 ± 1.57
1123.4
3-
662.7
3.21 ± 0.36
1109.4
2+
75
Table 6-2 Level sorted transition list. (Continued)
EL
JI
Ey
Norm. I
Li:
1771.7
(cont.)
723.9
6.71 ± 0.51
1048.1
0+
841.2
9.86 ± 0.64
930.8
2+
1016.1
14.13 ± 0.87
755.5
4+
1427.0
25.59 ± 1.52
344.3
2+
1808.0
1839.9
(4-)
3+
J"
337.6
9.43 ± 1.50
1470.7
5(-)
490.2
8.88 ± 0.83
1318.6
2+
684.3
10.92 ± 0.73
1123.4
3-
877.8
9.66 ± 0.71
930.8
2+
1052.4
61.11 ± 3.49
755.5
4+
557.7
7.79 ± 0.48
1282.4
4+
730.8
12.10 ± 0.91
1109.4
2+
909.2
39.68 ± 2.13
930.8
2+
1084.3
13.05 ± 0.74
755.5
4+
1495.4
27.38 ± 1.52
344.3
2+
100.00 ± 30.32
1227.1
6+
2+
1860.8
5+
633.6
1862.2
2+
753.0
1.22 ± 0.11
1109.4
738.9
12.86 ± 0.69
1123.4
3-
169.5
1.42 ± 0.09
1692.5
3+
218.5
0.86 ± 0.06
1643.9
2-
311.7
0.56 ± 0.04
1550.2
4+
428.0
1.14 ± 0.07
1434.1
3+
544.0
9.07 ± 0.52
1318.6
2+
547.4
2.49 ± 0.21
1314.7
1-
579.9
1.94 ± 0.12
1282.4
4+
814.3
1.94 ± 0.12
1048.1
0+
931.5
5.00 ± 0.29
930.8
2+
1106.6
16.85 ± 0.89
755.5
4+
1246.7
1.14 ± 0.08
615.5
0+
1517.8
23.19 ± 1.28
344.3
2+
1862.3
20.33 ± 1.15
0.0
0+
1915.5
3+
597.8
1.73 ± 0.19
1318.6
2+
633.5
1.32 ± 0.11
1282.4
4+
792.6
6.17 ± 0.40
1123.4
3-
806.6
4.91 ± 0.43
1109.4
2+
1159.9
53.45 ± 2.84
755.5
4+
1571.1
32.42 ± 1.73
344.3
2+
76
Table 6-2 Level sorted transition list. (Continued)
EL
J'j
Ey
Norm. I
Lr
1941.5
2+
248.8
1.86 ± 0.11
1692.5
3+
297.8
0.17 ± 0.02
1643.9
2-
335.6
1.37 ± 0.23
1605.8
2+
391.1
0.53 ± 0.04
1550.2
4+
J'
623.0
19.39 ± 1.01
1318.6
2+
659.2
0.48 ± 0.03
1282.4
4+
818.1
1.76 ± 0.10
1123.4
3-
832.3
2.41 ± 0.15
1109.4
2+
893.6
16.74 ± 0.86
1048.1
0+
1010.8
8.83 ± 0.45
930.8
2+
1185.9
4.70 ± 0.25
755.5
4+
1325.9
18.43 ± 0.94
615.5
0+
1596.9
8.22 ± 0.46
344.3
2+
1941.3
15.12 ± 0.76
0.0
0+
100.00 ± 8.42
930.8
2+
1962.1
-
1031.3
1975.8
2+
1219.4
4.26 ± 0.70
755.5
4+
1360.3
19.57 ± 1.11
615.5
0+
1631.5
38.23 ± 1.98
344.3
2+
1975.8
37.94 ± 1.96
0.0
0+
2011.8
2,3+
2103.0
-
2121.1
4+
2133.6
2169.8
2+
2-
577.7
3.88 ± 0.27
1434.1
3+
693.6
3.58 ± 0.27
1318.6
2+
697.2
1.73 ± 0.21
1314.7
1-
902.7
18.24 ± 1.13
1109.4
2+
1081.4
1.25 ± 0.12
930.8
2+
1667.5
71.32 ± 3.79
344.3
2+
100.00 ± 8.44
1314.7
1-
1282.4
4+
755.5
4+
2+
788.3
839.2
3.23 ± 0.48
1365.6
96.77 ± 5.62
1789.3
79.93 ± 4.12
344.3
818.9
8.24 ± 0.80
1314.7
1-
1203.0
6.01 ± 0.41
930.8
2+
1378.1
1.76 ± 0.16
755.5
4+
1518.2
4.07 ± 0.28
615.5
0+
24.18 ± 2.47
855.3
1314.7
1-
1554.8
3.17 ± 0.33
615.5
0+
1825.4
72.65 ± 3.93
344.3
2+
77
Table 6-2 Level sorted transition list. (Continued)
EL
J'
Ey
Norm. I
LF
2193.3
-
1069.6
24.51 ± 1.96
1123.4
3-
1064.1
46.25 ± 3.67
1109.4
2+
1262.5
27.24 ± 2.00
930.8
2+
1092.7
15.31 ± 1.42
1109.4
2+
1271.6
4.54 ± 0.48
930.8
2+
1446.4
20.70 ± 1.18
755.5
4+
2201.8
2247.0
2258.2
2265.5
2287.8
2+
2+
-
2(+I-)
-
2291.5
2300.0
2-
Jf
1857.5
55.15 ± 2.88
344.3
2+
2201.4
4.31 ± 0.26
0.0
0+
490.8
1.97 ± 0.15
1757.1
1-
407.0
1.12 ± 0.06
1839.9
3+
566.3
0.21 ± 0.12
1681.1
0+
641.5
1.43 ± 0.15
1605.8
2+
813.0
5.36 ± 0.31
1434.1
3+
928.6
8.17 ± 0.43
1318.6
2+
932.1
5.24 ± 0.36
1314.7
1-
1123.5
1.85 ± 0.12
1123.4
3-
1137.9
20.61 ± 1.27
1109.4
2+
1316.2
6.59 ± 0.35
930.8
2+
1491.5
0.56 ± 0.04
755.5
4+
1631.5
4.08 ± 0.21
615.5
0+
1902.6
42.31 ± 2.13
344.3
2+
2246.4
0.49 ± 0.04
0.0
0+
2+
940.3
20.14 ± 1.70
1318.6
1149.1
28.62 ± 2.06
1109.4
2+
1502.9
16.27 ± 1.05
755.5
4+
1913.2
34.98 ± 2.19
344.3
2+
1-
952.5
8.85 ± 0.80
1314.7
1142.2
6.92 ± 0.50
1123.4
3-
1921.1
84.23 ± 4.29
344.3
2+
1532.4
100.00 ± 7.69
755.5
4+
1536.0
100.00 ± 8.70
755.5
4+
(4-)
492.2
0.64 ± 0.06
1808.0
656.4
3.66 ± 0.26
1643.9
2-
865.8
4.39 ± 0.30
1434.1
3+
985.3
6.32 ± 0.54
1314.7
1-
1176.5
1.46 ± 0.14
1123.4
3-
78
Table 6-2 Level sorted transition list. (Continued)
EL
2300.0
2325.8
2327.6
J
(cont.)
I
2,3+
Jflf
Ey
Norm. I
L1r
1190.5
40.49 ± 2.35
1109.4
1369.1
13.59 ± 0.79
930.8
2+
1955.8
29.46 ± 1.61
344.3
2+
1201.9
47.69 ± 10.59
1123.4
3-
1395.4
19.48 ± 7.12
930.8
2+
1570.8
32.83 ± 3.31
755.5
4+
2+
1203.9
25.61 ± 2.20
1123.4
3-
1218.2
11.80 ± 1.34
1109.4
2+
1983.5
62.59 ± 3.66
344.3
2+
2330.7
3,4,5
1575.2
100.00 ± 6.12
755.5
4+
2345.2
1,2+
1729.7
100.00 ± 9.16
615.5
0+
2347.8
1,2+
2004.1
13.27 ± 2.99
344.3
2+
2347.7
86.73 ± 4.64
0.0
0+
2387.3
2401.8
1-2-3-
2+
2430.7
2437.8
2+
1072.7
3.56 ± 0.43
1314.7
1-
1263.8
50.36 ± 3.13
1123.4
3-
1457.6
3.10 ± 1.55
930.8
2+
2043.1
42.97 ± 2.60
344.3
2+
709.5
16.74 ± 1.09
1692.5
3+
1083.8
3.41 ± 0.45
1318.6
2+
1086.9
51.16 ± 4.49
1314.7
1-
1278.2
11.40 ± 0.83
1123.4
3-
1470.9
4.92 ± 0.50
930.8
2+
1646.5
2.98 ± 0.34
755.5
4+
1786.8
4.57 ± 0.39
615.5
0+
2058.2
4.82 ± 0.71
344.3
2+
2086.5
100.00 ± 12.61
344.3
2+
756.8
3.64 ± 2.08
1681.1
0+
1155.5
5.42 ± 0.47
1282.4
4+
1314.5
28.09 ± 1.75
1123.4
3-
1507.0
18.61 ± 1.32
930.8
2+
1821.5
2.03 ± 0.24
615.5
0+
2093.5
42.22 ± 2.32
344.3
2+
79
Table 6-2 Level sorted transition list. (Continued)
EL
J'
Ey
Norm. I
Li
2495.2
1-,2
1372.0
1123.4
3-
930.8
2+
344.3
2+
2495.7
19.42 ± 1.22
4.68 ± 0.40
62.70 ± 3.73
13.01 ± 0.70
0.0
0+
1564.7
2150.9
J
2500.1
3-4,5
1029.4
100.00 ± 9.55
1470.7
5(-)
2503.6
2+,34
1069.4
81.89 ± 5.64
18.11 ± 2.30
1434.1
3+
1748.4
755.5
4+
2168.9
87.68 ± 9.11
344.3
2+
2513.8
12.32 ± 2.53
0.0
0+
768.1
1757.1
1-
2180.0
3.22 ± 0.37
41.07 ± 2.71
16.47 ± 0.99
11.62 ± 0.73
0.83 ± 0.11
2.19 ± 0.20
9.69 ± 1.50
2524.4
721.8
2513.3
2524.1
1,2+
2+
1209.1
1400.6
1593.2
1769.3
1908.4
2529.6
3(+)
837.2
979.6
1247.2
1406.4
1599.0
2185.0
2540.3
3+
1222.0
1417.5
1609.1
1784.7
2195.9
2544.6
(2+)
1421.1
1613.3
1790.7
1928.9
1314.7
1-
1123.4
3-
930.8
2+
755.5
4+
615.5
0+
344.3
2+
14.90 ± 0.77
0.0
0+
0.46 ± 0.05
2.28 ± 0.20
8.69 ± 0.45
1808.0
(4-)
1692.5
3+
1550.2
4+
16.03 ± 0.97
12.73 ± 0.75
1282.4
4+
1123.4
3-
30.70 ± 1.69
29.11 ± 1.75
930.8
2+
344.3
2+
10.90 ± 1.17
12.91 ± 1.30
3.38 ± 0.72
26.75 ± 1.68
46.06 ± 4.08
1318.6
2+
49.99 ± 3.36
25.93 ± 1.94
10.39 ± 0.91
13.70 ± 1.29
1123.4
3-
930.8
2+
755.5
4+
615.5
0+
1123.4
3-
930.8
2+
755.5
4+
344.3
2+
Table 6-2 Level sorted transition list. (Continued)
EL
J1
E'y
Norm. I
L1
J1
2551.5
-
1117.3
20.21 ± 1.47
1434.1
3+
1442.1
69.38 ± 5.16
1109.4
2+
1620.7
10.41 ± 0.98
930.8
2+
2558.1
2+
2580.4
-
2599.0
(2+)
2604.4
2642.0
2667.7
2687.1
2691.8
2709.7
2(-)
2,3-
1+2+
1,2+
1+2+
2+
914.6
33.69 ± 2.32
1643.9
2-
1434.9
13.50 ± 1.11
1123.4
3-
1802.5
36.05 ± 2.19
755.5
4+
2557.7
16.76 ± 0.93
0.0
0+
2236.1
100.00 ± 10.72
344.3
2+
993.3
19.14 ± 2.12
1605.8
2+
1165.0
4.31 ± 0.46
1434.1
3+
1489.4
23.16 ± 1.79
1109.4
2+
1668.1
7.06 ± 0.61
930.8
2+
2254.7
37.56 ± 2.87
344.3
2+
2598.9
8.77 ± 0.59
0.0
0+
1-
1289.3
12.54 ± 1.75
1314.7
1481 .2
43.40 ± 2.57
1123.4
3-
2259.9
44.05 ± 3.22
344.3
2+
1327.3
25.12 ± 2.57
1314.7
1-
1518.6
65.33 ± 3.65
1123.4
3-
1711.2
9.56 ± 0.81
930.8
2+
975.1
24.46 ± 1.93
1692.5
3+
1352.9
25.56 ± 2.57
1314.7
1-
1544.3
19.63 ± 1.33
1123.4
3-
1736.9
26.18 ± 1.80
930.8
2+
2051.9
4.17 ± 0.41
615.5
0+
1757.5
6.68 ± 1.03
930.8
2+
2342.5
72.70 ± 3.98
344.3
2+
2687.9
20.62 ± 1.10
0.0
0+
1257.4
17.01 ± 1.26
1434.1
3+
1582.1
35.25 ± 3.13
1109.4
2+
2076.0
23.82 ± 1.56
615.5
0+
2348.5
23.92 ± 1.65
344.3
2+
698.0
0.33 ± 0.03
2011.8
2,3+
953.6
2.37 ± 0.19
1757.1
1-
81
Table 6-2 Level sorted transition list. (Continued)
EL
2709.7
2719.6
2729.3
2734.3
2742.4
2749.2
J
(cont.)
2+
2+
1+
-
3+
Ey
Norm. I
Lf
1017.2
2.62 ± 0.17
1692.5
3+
1066.3
0.41 ± 0.04
1643.9
2-
1275.7
0.98 ± 0.08
1434.1
3+
1586.3
51.64 ± 2.74
1123.4
3-
1779.0
4.80 ± 0.27
930.8
2+
2094.0
4.13 ± 0.27
615.5
0+
2365.1
22.86 ± 1.20
344.3
2+
2709.9
9.87 ± 0.50
0.0
0+
454.7
0.09 ± 0.05
2265.5
2(+/-)
8045
0.81 ± 0.08
1915.5
3+
857.9
2.43 ± 0.26
1862.2
2+
3+
J'
1027.3
0.61 ± 0.06
1692.5
1076.2
1.96 ± 0.14
1643.9
2-
1400.7
11.13 ± 0.65
1318.6
2+
1596.5
11.01 ± 0.60
1123.4
3-
1769.1
4.38 ± 0.26
930.8
2+
2104.1
1.56 ± 0.11
615.5
0+
2375.2
48.09 ± 2.51
344.3
2+
2719.9
17.92 ± 0.92
0.0
0+
595.8
0.55 ± 0.31
2133.6
2+
813.9
2.33 ± 0.21
1915.5
3+
1036.9
11.33 ± 0.71
1692.5
3+
1085.9
11.76 ± 0.77
1643.9
2-
1410.8
24.32 ± 1.34
1318.6
2+
1606.0
14.89 ± 0.82
1123.4
3-
1681.6
2.66 ± 0.20
1048.1
0+
1798.5
9.91 ± 0.57
930.8
2+
1974.0
0.37 ± 0.06
755.5
4+
2113.6
8.36 ± 0.55
615.5
0+
2384.3
11.90 ± 0.69
344.3
2+
2728.9
1.62 ± 0.13
0.0
0+
2118.6
38.93 ± 2.58
615.5
0+
2734.4
61.07 ± 3.12
0.0
0+
1633.5
20.19 ± 2.39
1109.4
2+
1812.6
8.06 ± 0.96
930.8
2+
2397.8
71.75 ± 4.66
344.3
2+
834.2
1.37 ± 0.12
1915.5
3+
887.5
2.82 ± 0.32
1862.2
2+
1057.0
1.46 ± 0.11
1692.5
3+
82
Table 6-2 Level sorted transition list. (Continued)
EL
2749.2
2773.1
2776.4
2833.1
J
(cont.)
2+,3
2+3,4+
1,2+
Ey
Norm. I
LF
Jg
1430.9
5.00 ± 0.29
1318.6
2+
1640.1
3.21 ± 0.28
1109.4
2+
1993.8
5.99 ± 0.34
755.5
4+
2404.8
80.15 ± 4.17
344.3
2+
3+
857.5
21.55 ± 1.64
1915.5
1128.9
15.09 ± 1.27
1643.9
2-
1338.4
7.33 ± 0.72
1434.1
3+
1454.2
9.91 ± 0.73
1318.6
2+
1663.4
10.50 ± 1.45
1109.4
2+
1841.8
11.97 ± 1.03
930.8
2+
2018.1
9.85 ± 0.79
755.5
4+
2429.9
13.81 ± 2.39
344.3
2+
1845.2
61.88 ± 10.15
930.8
2+
2021.4
38.12 ± 7.57
755.5
4+
2488.8
88.46 ± 7.62
344.3
2+
2833.5
11.54 ± 1.03
0.0
0+
100.00 ± 13.81
1048.1
0+
1-
2853.3
1,2+
1805.2
2862.6
23-
1548.0
8.63 ± 0.85
1314.7
1739.5
24.36 ± 1.40
1123.4
3-
1932.2
1.43 ± 0.28
930.8
2+
2518.2
65.58 ± 4.10
344.3
2+
634.0
0.10 ± 0.03
2247.0
2+
747.4
0.37 ± 0.21
2133.6
2+
869.1
0.50 ± 0.05
2011.8
2,3+
2880.9
2+
965.6
3.58 ± 0.27
1915.5
3+
1188.2
1.83 ± 0.14
1692.5
3+
1237.3
0.78 ± 0.07
1643.9
2-
1275.2
3.86 ± 0.41
1605.8
2+
1446.7
10.58 ± 0.62
1434.1
3+
1562.5
3.23 ± 0.22
1318.6
2+
1566.2
4.85 ± 0.36
1314.7
1-
1757.5
34.07 ± 1.85
1123.4
3-
1771.5
16.23 ± 0.99
1109.4
2+
1950.1
0.61 ± 0.10
930.8
2+
2265.1
3.68 ± 0.23
615.5
0+
2536.3
15.75 ± 0.96
344.3
2+
83
Table 6-2 Level sorted transition list. (Continued)
jfl1
Ey
2+
1191.7
6.22 ± 0.77
1692.5
3+
1954.0
5.74 ± 1.09
930.8
2+
2128.7
12.03 ± 0.86
755.5
4+
2882.5
76.01 ± 3.87
0.0
0+
2895.4
2551.1
100.00 ± 8.94
344.3
2+
2901.9
1792.5
89.67 ± 6.29
1109.4
2+
1970.8
10.33 ± 1.66
930.8
2+
EL
2882.9
2914.2
2919.9
2923.8
2928.1
2932.6
2946.7
2+
23-
1,2+
2+
2+
-
Norm. I
Lr
J
1364.2
8.20 ± 0.66
1550.2
4+
2158.8
14.47 ± 0.87
755.5
4+
2298.8
2.87 ± 0.21
615.5
0+
2569.9
71.76 ± 3.79
344.3
2+
2915.1
2.70 ± 0.16
0.0
0+
1486.3
7.98 ± 0.74
1434.1
3+
1605.7
6.82 ± 1.11
1314.7
1-
1797.0
36.27 ± 2.15
1123.4
3-
1810.5
11.39 ± 1.17
1109.4
2+
2575.1
37.53 ± 3.32
344.3
2+
2306.5
3.00 ± 0.53
615.5
0+
2579.5
97.00 ± 9.70
344.3
2+
1013.0
5.67 ± 0.47
1915.5
3+
1171.9
10.99 ± 0.59
1757.1
1-
1235.5
8.91 ± 0.71
1692.5
3+
1284.5
15.44 ± 1.09
1643.9
2-
1818.7
10.44 ± 0.81
1109.4
2+
1996.0
0.87 ± 0.17
930.8
2+
2172.1
6.77 ± 0.45
755.5
4+
2313.0
0.30 ± 0.11
615.5
0+
2583.9
32.27 ± 2.43
344.3
2+
2927.6
8.35 ± 0.43
0.0
0+
1809.5
15.00 ± 0.88
1123.4
3-
2177.0
5.24 ± 0.37
755.5
4+
2317.5
1.94 ± 0.18
615.5
0+
2588.2
77.82 ± 4.03
344.3
2+
1836.0
0.13 ± 0.02
1109.4
2+
2015.3
8.43 ± 0.68
930.8
2+
2602.5
88.45 ± 5.32
344.3
2+
2949.3
3.00 ± 0.25
84
Table 6-2 Level sorted transition list. (Continued)
EL
2964.1
2981.5
2999.8
3006.5
3009.4
J
3(+)
24,3,4+
2+
(3-)
(2+)
Ey
Norm. I
L,
J'
1048.7
4.79 ± 0.43
1915.5
3+
1414.3
6.07 ± 0.56
1550.2
4+
1530.3
1.29 ± 0.15
1434.1
3+
1646.1
5.87 ± 0.51
1318.6
2+
1682.3
1.88 ± 0.19
1282.4
4+
1841.0
9.20 ± 0.56
1123.4
3-
2033.9
24.51 ± 1.38
930.8
2+
2209.1
2.10 ± 0.17
755.5
4+
2619.1
44.28 ± 2.28
344.3
2+
2050.9
31.83 ± 2.44
930.8
2+
2225.9
29.85 ± 2.08
755.5
4+
2637.2
38.32 ± 3.09
344.3
2+
830.0
0.74 ± 0.44
2169.8
2-
1394.1
12.57 ± 1.45
1605.8
2+
1-
1684.8
4.42 ± 0.87
1314.7
1876.4
3.85 ± 0.38
1123.4
3-
1890.4
6.59 ± 0.84
1109.4
2+
2069.1
26.34 ± 1.55
930.8
2+
2655.1
38.81 ± 3.30
344.3
2+
3001.2
6.68 ± 0.45
0.0
0+
837.4
1.39 ± 0.81
2169.8
2-
1090.9
5.34 ± 0.54
1915.5
3+
(4-)
1199.4
2.40 ± 0.26
1808.0
1690.2
7.04 ± 1.18
1314.7
1-
1897.1
6.60 ± 0.93
1109.4
2+
2075.5
9.12 ± 1.31
930.8
2+
2251.2
19.55 ± 1.41
755.5
4+
2662.3
48.56 ± 6.17
344.3
2+
1168.3
8.96 ± 2.80
1839.9
3+
1253.1
5.03 ± 0.49
1757.1
1-
1364.1
1.00 ± 1.14
1643.9
2-
1690.6
7.33 ± 0.92
1318.6
2+
1694.5
4.40 ± 0.84
1314.7
1-
1886.4
9.37 ± 0.74
1123.4
3-
2078.8
20.16 ± 1.48
930.8
2+
2665.0
41.52 ± 8.97
344.3
2+
3008.4
2.22 ± 0.15
0.0
0+
Table 6-2 Level sorted transition list. (Continued)
EL
3012.1
3025.3
3042.3
j1C1
Ey
2+,3,4+
681.6
2+3,4+
(2+)
3066.5
3080.3
3085.3
3088.3
3098.9
3106.6
1+2,3-
2+,3
2+3,4+
1,2+
(2+)
2+,3+
2+
Lr
2330.7
J
3,4,5
1901.9
15.87 ± 1.93
1109.4
2+
2256.6
8.99 ± 0.78
755.5
4+
2668.0
75.14 ± 9.30
344.3
2+
1916.1
14.83 ± 1.94
1109.4
2+
2270.0
4.31 ± 0.60
755.5
4+
2681.0
80.87 ± 8.97
344.3
2+
1126.9
5.55 ± 0.47
1915.5
3+
1437.1
11.03 ± 1.26
1605.8
2+
1727.4
17.61 ± 2.24
1314.7
1-
1933.2
8.77 ± 0.98
1109.4
2+
3.52 ± 0.70
930.8
2+
2697.8
53.52 ± 4.11
344.3
2+
1613.5
15.31 ± 1.29
1434.1
3+
1732.3
19.92 ± 3.23
1314.7
1-
2702.8
64.76 ± 5.09
344.3
2+
2111.7
3047.1
Norm. I
<1.0
1307.8
0.80 ± 0.28
1757.1
1-
2311.5
10.43 ± 0.82
755.5
4+
2722.2
88.77 ± 7.00
344.3
2+
1164.1
8.72 ± 1.49
1915.5
3+
1646.3
17.92 ± 1.49
1434.1
3+
1761.7
32.44 ± 2.98
1318.6
2+
1956.8
10.48 ± 1.03
1123.4
3-
2150.2
15.70 ± 1.25
930.8
2+
2324.4
14.73 ± 1.32
755.5
4+
2740.8
54.59 ± 23.27
344.3
2+
3085.7
45.41 ± 7.33
0.0
0+
1965.5
13.73 ± 1.28
1123.4
3-
2334.0
4.83 ± 0.58
755.5
4+
2743.9
76.64 ± 10.68
344.3
2+
3088.5
4.79 ± 1.65
0.0
0+
2168.6
22.96 ± 1.61
930.8
2+
2754.5
77.04 ± 9.37
344.3
2+
2350.0
30.39 ± 2.90
755.5
4+
3107.1
69.61 ± 4.09
0.0
0+
Table 6-2 Level sorted transition list. (Continued)
EL
Ji
Ey
Norm. I
Lir
Jf
3112.5
1.2+
2181.7
23.34 ± 2.73
930.8
2+
2497.0
28.29 ± 4.51
615.5
0+
2768.3
48.37 ± 6.02
344.3
2+
3122.6
2+3,4+
3132.4
3134.6
3139.8
3143.8
3153.2
2+
2+
2+, 3,4+
2+3,4+
3164.8
3182.5
3189.7
2+3,4+
-
2367.5
14.86 ± 1.86
755.5
4+
2778.2
85.14 ± 10.82
344.3
2+
2201.8
32.26 ± 3.12
930.8
2+
2787.9
67.74 ± 9.26
344.3
2+
755.5
4+
0.0
0+
2378.7
36.99± 13.28
3134.9
63.01 ± 6.15
1331.2
2.18 ± 0.26
1808.0
(4-)
2092.7
4.67 ± 0.53
1048.1
0+
2208.5
9.34 ± 0.84
930.8
2+
2382.4
11.20 ± 1.18
755.5
4+
2525.1
15.02 ± 2.36
615.5
0+
2795.5
45.72 ± 5.87
344.3
2+
3140.6
11.87 ± 0.66
0.0
0+
2213.2
13.92 ± 1.69
930.8
2+
2388.8
26.74 ± 2.41
755.5
4+
2799.2
59.34 ± 12.48
344.3
2+
1347.1
5.36 ± 0.68
1808.0
(4-)
1870.9
10.37 ± 1.01
1282.4
4+
2043.8
20.27 ± 2.41
1109.4
2+
2223.4
5.05 ± 0.71
930.8
2+
2397.2
15.70 ± 1.38
755.5
4+
2808.8
43.26 ± 5.23
344.3
2+
2233.4
15.42 ± 2.47
930.8
2+
2820.6
84.58 ± 10.58
344.3
2+
2059.2
11.74 ± 1.15
1123.4
3-
2251 .6
13.67 ± 2.33
930.8
2+
2426.9
22.02 ± 2.12
755.5
4+
2838.2
52.57 ± 6.62
344.3
2+
1875.1
42.95 ± 6.64
1314.7
1-
2259.6
30.13 ± 4.40
930.8
2+
2844.6
26.92 ± 4.65
344.3
2+
L
87
Table 6-2 Level sorted transition list. (Continued)
EL
Ji
3205.8
2+
3212.9
3226.3
3233.0
3236.5
3250.9
3265.5
3269.9
3285.2
1+,2+
2+3,4+
2+3-
2+
2+3,4+
1-,2,3-
1,2+
1-,2
Ey
Norm. I
Jflf
Li:
1772.1
13.19 ± 10.53
1434.1
3+
2275.4
8.85 ± 1.33
930.8
2+
2449.9
6.00 ± 0.73
755.5
4+
2861.1
47.31 ± 3.22
344.3
2+
3206.2
24.64 ± 1.36
0.0
0+
1521.2
13.63 ± 1.51
1692.5
3+
1894.3
14.10 ± 1.11
1318.6
2+
1896.9
9.49 ± 1.59
1314.7
1-
2102.8
11.53 ± 1.51
1109.4
2+
2281.3
10.98 ± 1.44
930.8
2+
2596.9
12.41 ± 1.94
615.5
0+
2869.3
27.85 ± 1.97
344.3
2+
2471.9
9.66 ± 1.40
755.5
4+
2882.0
90.34 ± 7.69
344.3
2+
1918.0
28.44 ± 3.67
1314.7
1-
2108.4
13.92 ± 1.70
1123.4
3-
2479.0
18.11 ± 2.73
755.5
4+
2888.8
39.54 ± 4.54
344.3
2+
1544.3
6.08 ± 0.74
1692.5
3+
2128.2
10.42 ± 1.34
1109.4
2+
2306.0
19.19 ± 2.39
930.8
2+
2482.2
5.00 ± 1.08
755.5
4+
2892.7
28.23 ± 2.54
344.3
2+
3235.3
31.06 ± 3.38
0.0
0+
2127.3
9.09 ± 1.09
1123.4
3-
2320.1
4.64 ± 0.96
930.8
2+
2495.4
31.65 ± 3.33
755.5
4+
2906.7
54.62 ± 3.80
344.3
2+
1-
1951.5
27.63 ± 4.50
1314.7
2140.3
20.24 ± 2.42
1123.4
3-
2335.0
18.66 ± 2.85
930.8
2+
2921.6
33.47 ± 3.59
344.3
2+
2655.0
42.47 ± 3.39
615.5
0+
3269.6
57.53 ± 4.44
0.0
0+
1344.0
5.96 ± 0.54
1941.5
2+
1528.9
2.24 ± 0.35
1757.1
1-
1970.4
13.72 ± 1.44
1314.7
1-
2161.7
10.62 ± 0.78
1123.4
3-
88
Table 6-2 Level sorted transition list. (Continued)
EL
J'
Ey
Norm. I
LF
J
3285.2
(cont.)
2176.0
5.23 ± 0.70
1109.4
2+
2354.3
7.16 ± 0.92
930.8
2+
2940.9
55.07 ± 3.62
344.3
2+
2181.9
30.90 ± 2.65
1123.4
3-
2961.0
69.10 ± 8.87
344.3
2+
3305.3
3309.7
3314.7
3325.2
-
2+3,4+
-
2+
1021.6
5438 ± 3.07
2287.8
-
2554.9
19.72 ± 2.20
755.5
4+
2965.7
25.91 ± 5.02
3443
2+
2190.9
65.98 ± 5.88
1123.4
3-
2971 .2
34.02 ± 7.27
344.3
2+
2012.2
13.24 ± 4.24
1314.7
1-
2570.8
3.24 ± 0.39
755.5
4+
2710.7
7.55 ± 0.59
615.5
0+
2980.5
51.58 ± 9.17
344.3
2+
3324.9
24.38 ± 1.41
0.0
0+
0+
3329.0
1,2+
3329.0
100.00 ± 7.94
0.0
3335.3
2+3,4+
1642.4
23.84 ± 2.96
1692.5
3+
1785.2
23.98 ± 3.04
1550.2
4+
3340.8
(2+)
2211.7
25.43 ± 3.31
1123.4
3-
2405.0
26.75 ± 4.48
930.8
2+
1424.6
5.60 ± 1.00
1915.5
3+
2021.9
2.58 ± 0.40
1318.6
2+
2217.4
26.95 ± 1.86
1123.4
3-
2585.2
15.97 ± 1.26
755.5
4+
2995.2
46.75 ± 4.30
344.3
2+
3338.4
2.14 ± 0.15
0.0
0+
930.8
2+
3350.9
-
2420.1
100.00 ± 20.63
3359.3
1-23-
2044.2
28.63 ± 5.45
1314.7
1-
2236.2
13.46 ± 1.90
1123.4
3-
2428.5
15.50 ± 2.73
930.8
2+
3015.3
42.41 ± 4.23
344.3
2+
2436.3
16.29 ± 2.91
930.8
2+
3023.1
83.71 ± 15.77
344.3
2+
3367.3
-
Table 6-2 Level sorted transition list. (Continued)
LF
Jf
0.0
0+
EL
J"1
E'y
3381.2
1,2+
3381.2
100.00 ± 7.02
3386.4
2+2,4+
2262.4
20.24 ± 2.11
1123.4
3-
2629.7
12.30 ± 1.17
755.5
4+
3042.5
67.46 ± 6.01
344.3
2+
3+
3400.9
3413.1
3439.2
3450.0
3484.1
3499.6
3502.6
3508.9
2+,3
1,2+
2+,3,4+
2+,3,4
2+3,4+
2+,3-
-
(2+)
3518.8
3534.9
2+
Norm. I
1484.5
4.44 ± 0.60
1915.5
1645.2
13.39 ± 1.56
1757.1
1-
1758.2
11.71 ± 1.27
1643.9
2-
2276.7
14.89 ± 1.45
1123.4
3-
2644.5
16.24 ± 1.33
755.5
4+
3056.6
39.33 ± 3.74
344.3
2+
3068.7
81.05 ± 9.39
344.3
2+
3413.4
18.95 ± 1.47
0.0
0+
2684.1
15.90 ± 2.62
755.5
4+
3094.8
84.10 ± 4.98
344.3
2+
2327.2
31.93 ± 5.90
1123.4
3-
2694.3
68.07 ± 7.56
755.5
4+
2360.3
31.06 ± 3.07
1123.4
3-
2728.9
14.19 ± 1.66
755.5
4+
3139.9
54.75 ± 10.68
344.3
2+
3+
1807.1
11.19 ± 1.23
1692.5
2184.8
28.60 ± 3.80
1314.7
1-
2376.3
37.69 ± 3.58
1123.4
3-
2744.1
22.53 ± 2.28
755.5
4+
2572.2
14.09 ± 1.19
930.8
2+
3158.3
85.91 ± 16.46
344.3
2+
2751.7
4.29 ± 0.46
755.5
4+
3164.7
95.71 ± 16.19
344.3
2+
3174.5
100.00 ± 17.03
344.3
2+
2220.9
13.85 ± 2.23
1314.7
1-
2411.9
17.23 ± 1.75
1123.4
3-
2426.0
14.57 ± 2.77
1109.4
2+
2603.8
12.22 ± 1.63
930.8
2+
Table 6-2 Level sorted transition list. (Continued)
EL
E'y
3539.0
3551.2
3567.8
2+,3,4+
2+3,4+
3572.9
6.3
Norm. I
LF
J
2779.8
3.20 ± 0.45
755.5
4+
3190.0
37.45 ± 7.47
344.3
2+
3535.9
1.48 ± 0.17
0.0
0+
2608.0
43.26 ± 10.58
930.8
2+
3194.9
56.74 ± 25.90
344.3
2+
2440.9
31.28 ± 6.84
1109.4
2+
2619.3
17.85 ± 3.00
930.8
2+
2796.7
50.87 ± 4.11
755.5
4+
2635.9
5.52 ± 1.04
930.8
2+
2811.9
5.83 ± 0.64
755.5
4+
3223.6
88.65 ± 16.43
344.3
2+
2462.7
19.68 ± 3.94
1109.4
2+
3228.8
80.32 ± 15.82
344.3
2+
3574.6
1,2+
3574.6
100.00 ± 12.49
0.0
0+
3589.4
-
3245.1
100.00 ± 27.83
344.3
2+
3596.1
-
3251.8
100.00 ± 22.88
344.3
2+
3620.9
3276.6
100.00 ± 20.01
344.3
2+
3628.1
3283.9
100.00 ± 20.34
344.3
2+
3655.7
3311.5
100.00 ± 39.03
344.3
2+
3703.4
2772.5
100.00 ± 21.92
930.8
2+
3709.4
3365.1
100.00 ± 23.05
344.3
2+
Comparison to previous results
6.3.1
New levels
54 new levels have been established by this study. Eighteen of those new
levels above 1.9 MeV have only one transition and thus have low confidence. Table
6-3 shows a comparison of the levels in this experiment and those published in
;!JI
Adams's recent35 paper and in the
6.3.2
TORI68
New transitions
The Adam et
al.
data is the most recently published, but it has not been
combined with the Nuclear Data Sheets (NDS). Furthermore, some of the methods
used to assign transitions by Adam et
al.
are suspect. The Table of Radioactive
Isotopes (TORI) based on the NDS has better reviewed data though it lacks the depth
of the more recent data. Both the Adam et
al.
data and the NDS data are compared to
the data from this experiment in Table 6-4. In both cases the quality of coincidence
data has led to vast improvements in the power to place y-rays. The improvements to
the TORI68 data are primarily due to increased detector resolution and higher statistics.
Many of the differences in Adam's data are due to the method of placing transitions by
energy sums alone. All of the placements in the present study were done by
coincidence, which has a higher level of confidence. There are 306 transitions that are
not published in the Adam et
Adam or TORI data.
al.
study and 266 that are not published in either the
92
Table 6-3 Comparison of published levels to those proposed in this work. "A" is for
Adam ez' al. and "T" is for data from the Table of Radioactive Isotopes (TORI).
EL
Spin
EL(A)
Spin (A)
I
1109.4
0+
2+
0+
4+
2+
0+
2+
1123.4
0.0
0
EL(T)
Spin (1)
1109.19
0+
2+
0+
4+
2+
0+
2+
1109.17
0+
2+
0+
4+
2+
0+
2+
3-
1123.18
3-
1123.19
3-
1227.1
6+
1227.37
1282.4
4+
1282.27
6+
2+
4+
1282.26
4+
1314.7
1-
1314.64
1-
1314.65
1-
1318.6
1318.35
2+
3+
1470.7
5(-)
1470.61
2+
3+
2+
1318.42
1434.1
2+
3+
1475.2
0+
1550.2
4+
2+
1550.15
2+,3,4+
1550.21
1605.58
2+
1605.6
4+
2+
1643.9
2-
1643.43
2-
1643.41
2-
1668.2
6+
0+
3+
1680.76
1692.41
3+
1771.57
(2+,3-)
1807.66
4+
1839.62
(2+)
1862.05
2+
1862.06
2+
2+
2+
1915.19
4+,5,6+
1915.42
(3-,4+)
1915.69
2+,3,4+
1941.16
2+
1941.16
2+
344.3
615.5
755.5
930.8
1048.1
344.28
615.37
755.4
930.55
1047.77
1274.25
1434.02
0
344.28
615.4
755.4
930.55
1047.85
1434.02
1533.91
1605.8
1681.1
1692.5
1692.42
1734.44
1757.1
1-
1755.76
1-,2-,3
1771.7
2+
1771.56
2+
2+
1785.24
1808.0
(4-)
1807.53
1808.95
1839.9
1860.8
1862.2
1915.5
3+
5+
2+
3+
1941.5
2+
1962.1
--
1839.7
1861.9
1975.8
2+
1975.67
1+,2+
1975.67
1,2+
2011.8
2,3+
2011.65
1+,2+,3
2011.63
(3)+
2103.0
--
2201.79
3+
2121.1
4+
2+
2133.6
2120.96
2+,3,4+
2133.39
1+,2+
93
Table 6-3 Comparison of published levels to those proposed in this work. (Continued)
EL
2169.8
Spin
2-
EL(A)
2169.58
Spin (A)
EL(T)
Spin (1)
1,2+
2193.3
--
2201.8
2201.73
2247.0
2+
2+
2246.77
2+
2+
2258.2
--
2258.14
2+,3,4+
2265.5
2(+/-)
2264.83
1-,2,3-
2265.28
1+,2+,3
2246.83
3+
2265.19 (1+,2+,3+)
2267.71
2287.8
2291.5
--
2300.0
2-
2299.64
2325.8
I
2325.82
--
2327.6
2,3+
2330.7
2345.2
3,4,5
2330.7
2+
2299.66
3-
2462.77
(2+)
2+,3,4+
1,2+
2347.8
1,2+
2387.3
1-,2-3-
2386.95
1-,2,3-
2401.8
2+
2401.49
1+,2,3-
2437.44
1+2+
2430.7
--
2437.8
2+
2447.82
2495.2
1-,2
2500.1
3-,4,5
2503.6
2+,3,4+
2513.3
1,2+
2513.9
1+,2+
2524.1
2+
2523.8
2+
2529.6
2540.3
2544.6
2551.5
3(+)
2529.39
3+
2540.45
--
2551.12
2558.1
2+
2557.84
2+
2580.4
--
2599.0
(2+)
2598.78
1+2+
2604.4
2642.0
2(-)
1-2,3-
2,3-
2604.33
2641.56
2667.7
1+2+
2667.54
1-
2687.1
1,2+
2686.85
li-,2i-,3
2691.8
1+,2+
2709.7
2+
2+
2709.42
2+
2719.67
2+
2+
2709.32
2719.6
2719.73
(2+)
2729.3
2+
2729.17
2+
2729.22
2+
(2+)
2495.17
1+,2+,3
2495.3
1+
2523.72
2+
2529.39
(3+)
2599.28
(2+)
2687.1
(2+)
2+,3+
2544
94
Table 6-3 Comparison of published levels to those proposed in this work. (Continued)
EL
Spin
EL(A)
2734.3
2742.4
1+
2734.04
--
2744.05
2749.2
3+
2773.1
2+,3
2776.4
2+,3,4+
2833.1
1,2+
2853.3
1,2+
2862.6
2,3-
2749.2
2772.36
Spin (A)
Spin (T)
1-
2+,3+
2749.21
(2+)
2+
2862.64
2869.76
EL(T)
1+
2862.6
3+
1,2+
2+
2+
2880.65
1+,2+
2880.61
1-
2901.9
2914.2
2+
2913.98
2+
2,3-
2914.15
2920.08
2+
2919.9
2923.8
1,2+
2928.1
2+
2927.85
24-,3+
2928.8
3+
2+
2932.6
(2+3+)
2-,3-
2964.2
2+
3007.2
3-
3024.3
1+,2+
2880.9
2882.9
2895.4
2928.68
2+
2932.66
2964.1
3(+)
2964.33
2981.5
2+,3,4+
2981.38
2999.8
2+
2999.52
3006.5
3009.4
(3-)
3006.71
2+
(2+)
3009.16
3012.06
2-,3-
2932.6
2946.7
2+,3,4+
2989.02
3012.1
2+,3,4+
3025.3
2+,3,4+
3042.3
3047.1
(2+)
1+,2,3-
3066.5
2+,3
3080.3
2+,3,4+
3085.3
3088.3
3098.9
3106.6
1,2+
(2+)
2+,3+
2+
3042.3
1+,2+
2+,3+
0+,1+,2
2+
3085.2
2+
3067.4
3074.86
3079.64
3+,4+
3090.4
3098.99
3105.49
2+
3112.5
1.2+
3110.9
1+,(2+)
3122.6
2+,3,4+
3112.5
1+,2+
3132.4
--
3134.6
2+
2+
3139.8
3042.16
3099.36
3106.4
(+)
1,2+
95
Table 6-3 Comparison of published levels to those proposed in this work. (Continued)
EL
Spin
3143.8
2+, 3,4+
3153.2
3164.8
3182.5
3189.7
3205.8
24,3,4+
3212.9
3226.3
3233.0
3236.5
3250.9
3259.4
3265.5
3269.9
3285.2
3305.3
3309.7
3314.7
3325.2
3329.0
3335.3
3340.8
3350.9
3359.3
3367.3
3381.2
3386.4
3400.9
3413.1
3439.2
3450.0
3484.1
3499.6
3502.6
3508.9
3518.8
3534.9
3539.0
(
Spin (A)
EL(A)
3140.17 1+,2+
3143.96
3152.98 24,3,4+
--
24,3,4+
-2+
1+,2+
24,3,4+
2+,32+
2+,3,4+
-1-,2,31,2+
1-,2
-2+,3,4+
-2+
1,2+
2+,3,4+
(2+)
-1-,2,3-1,2+
2+,2,4+
2+,3
1,2+
24,3,4+
24,3,4
2+,3,4+
2+,3-(2+)
-2+
--
I
Spin (T)
EL(T)
3140
1-
3159.6
3165.1
1,2+
1,2+
3189.5
3191.3
3205.4
1-2+
3250.9
(1)-
3284.9
(1+,2+)
3309.7
1,2+
3324.2
3328.8
3337.8
(1,2)
1,2+
1-
3214.23
3232.05
3236.92
3285.12
24,3,4+
2+
3340.6
3-
3358.26
2+
1,2+
(1,2+)
3357.98
(2+)
3393.27
2+
3411.5
3433.2
(2)+
2+
3478.9
1,2+
Table 6-3 Comparison of published levels to those proposed in this work. (Continued)
EL
Spin
3551.2
2+,3,4+
3567.8
2+,3,4+
EL(T)
Spin (T)
3572.9
3574.6
1,2+
3589.4
--
3596.1
--
3620.9
-
3628.1
--
3655.7
3703.4
3709.4
3573.2
(1,2+)
97
Table 6-4 Transition comparison. The leftmost data is from this study, the center data
is from Adam et al., and the right is from the Table of Radioactive Isotopes (TORI)
data. Since the Adam et al. intensities are normalized by level, the data from this
experiment have been normalized by level. The intensities for the TORI data are
normalized to the 344 keV yray. The appendix contains a listing of the values from
this experiment normalized in the same way as the TORI data. Three transitions are
purely electric monopole, they are listed as "E0". The intensity of these transitions
was not measured in this experiment. Some Adam et al. measurements show error of
0.00, or are blank. This indicates that the provided intensity is a lower limit.
EL
This Experiment
E7
I
out of level
Ey (A)
Adam et al.
I out of level
TORI
Ey(T)
I
344.3
344.3
100.00 ± 0.00
344.279
100 ± 2.5
344.28
1000
615.5
271.2
615.5
100.00 ± 5.33
271.09
615.6
99.97 ± 2.2
0.03 ± 0.00
271.08
615.6
132
19.8
755.5
411.2
100.00 ± 5.01
411.1165
100 ± 2.47
411.08
63
930.8
175.2
315.2
586.7
930.2
0.02
0.37
3.98
0.25
175.14
315.16
586.27
930.58
0.21 ± 0.02
175
7.04 ± 0.15
80.04 ± 1.65
12.72 ± 0.44
315.2
586.29
930.7
5.70 ± 0.34
117.25
432.5
703.494
1047.9
3.19 ± 0.09
0.12 ± 0.00
96.17 ± 2.84
0.53 ± 0.00
117.4
432.5
703.34
1047.9
0.22
0.52
2.59
50.14
46.54
2.1
± 1.04
494
764.88
1109.2
367.8
778.86
5.5
89
1048.1
1109.4
1123.4
1227.1
117.2
432.6
703.9
1048.1
EU
0.42
7.38
79.55
12.64
±
±
±
±
EU
94.30 ± 8.08
EU
178.6
353.7
494.0
765.2
1109.3
0.24
0.43
2.67
50.82
45.85
± 2.31
178.58
353.78
493.81
764.89
1109.2
367.8
779.1
5.88 ± 0.31
94.12 ± 4.78
367.8
778.9045
5.93 ± 0.15
94.07 ± 1.94
471.7
100.00 ± 8.15
471.98
100 ± 4.14
658.83
100 ± 6.7
± 0.06
± 0.02
0.14
± 2.55
±
1274.25
1282.4
1314.7
0.69
13.3
145
28
0.8
8
26
0.35
± 0.02
±
0.02
± 0.07
± 1.16
45
41
158.4
351.7
527.0
6.44 ± 0.43
48.05 ± 2.45
45.51 ± 2.40
159.16
351.73
526.85
1.85 ± 0.2
46.06 ± 1.13
351.7
526.9
3.6
52.1 ± 1.13
699.6
970.5
1314.7
4.02 ± 0.22
35.47 ± 1.81
60.51 ± 3.03
699.25
970.32
1314.635
3.97 ± 0.28
37.45 ± 0.79
58.58 ± 2.2
699
970.4
1314.7
1.6
14.3
4
22
Table 6-4 Transition comparison. (Continued)
EL
Ey
1 out of level
1318.6
195.1
8.13 ± 0.43
195.17
7.95 ± 0.18
195.2
6.3
208.9
0.67 ± 0.05
209.14
0.72 ± 0.03
209.3
0.4
270.3
9.95 ± 6.99
270.55
6.5
387.7
7.27 ± 0.37
387.8
7.46 ± 0.25
387.8
6.4
563.2
1.04 ± 0.06
562.98
1.34 ± 0.04
563.3
703.3
14.96 ± 1.28
702.976
17.07 ± 0.64
703.34
974.3
1434.1
1470.7
1475.2
1605.8
1643.9
I out of level
Ey(T)
1.1
12.1
53.04 ± 2.67
974.05
1318.6
4.94 ± 0.39
1318.24
324.7
2.93 ± 0.23
324.9
0.15
325.3
<1.0
503.6
6.07 ± 0.33
503.43
5.25 ± 0.14
503.5
0.9
678.8
18.91 ± 1.00
678.61
18.24 ± 0.41
678.6
4.1
1089.8
72.09 ± 4.05
1089.737
1089.9
20
115.3
0.06
1.34
441
794.7
-0.4
715.3
100.00 ± 5.73
160.4
11.48 ± 1.03
1131.0
88.52 ± 5.26
1533.91
1550.2
Ey (A)
715.19
60.11 ±
1.27
974.1
5.35 ± 0.22
1318.2
3.42 ±
73.1 ± 1.5
68.8 ±
48
6
1.73
855.237
31.2 ± 6.07
603.18
100 ± 6.86
441.0
11.52 ± 0.86
441.02
13.71 ± 0.36
794.9
56.12 ± 2.99
794.73
52.54 ±
1205.5
32.36 ± 1.99
1205.83
33.75 ± 1.34
1206
3
482.5
2.08 ± 0.11
482.34
2.17 ± 0.05
496.4
5.31 ± 0.31
496.37
5.46 ±
0.12
482.3
496.4
2.1
557.9
3.17 ± 0.17
557.81
2.71 ± 0.26
557.6
1.6
675.2
20.39 ± 1.04
675.01
19.83 ±
675.1
2.2
850.4
0.69 ± 0.04
850.49
1.12 ±
990.4
28.53 ± 1.45
32.85 ± 1.67
990.19
26.69 ± 0.55
990.3
9
1261.4
1261.32
33.72 ± 0.71
1261.4
16.6
1605.8
6.98 ± 0.35
1605.584
1605.8
2.4
211.6
0.30 ± 0.09
520.4
3.32 ± 0.18
520.3
2.69 ± 0.11
520.3
534.4
2.41 ± 0.15
534.21
2.29 ± 0.06
534.1
713.1
5.78 ± 0.30
712.82
4.91 ± 0.17
713
1299.2
88.19 ± 4.41
1299.14
90.12 ± 1.94
1299.11
912.7
100.00 ± 36.11
8.31 ±
0.4
0.5
3
0.09
1.19
S I
1668.2
1.8
2
1.9
0.043
Table 6-4 Transition comparison. (Continued)
EL
Ey
1681.1
365.3
3.12 ± 1.26
750.5
14.37 ± 0.92
366.15
750.06
1336.8
82.50 ± 4.36
1336.54
1692.5
l
out of level
762.0
1.16 ± 0.10
937.3
15.99 ± 0.86
937.04
1348.2
82.85 ± 4.16
1348.15
1734.44
1757.1
1412.9
1771.7
296.1
<0.05
456.8
11.90 ± 0.94
100.00 ± 5.13
1860.8
out of level
7.5 ± 0.76
74.61 ±
1.52
16.01 ± 0.63
83.99 ±
100 ± 5.77
1411.48
100 ± 5.88
12.06 ± 0.5
489.59
7.06 ± 0.56
648.31
30.85 ± 0.74
28.59 ± 1.57
3.21 ± 0.36
723.9
6.71 ± 0.51
723.67
5.98 ± 0.24
841.2
9.86 ± 0.64
841.1
13.38 ± 0.74
1016.1
14.13 ± 0.87
1427.0
25.59 ± 1.52
337.6
9.43 ± 1.50
490.2
8.88 ± 0.83
684.3
10.92 ± 0.73
877.8
9.66 ± 0.71
1052.4
61.11 ± 3.49
1427.32
30.66 ± 0.74
662.02
38.44 ± 4.2
854.69
61.56 ±
1052.15
100 ± 2.16
70.77 ± 2.31
557.433
12.47 ± 2.45
7.79 ± 0.48
730.8
12.10 ± 0.91
909.2
39.68 ± 2.13
909.15
1084.3
13.05 ± 0.74
1495.4
27.38 ± 1.52
1084.305
1495.44
633.6
100.00 ± 30.32
3
1348.1
-13
456.9
2
648.4
2
840.8
2
1016.4
2
1427.4
2
12.01
490.66
878.13
557.7
937
1.69
979.04
456.92
E1(T)
17.89 ± 0.99
662.7
1808.95
1839.9
I
648.5
1785.24
1808.0
Ey (A)
1052.3
29.23 ± 2.31
715.5
3
730.4
2
1.23
909.1
2
14.31 ± 3.27
1084.1
4
33.33 ±
1495.6
1.6
39.88 ±
1.23
100
Table 6-4 Transition comparison. (Continued)
EL
E7
I out of level
1862.2
169.5
1.42 ± 0.09
218.5
0.86 ± 0.06
311.7
0.56 ± 0.04
1.14 ± 0.07
427.85
2.04 ± 0.14
9.07 ± 0.52
543.58
19.58 ± 0.45
547.4
2.49 ± 0.21
579.9
1.94 ± 0.12
579.63
3.04 ± 0.16
738.9
12.86 ± 0.69
738.69
21.72 ± 0.58
753.0
1.22 ± 0.11
752.59
3.23 ± 0.26
814.3
1.94 ± 0.12
814.123
2.46 ± 0.45
931.5
5.00 ± 0.29
1106.6
16.85 ± 0.89
1246.7
1.14 ± 0.08
1517.8
23.19 ± 1.28
1862.3
20.33 ± 1.15
597.8
806.6
1861.94
46.53 ± 0.97
547.47
7.34 ± 0.19
1106.59
39.94± 1.19
1517.78
52.72 ± 3.95
1.73 ± 0.19
597.57
5.14 ± 0.34
1.32 ± 0.11
633.6
792.56
9.64 ± 0.61
1571.25
76.24 ± 1.53
6.17 ± 0.40
4.91 ± 0.43
1159.9
53.45 ± 2.84
1571.1
32.42 ± 1.73
E?(T)
I
1.41 ± 0.07
544.0
633.5
792.6
1915.19
218.42
I out of level
428.0
1862.06
1915.5
Ey (A)
543.7
3
547.5
2
738.7
3
1106.7
7
1517.8
-0.28
1861.9
7.6
143.8
5
1160
6
1570.8
3
8.97 ± 0.34
687.62
3.52 ± 0.94
1159.82
96.48 ± 2.35
101
Table 6-4 Transition comparison. (Continued)
EL
Ey
1941.5
248.8
1.86 ± 0.11
248.75
1.46 ± 0.18
248.5
1.7
297.8
0.17 ± 0.02
298.06
0.16 ± 0.02
335.5
<1.0
335.6
1.37 ± 0.23
335.56
1.37 ± 0.04
391.1
0.53 ± 0.04
390.82
623.0
19.39 ± 1.01
622.79
659.2
0.48 ± 0.03
818.1
1.76 ± 0.10
817.974
2.21 ± 0.37
818.2
832.3
2.41 ± 0.15
831.94
2.63 ± 0.07
14.85 ± 0.31
1962.1
I
Ey (A)
out of level
893.6
16.74 ± 0.86
893.34
1010.8
8.83 ± 0.45
1010.6
1185.9
4.70 ± 0.25
1325.9
I out of level
2103.0
2121.1
0.44
1
658.8
831.9
2
2
3
893.3
10.3
1010.7
6.5
1185.73
4.96 ± 0.12
1185.6
3.7
18.43 ± 0.94
1325.86
18.23 ± 0.38
1325.8
14
1596.9
8.22 ± 0.46
1596.877
7.03 ± 0.37
1596.9
-0.28
1941.3
15.12 ± 0.76
1941.23
18.3± 0.34
1941.1
11.1
1031.3
100.00 ± 8.42
1219.4
4.26 ± 0.70
9.3 ±
113.5
1360.3
19.57 ± 1.11
1360.43
16.92 ± 0.77
1360
5
1631.5
38.23 ± 1.98
1631.39
39.84 ± 2.92
1631.5
4
1975.8
37.94 ± 1.96
1975.65
43.24 ± 0.95
1975.5
2
577.7
3.88 ± 0.27
577.57
693.6
3.58 ± 0.27
693.13
3.1 ± 0.21
694.1
2
697.2
1.73 ± 0.21
697.2
1.77 ± 0.59
902.46
16.64 ± 0.44
902.4
2
902.7
18.24 ± 1.13
1081.4
1.25 ± 0.12
1667.5
71.32 ± 3.79
788.3
839.2
1667.38
1789.3
2.03 ± 0.1
76.46 ±
1.77
100.00 ± 8.44
3.23 ± 0.48
839.6
96.77 ± 5.62
1365.69
1776.3
21698
622.8
0.19
1365.6
2133.6
I
0.17 ± 0.03
21.33 ±
1975.8
2011.8
E'y(T)
11.67 ± 2.22
75.56 ±
1.67
12.78 ± 1.67
79.93 ± 4.12
818.9
8.24 ± 0.80
1203.0
6.01 ± 0.41
1378.1
1.76 ± 0.16
151 8.2
4.07 ± 0.28
t
818.755
1.17 ± 0.47
1202.84
5.01 ±
1.4
1518.017
5.83 ± 1.17
1789.11
88 ± 2.33
8553
2418 ±247
854945
911 ± 245
1554.8
3.17 ± 0.33
1554.04
7.47 ± 0.67
1825.4
72.65 ± 3.93
1825.37
83.42 ±
1.75
1667.4
0.26
102
Table 6-4 Transition comparison. (Continued)
EL
Ey
2193.3
1069.6
24.51 ± 1.96
1084.1
48.25 ± 3.67
1262.5
27.24 ± 2.00
1092.7
15.31 ± 1.42
1271.6
4.54 ± 0.48
1446.4
1857.5
2201.4
2201.8
2247.0
2258.2
l
out of level
ET (A)
I out of level
Ey(T)
I
1092.26
11.32 ± 0.63
20.70 ± 1.18
1446.335
27.47 ± 2.73
1446.5
55.15 ± 2.88
1857.48
57.04 ±
1857.3 -0.07
4.31 ± 0.26
2201.65
4.17 ± 0.42
407.12
0.37 ± 0.05
1.26
490.8
1.97 ± 0.15
407.0
1.12 ± 0.06
566.3
0.21 ± 0.12
641.5
1.43 ± 0.15
641.2
1.58 ±
0.04
641.3
813.0
5.36 ± 0.31
812.8
5.32 ± 0.14
812.8
3
928.6
8.17 ± 0.43
928.43
9.63 ± 0.2
928.7
7
932.09
5.17 ± 0.19
0.6
932.1
5.24 ± 0.36
1123.5
1.85 ± 0.12
1123.3
3
1137.9
20.61 ± 1.27
1137.56
22.87 ± 0.49
1137.6
-9
1316.2
1491.5
6.59 ± 0.35
0.56 ± 0.04
1316.32
5.25 ± 0.41
1316
5
1491.62
0.45 ± 0.03
1631.5
4.08 ± 0.21
1631.399
1902.6
42.31 ± 2.13
1902.492
45.09 ±
1.02
2246.4
0.49 ± 0.04
36.81 ±
1.25
4.27 ± 0.25
940.3
20.14 ± 1.70
939.84
1149.1
28.62 ± 2.06
1148.99
46.53 ± 2.08
1502.9
16.27 ± 1.05
1502.62
16.67 *
1913.2
34.98 ± 2.19
2265.5
947.08
11.66 ± 2.12
8.85 ± 0.80
950.34
26.74 ±
1142.2
6.92 ± 0.50
1141.68
1921.1
84.23 ± 4.29
1921
100 ± 2.12
2267.71
953.07
90.54 ± 2.27
1040.6
9.46 ± 1.99
2291.5
1536.0 100.00 ± 8.70
1920.9
6.6
1.18
61.6 ± 2.83
2265.28
1532.4 100.00 ± 7.69
-0.11
0.56
952.5
2287.8
1902.4
103
Table 6-4 Transition comparison. (Continued)
EL
Ey
2300.0
492.2
0.64 ± 0.06
656.4
3.66 ± 0.26
656.42
3.35 ± 0.15
865.8
4.39 ± 0.30
865.62
3.76 ± 0.15
l
out of level
Ey (A)
I out of level
Ey('I)
656.6
0.6
985.1
2
985.3
6.32 ± 0.54
984.9
1176.5
1.46 ± 0.14
1176.53
1190.5
40.49 ± 2.35
1190.44
37.7 ± 0.75
1190.5
0.28
1369.1
13.59 ± 0.79
1369.04
12.48 ± 0.31
1369.2
0.35
5.8 ±
0.31
2.7 ± 0.11
1544
2325.8
2327.6
2330.7
1955.8
29.46 ± 1.61
1955.36
1201.9
47.69 ± 10.59
1202.64
1395.4
19.48 ± 7.12
1570.8
32.83 ± 3.31
1203.9
25.61 ± 2.20
1218.2
11.80 ± 1.34
1983.5
62.59 ± 3.66
1575.2 100.00 ± 6.12
1575.3
1986.8
2345.2
1729.7 100.00 ± 9.16
2347.8
2004.1
13.27 ± 2.99
2347.7
86.73 ± 4.64
2387.3
2401.8
2430.7
I
34.2 ± 0.75
100 ± 21.74
92.61 ± 2.46
7.39 ±
1.48
1.59
1072.7
3.56 ± 0.43
1072.16
12.35 ±
1263.8
50.36 ± 3.13
1263.84
43.82 ± 1.59
2042.67
43.82 ±
1457.6
3.10 ± 1.55
2043.1
42.97 ± 2.60
3.19
709.5
16.74 ± 1.09
708.98
1083.8
3.41 ± 0.45
1083.141
16.42 ± 3.79
1086.9
51.16 ± 4.49
1087.12
65.38 ± 2.53
1278.2
11.40 ± 0.83
1470.9
4.92 ± 0.50
1646.5
2.98 ± 0.34
1786.8
4.57 ± 0.39
2058.2
4.82 ± 0.71
2086.5 100.00 ± 12.61
18.19 ± 0.66
1955.3
5
0.27
104
Table 6-4 Transition comparison. (Continued)
EL
Ey
l out of level
2437.8
756.8
3.64 ± 2.08
Ey (A)
I out of level
E7(T)
I
J
1155.5
5.42 ± 0.47
1314.5
28.09 ± 1.75
1314.257
1507.0
18.61 ± 1.32
1506.9
11.78± 0.44
1821.5
2093.5
2.03 ± 0.24
2093.16
31.86 ± 2.72
42.22 ± 2.32
2437.11
1.99 ± 0.15
2103.54
100 ± 21.28
2447.82
2495.2
2500.1
2503.6
2513.3
1372.0
19.42 ± 1.22
1564.7
4.88 ± 0.40
2150.9
62.70 ± 3.73
2495.7
13.01 ± 0.70
7.55
857.1
2
1353
<1.5
1532.3
1.4
2118.5
0.8
2150.9
-0.6
2495.6
-1.7
42.42 ± 0.94
1209.1
0.06
14.42 ±
1400.6
3
1908.5
0.5
1372.04
18.01 ± 0.54
2150.85
81.99 ±
1.63
1029.4 100.00 ± 9.55
1069.4
1748.4
81.89 ± 5.64
18.11 ± 2.30
2168.9
87.68 ± 9.11
2169.16
2513.8
12.32 ± 2.53
2513.9
9.99 ± 2.53
684.12
2.53 ± 0.28
880.29
6.08 ± 0.2
2524.1
768.1
2529.6
54.36 ±
90.01 ± 25.32
3.22 ± 0.37
1209.1
41.07 ± 2.71
1209.03
1400.6
1593.2
16.47 ± 0.99
1400.617
1593.37
1769.3
0.83 ± 0.11
1908.4
2.19 ± 0.20
2180.0
2524.4
9.69 ± 1.50
2179.42
8.71 ± 0.23
2179.1
1
14.90 ± 0.77
2523.92
12.27 ± 0.28
2523.9
1.4
721.8
0.46 ± 0.05
722
1.83 ± 0.13
837.2
2.28 ± 0.20
1247.07
19.12 ± 0.55
11.62 ± 0.73
1.22
13.58 ± 0.37
979.6
8.69 ± 0.45
1247.2
16.03 ± 0.97
1247.1
2
1406.4
12.73 ± 0.75
1406.16
14.64 ± 0.37
1406.1
1.5
1420.6
2
1599.0
30.70 ± 1.69
1598.9
31.66 ± 0.73
1598.9
2185.0
29.11 ± 1.75
2185.24
32.75 ± 0.64
2185
7
3.3
/
105
Table 6-4 Transition comparison. (Continued)
EL
Ey
2540.3
1222.0
1417.5
10.90 ± 1.17
1221.95
11.51 ± 0.76
12.91 ± 1.30
1417.18
10.85 ± 0.55
1609.1
3.38 ± 0.72
2544.6
2551.5
2558.1
2580.4
2599.0
1 out of level
Ey (A)
I out of level
1784.7
26.75 ± 1.68
1785.15
2195.9
46.06 ± 4.08
2196.2
1421.1
49.99 ± 3.36
1420.76
51.13 ± 1.42
1613.3
25.93 ± 1.94
1613.53
48.87 ±
1790.7
10.39 ± 0.91
1928.9
13.70 ± 1.29
1117.3
20.21 ± 1.47
1117.15
16.86 ± 0.64
1442.1
69.38 ± 5.16
1441.91
83.14 ± 2.28
1620.7
10.41 ± 0.98
26.69 ± 1.39
50.95 ±
914.6
33.69 ± 2.32
914.35
1434.9
13.50 ± 1.11
1802.5
36.05 ± 2.19
1434.54
1802.67
38.17 ±
2211.7
0±
2557.7
16.76 ± 0.93
2236.1
100.00 ± 10.72
993.3
19.14 ± 2.12
1165.0
4.31 ± 0.46
1489.4
23.16 ± 1.79
1668.1
7.06 ± 0.61
2254.7
37.56 ± 2.87
2598.9
8.77 ± 0.59
Ey(T)
30.53 ±
1.04
1.66
0.89
16.81 ± 0.82
1.01
2557.91
14.5 ± 0.45
993.14
21.24 ± 0.86
1489.6
22.09 ±
1284.6
1983.41
2604.4
2642.0
2667.7
2254.54
0.64
1489.8
2
3
24.5 ± 0.58
32.18 ±
0.64
1289.3
12.54 ± 1.75
1289.64
18.98 ± 0.6
1481.2
43.40 ± 2.57
39.25 ± 2
2259.9
44.05 ± 3.22
1481.18
2260.05
1327.3
25.12 ± 2.57
1518.6
65.33 ± 3.65
1518.377
83.89 ± 6.23
1711.2
9.56 ± 0.81
1711.02
16.11 ± 0.53
41.77 ±
2255.2
2599.4
1.2
1372
0.7
2
I
975.1
24.46 ± 1.93
1352.9
25.56 ± 2.57
1352.98
22.32 ± 2.43
1544.3
19.63 ± 1.33
1544.29
45.9 ± 1.12
1736.9
26.18 ± 1.80
1737.03
31.78 ± 0.82
2051.9
4.17 ± 0.41
106
Table 6-4 Transition comparison. (Continued)
E
2687.1
2691.8
I
Ey
I
Loutoflevel
1757.5
2342.5
2687.9
6.68 ± 1.03
72.70 ± 3.98
20.62 ± 1.10
1257.4
17.01 ± 1.26
1582.1
35.25 ± 3.13
23.82 ± 1.56
23.92 ± 1.65
2076.0
2348.5
:
EyA)
2342.57
I out of level
100± 1.97
2709.7
454.7
804.5
857.9
1027.3
1076.2
1400.7
1596.5
I
2.2
2
0.26
0.33 ± 0.03
2.37 ± 0.19
2.62 ± 0.17
0.41 ± 0.04
0.98 ± 0.08
51.64 ± 2.74
4.80 ± 0.27
4.13 ± 0.27
22.86 ± 1.20
9.87 ± 0.50
0.09 ± 0.05
0.81 ± 0.08
2.43 ± 0.26
0.61 ± 0.06
1066.23
0.66 ± 0.05
1586.22
1778.78
2094.047
2365.13
2709.47
55.81 ± 1.15
6.35 ± 0.19
4.7 ± 0.42
21.94 ± 0.54
10.55 ± 0.23
454.82
0.36 ± 0.08
1027.16
0.77 ± 0.09
1401.321
1596.487
1789.12
2104.297
2375.34
2719.61
4.13 ± 0.37
11.14± 0.83
6.6 ± 0.5
2.48 ± 0.55
56.15± 1.19
813.475
1036.74
1085.68
1258.45
1410.816
1605.982
1681.53
1798.45
1.08 ± 0.51
10.92 ± 0.25
13.65 ± 0.44
10.03 ± 0.38
1411.5
1605.8
1681.4
1797.8
2113.7
2384.94
2729.25
8.64 ± 0.19
9.21 ± 0.19
1.66 ± 0.06
2114
2384.7
2729
1275.1
1.6
1586.23
1778.6
2093.3
2365.3
2709.4
0.19
1596.9
0.25
0.26
1.3
1
6.7
3
1.96 ± 0.14
2375.2
2719.9
11.13 ± 0.65
11.01 ± 0.60
4.38 ± 0.26
1.56 ± 0.11
48.09 ± 2.51
17.92 ± 0.92
595.8
0.55 ± 0.31
813.9
1036.9
1085.9
2.33 ± 0.21
11.33 ± 0.71
11.76 ± 0.77
1410.8
1606.0
1681.6
1798.5
1974.0
2113.6
2384.3
2728.9
24.32 ± 1.34
14.89 ± 0.82
2.66 ± 0.20
9.91 ± 0.57
0.37 ± 0.06
8.36 ± 0.55
11.90 ± 0.69
1.62 ± 0.13
1789.1
2104.1
2729.3
2342.8
2687.3
180
698.0
953.6
1017.2
1066.3
1275.7
1586.3
1779.0
2094.0
2365.1
2709.9
2719.6
Ey(T)
18.38 ± 0.41
4.76 ± 0.18
20.96 ± 1.27
14.92 ± 1.91
4.17± 0.11
1789.1
2375.3
2719.82
0.15
6
788
2
1037
2
1086.3 -0.18
4.3
7
2
3
1.5
2.8
107
Table 6-4 Transition comparison. (Continued)
EL
Ey
2734.3
2118.6
2734.4
2742.4
Ey (A)
I out of level
38.93 ± 2.58
2118.66
38.1 ±
61.07 ± 3.12
2734.06
61.9 ± 1.31
1633.5
20.19 ± 2.39
1634
8.14 ± 1.89
1812.6
8.06 ± 0.96
2397.8
71.75 ± 4.66
2744.1
91.86 ± 1.96
301.82
0.31 ± 0.09
I
out of level
2749.2
834.2
1.37 ± 0.12
887.5
2.82 ± 0.32
1057.0
1.46 ± 0.11
1430.9
5.00 ± 0.29
1640.1
2773.1
3.21 ± 0.28
1.42 ± 0.05
1215.2
0.66 ± 0.07
1430.76
5.91 ± 0.24
1640.08
2853.3
0.2
5.99 ± 0.34
1993.87
2404.8
80.15 ± 4.17
2405
82.62 ±
1.6
857.5
21.55 ± 1.64
857.33
27.89 ±
1.99
1128.9
1338.4
2833.1
0.6 ±
2.73 ± 0.09
1993.8
1016.6
2776.4
I
1056.79
1475.04
5.75 ± 0.12
24.8 ± 0.66
15.09 ± 1.27
1128.65
7.33 ± 0.72
1338.5
1454.2
9.91 ± 0.73
1454.08
1663.4
10.50 ± 1.45
1663.67
14.83 ±
0.89
1841.8
11.97 ± 1.03
1841.81
9.08±
1.11
2018.1
9.85 ± 0.79
2429.9
13.81 ± 2.39
2772.44
1.77 ± 0.11
1845.2
2021.4
61.88 ± 10.15
2488.8
2833.5
88.46 ± 7.62
38.12 ± 7.57
11.54 ± 1.03
1805.2 100.00 ± 13.81
9.52 ±
Ey(T)
1.11
4.27 ± 0.58
7.84 ± 0.44
1640.8
0.8
1818.5
0.8
1993.6
2405
3
22.9
108
Table 6-4 Transition comparison. (Continued)
EL
Ey
2862.6
1548.0
E7 (A)
I out of level
8.63 ± 0.85
1547.95
17.7 ± 0.49
1739.5
24.36 ± 1.40
1739.46
33.26 ± 0.74
1739.2
3
1932.2
1.43 ± 0.28
2518.2
65.58 ± 4.10
2518.42
49.04 ±
2518.5
0.21
634.1
0.3
I
out of level
2869.76
2880.9
2882.9
1.1
2254.44
100 ± 2
2525.43
0 ±
634.0
0.10 ± 0.03
747.4
0.37 ± 0.21
747.29
0.55 ± 0.04
869.1
0.50 ± 0.05
868.94
1.44 ± 0.05
965.6
3.58 ± 0.27
1188.37
1.96 ± 0.08
5.39 ± 0.14
1188.2
1.83 ± 0.14
1237.3
0.78 ± 0.07
Ey(T)
I
1275.2
3.86 ± 0.41
1275.04
1446.7
10.58 ± 0.62
1446.635
8.91 ± 0.9
1446.5
2.8
1562.5
3.23 ± 0.22
1562.45
4.49 ± 0.1
1562.3
1.1
1566.2
4.85 ± 0.36
1565.97
5.55 ± 0.01
1566.2
3
1757.5
1771.5
34.07 ± 1.85
16.23 ± 0.99
1757.42
1771.43
1757.4
1771.4
11.1
1950.1
0.61 ± 0.10
35.36 ±
0.8
18.03 ± 0.38
2265.1
3.68 ± 0.23
2265.33
2536.3
15.75 ± 0.96
2536.3
13.75 ± 0.38
1191.7
6.22 ± 0.77
998.37
5.18 ± 0.28
1954.0
5.74 ± 1.09
2128.7
12.03 ± 0.86
2882.5
76.01 ± 3.87
2895.4
2551.1
100.00 ± 8.94
2901.9
1792.5
1970.8
89.67 ± 6.29
1364.2
8.20 ± 0.66
2265
1.3
2536.3
4.9
1598.9
13
10.33 ± 1.66
2914.2
2158.8
4.59 ± 0.1
4.6
14.47 ± 0.87
2158.72
27.81 ± 0.76
1983A
2
2158.6
1.3
2298.8
2.87 ± 0.21
2569.9
71.76 ± 3.79
2569.85
63.95 ± 1.52
2570
2915.1
2.70 ± 0.16
2914.42
3.06 ± 0.15
2914.5
3
0.4
ri
Table 6-4 Transition comparison. (Contmued)
Ey
EL
l
out of level
ET (A)
I out of level
E'y(J)
I
2919.9
1486.3
2923.8
1004.2
6.09 ± 0.92
7.98 ± 0.74
1605.7
6.82 ± 1.11
1797.0
36.27 ± 2.15
1796.83
51.08 ± 3.08
1810.5
11.39 ± 1.17
1811.33
2575.1
37.53 ± 3.32
2575.82
15.38± 1.85
27.45± 1.17
2306.5
3.00 ± 0.53
2579.5
97.00 ± 9.70
1013.0
5.67 ± 0.47
1171.9
10.99 ± 0.59
2928.1
465.8
1235.5
8.91 ± 0.71
1235.57
17.37 ± 0.6
1284.5
15.44 ± 1.09
1284.42
30.42 ± 0.72
1457.25
1610.11
6.95 ± 0.53
22.18 ± 1.88
1818.56
22.18 ± 0.67
2172.45
11.83± 0.41
2583
11.26± 1.92
2584.89
77.82 ± 7.16
1070.3
3
1809.53
17.93 ± 0.56
1809.8
3
2317.61
2588.36
1.45 ± 0.14
80.62 ± 1.69
2588.3
6.4
1818.7
10.44 ± 0.81
1996.0
0.87 ± 0.17
2172.1
6.77 ± 0.45
2313.0
2583.9
0.30 ± 0.11
32.27 ± 2.43
2927.6
8.35 ± 0.43
2928.68
2932.6
2946.7
1809.5
15.00 ± 0.88
2177.0
5.24 ± 0.37
2317.5
2588.2
1.94 ± 0.18
77.82 ± 4.03
1836.0
0.13 ± 0.02
2015.3
2602.5
8.43 ± 0.68
88.45 ± 5.32
2949.3
3.00 ± 0.25
1236.4
2584.7
L
110
Table 6-4 Transition comparison. (Continued)
EL
E7
I
out of level
2964.1
E7 (A)
638.35
I out of level
Ey(T)
953
1048.7
4.79 ± 0.43
1155.48
6.25± 0.76
1414.3
6.07 ± 0.56
1414.4
1530.3
1.29 ± 0.15
1530.07
2.94 ± 0.25
1646.1
5.87 ± 0.51
1645.92
19.9 ± 0.49
1682.3
1.88 ± 0.19
1841.147
2033.89
15.54 ± 1.9
40.93 ± 0.95
3
1646
4
1840.6
5
11.2 ± 0.4
1841.0
9.20 ± 0.56
2033.9
2209.1
24.51 ± 1.38
2619.1
44.28 ± 2.28
2050.9
31.83 ± 2.44
2225.9
29.85 ± 2.08
2226.01
31.55 ± 2.1
2637.2
38.32 ± 3.09
2636.93
49.48 ± 1.16
2033.8 <+5.9
2.10 ± 0.17
2981.5
1047.9
1714.65
18.98 ±
1.86
21.14 ±
10.73 ± 1.46
2058.47
24.07 ± 2.11
2644.74
44.07 ± 2.76
830.0
0.74 ± 0.44
829.57
3.51 ± 0.92
1394.1
12.57 ± 1.45
1393.86
19.75 ± 0.52
1684.8
4.42 ± 0.87
1876.4
3.85 ± 0.38
1890.4
6.59 ± 0.84
2069.1
26.34 ± 1.55
2069
39.45 ± 0.82
2655.1
38.81 ± 3.30
23.72 ± 0.68
3001.2
6.68 ± 0.45
2655.29
2999.69
837.08
5.6 ± 0.29
1167
3.29 ± 0.69
1363.39
7.13 ± 0.43
1732.42
3.16 ± 0.28
837.4
1.39 ± 0.81
1090.9
5.34 ± 0.54
1199.4
2.40 ± 0.26
1690.2
7.04 ± 1.18
1897.1
6.60 ± 0.93
3
2619.7 -0.09
860.84
2989.02
3006.5
0.9
1048.1
2348.8
2999.8
I
3.24 ± 0.42
13.57 ± 0.22
2075.5
9.12 ± 1.31
2076.21
10.28 ± 0.4
2251.2
19.55 ± 1.41
2251.41
21.86 ± 0.49
2251.7
1.5
2662.3
48.56 ± 6.17
2662.55
46.64 ± 0.87
2663
3.5
3006.63
2.05 ± 0.07
111
Table 6-4 Transition comparison. (Continued)
EL
Ey
3009.4
1168.3
8.96 ± 2.80
1253.1
5.03 ± 0.49
1364.1
1.00 ± 1.14
3012.1
3025.3
3042.3
l
out of level
Ey (A)
I out of level
1253.48
11.61 ± 0.61
10.32 ± 0.44
1690.6
7.33 ± 0.92
1690.68
1694.5
4.40 ± 0.84
1694.6
1886.4
9.37 ± 0.74
1886.08
15.52 ±
1.01
2078.8
2665.0
20.16 ± 1.48
2078.63
17.58 ±
0.81
41.52 ± 8.97
2665.18
36.07 ± 0.94
3008.4
2.22 ± 0.15
681.6
<1.0
810.44
5.03 ± 0.58
3.96 ± 0.39
1096.6
10.06 ± 0.97
15.87 ± 1.93
1902.867
8.99 ± 0.78
2257.22
2668.0
75.14 ± 9.30
2668.13
1916.1
14.83 ± 1.94
2270.0
4.31 ± 0.60
2681.0
80.87 ± 8.97
8.91 ± 0.4
1000.41
1901.9
2256.6
Ey(T)
6.81 ±
1.3
7.65 ± 0.49
66.49 ± 1.3
1915.1
2680.5
1
3023
2
1126.9
5.55 ± 0.47
1437.1
11.03 ± 1.26
1436.67
1727.4
17.61 ± 2.24
1727.72
22.31 ± 0.5
1727.8
0.8
1933.2
8.77 ± 0.98
1932.94
10.99 ± 0.54
1932.6
0.6
2111.7
2697.8
3.52 ± 0.70
2697.99
53.9± 1.15
53.52 ± 4.11
1202.7
12.8 ± 0.37
1436
3066.5
1613.5
1732.3
15.31 ± 1.29
2702.8
64.76 ± 5.09
1307.8
0.80 ± 0.28
2311.5
2722.2
10.43 ± 0.82
19.92 ± 3.23
1944.8
3074.86
5.8 ±
2312
94.2 ± 2.71
1792.71
76.85 ± 5.76
1965.42
23.15 ± 1.34
88.77 ± 7.00
0.7
4
2697.9 <0.22
3042.1
3047.1
0.6
2
112
Table 6-4 Transition comparison. (Continued)
EL
Ey
I out of level
3080.3
1164.1
8.72 ± 1.49
1646.3
17.92 ± 1.49
1761.7
32.44 ± 2.98
1956.8
10.48 ± 1.03
2150.2
15.70 ± 1.25
14.73 ± 1.32
2324.4
Ey (A)
I out of level
1761.22
61.98 ± 3.48
2324.32
38.02 ± 2.02
3085.3
Ey(T)
155.1
1442
1802.6
3088.3
2740.8
54.59 ± 23.27
3085.7
45.41 ± 7.33
1965.5
2334.0
13.73 ± 1.28
2743.9
4.83 ± 0.58
76.64 ± 10.68
3088.5
4.79 ± 1.65
2168.6
2754.5
22.96 ± 1.61
3098.9
77.04 ± 9.37
3106.6
2350.0
30.39 ± 2.90
3107.1
69.61 ± 4.09
3110.9
3112.5
3122.6
3132.4
2181.7
23.34 ± 2.73
2497.0
2768.3
28.29 ± 4.51
48.37 ± 6.02
2367.5
14.86 ± 1.86
2778.2
85.14 ± 10.82
2201.8
32.26 ± 3.12
2787.9
67.74 ± 9.26
2
1.6
2741
2
3084.5
1
2335
100 ± 5.63
500.23
2168.44
2754.7
33.17 ± 8.09
2169
62.7 ± 1.21
2754.7
2
805.84
36 ± 1.56
1131
3
2761.2
3106.5
1
2350.3
4.13 ± 0.65
25.56 ±
1.56
2761.15
19.33 ± 0.78
3105.45
19.11 ± 0.78
2495.53
100 ± 2.17
583
23.84 ± 2.12
1171.19
31.26± 5.63
20.88± 1.01
2182.1
2768.27
3112.27
1.5
21.88 ± 0.53
2.14 ± 0.14
1
113
Table 6-4 Transition comparison. (Continued)
EL
Ey
3134.6
2378.7
36.99 ± 13.28
3134.9
63.01 ± 6.15
l
out of level
3139.8
Ey (A)
874.85
1198.97
1331.2
2.18 ± 0.26
2092.7
4.67 ± 0.53
2208.5
9.34 ± 0.84
2382.4
11.20 ± 1.18
2525.1
15.02 ± 2.36
2795.5
3140.6
45.72 ± 5.87
11.87 ± 0.66
3143.8
3153.2
3182.5
1.33
2209.71
22.24 ±
2795.92
46.08 ± 1.02
3140.2
12.76 ± 0.31
1022.73
2020.67
21.18 ± 1.37
26.74 ± 2.41
2388.72
40.04 ± 1.26
59.34 ± 12.48
2799.81
18.76 ± 0.74
27.36 ± 3.68
5.36 ± 0.68
10.37 ± 1.01
1870.55
2043.8
2223.4
2397.2
20.27 ± 2.41
2043.787
2808.8
43.26 ± 5.23
2795.7
3140.3
1.7
68.97 ±
2051.5
2815.5
12
3159.5
2
2821.3
3164.5
2
9.2
5.05 ± 0.71
15.70 ± 1.38
2233.4
15.42 ± 2.47
2820.6
84.58 ± 10.58
2059.2
2.2
20.02 ± 1.16
2388.8
2799.2
1870.9
1825.2
1.28
13.92 ± 1.69
1347.1
Ey(T)
2.97 ± 0.89
15.95 ±
2213.2
3159.6
3164.8
I out of level
11.74 ± 1.15
2251.6
13.67 ± 2.33
2426.9
22.02 ± 2.12
2838.2
52.57 ± 6.82
2808.61
3.68 ± 0
2
114
Table 6-4 Transition comparison. (Continued)
EL
Ey
3189.7
1875.1
42.95 ± 6.64
2259.6
30.13 ± 4.40
2844.6
26.92 ± 4.65
1
out of level
Ey (A)
I
lout of level
3191.3
3205.8
E7(T
2844.5
2
3189.5
1
2068.8
2
2260.1
2
2575.8
3
1290.4
2
3
1365.8
1772.1
13.19 ± 10.53
1886
1891.3
2275.4
8.85 ± 1.33
2449.9
6.00 ± 0.73
2861.1
47.31 ± 3.22
3206.2
24.64 ± 1.36
3212.9
3226.3
1521.2
13.63 ± 1.51
1894.3
14.10 ± 1.11
1896.9
9.49 ± 1.59
2102.8
11.53 ± 1.51
2281.3
10.98 ± 1.44
2596.9
12.41 ± 1.94
2869.3
27.85 ± 1.97
2471.9
2882.0
9.66 ± 1.40
90.34 ± 7.69
3233.0
1918.0
2108.4
2479.0
2888.8
2
4
28.44 ± 3.67
2860.8
3205.5
887.32
56.1 ± 2.07
1045.31
12.31 ± 1.63
1521.57
31.59± 3.27
788.88
39.53 ± 1.57
1626.39
19.81 ± 1.67
1917.55
47.59 ± 1.2
2004.93
10.09 ± 0.83
2887.52
22.5 ± 0.74
13.92 ± 1.70
18.11 ± 2.73
39.54 ± 4.54
1.3
2
115
Table 6-4 Transition comparison. (Continued)
EL
Ey
I
out of level
3236.5
3250.9
3265.5
3269.9
3285.2
3305.3
3309.7
Ey (A)
I out of level
911.73
17.02 ± 0.96
1544.3
6.08 ± 0.74
2128.2
10.42 ± 1.34
2306.0
19.19 ± 2.39
2306.15
36.82 ± 1.13
2482.2
5.00 ± 1.08
2481.75
6.63 ± 0.96
2892.7
28.23 ± 2.54
3235.3
31.06 ± 3.38
2127.3
9.09 ± 1.09
2320.1
4.64 ± 0.96
2495.4
2906.7
54.62 ± 3.80
Ey(T)
2127.8
2
2906.4
0.9
3250.7
4
1970.5
2
2940.5
1.4
31.65 ± 3.33
1951.5
27.63 ± 4.50
2140.3
20.24 ± 2.42
2335.0
18.66 ± 2.85
2921.6
33.47 ± 3.59
2655.0
42.47 ± 3.39
3269.6
57.53 ± 4.44
1344.0
5.96 ± 0.54
1528.9
2.24 ± 0.35
1970.4
2161.7
13.72 ± 1.44
1970.49
32.11 ± 0.86
10.62 ± 0.78
2162.05
21.01 ± 0.45
2176.0
5.23 ± 0.70
2940.15
46.88 ± 0.99
2354.3
7.16 ± 0.92
2940.9
55.07 ± 3.62
2181.9
30.90 ± 2.65
2961.0
69.10 ± 8.87
1021.6
54.38 ± 3.07
2554.9
19.72 ± 2.20
2965.7
25.91 ± 5.02
1343
±
3283
4
2693.5
3
2966
3309.8
3314.7
I
2190.9
65.98 ± 5.88
2971.2
34.02 ± 7.27
5
116
Table 6-4 Transition comparison. (Continued)
EL
Ey
3325.2
2012.2
13.24 ± 4.24
2570.8
3.24 ± 0.39
l
out of level
Ey (A)
I out of level
2710.7
7.55 ± 0.59
2980.5
51.58 ± 9.17
2980
2
3324.9
24.38 ± 1.41
3323.8
1
2398.4
4
2983.5
2
3328
7
2019
2
2994.5
2
3337
4
3329.0
3329.0 100.00 ± 7.94
3335.3
1642.4
23.84 ± 2.96
1785.2
23.98 ± 3.04
2211.7
25.43 ± 3.31
2405.0
26.75 ± 4.48
1424.6
5.60 ± 1.00
2021.9
2217.4
3340.8
3350.9
3359.3
3367.3
1075.87
26.3 ± 3.22
1424.76
10.31 ± 0.97
26.95 ± 1.86
2217.4
40.2 ± 1.02
2585.2
2995.2
15.97 ± 1.26
46.75 ± 4.30
2996.26
23.19 ± 0.54
3338.4
2.14 ± 0.15
2.58 ± 0.40
2420.1
100.00 ± 20.63
2044.2
2236.2
28.63 ± 5.45
13.46 ± 1.90
2428.5
15.50 ± 2.73
3015.3
42.41 ± 4.23
2436.3
16.29 ± 2.91
3023.1
83.71 ± 15.77
3381.2
3381.2 100.00 ± 7.02
3386.4
2262.4
2629.7
3042.5
3393.27
Ey(T)
2043.625
13.79 ± 3.45
2042.9
2
2428
2
2602.85
86.21 ± 2.59
2602.8
3
2075.4
1.2
2078.7
4
20.24 ± 2.11
12.30 ± 1.17
67.46 ± 6.01
2637.3
2
2778.1
0.5
117
Table 6-4 Transition comparison. (Continued)
EL
E1
3400.9
1484.5
L out of Ieve
1645.2
4.44 ± 0.60
13.39 ± 1.56
1758.2
11.71 ± 1.27
2276.7
14.89 ± 1.45
2644.5
16.24 ± 1.33
3056.6
39.33 ± 3.74
3413.1
Ey (A)
I out of level
E1(T)
2093.3
2480
2655
3068.7
81.05 ± 9.39
3068.5
1
3413.4
18.95 ± 1.47
3411.5
4
3433.2
3439.2
3450.0
2324
3089
2684.1
15.90 ± 2.62
3094.8
84.10 ± 4.98
2327.2
31.93 ± 5.90
2694.3
68.07 ± 7.56
3478.9
3484.1
3499.6
2360.3
31.06 ± 3.07
2728.9
14.19 ± 1.66
3139.9
54.75 ± 10.68
1807.1
11.19 ± 1.23
2184.8
28.60 ± 3.80
2376.3
37.69 ± 3.58
2744.1
22.53 ± 2.28
2572.2
3158.3
14.09 ± 1.19
3508.9
2751.7
3164.7
4.29 ± 0.46
95.71 ± 16.19
3518.8
3174.5 100.00 ± 17.03
3502.6
2
0.9
85.91 ± 16.46
3134.5
7
3479
6
118
Table 6-4 Transition comparison. (Continued)
EL
Ey
3534.9
2220.9
2411.9
13.85 ± 2.23
2426.0
14.57 ± 2.77
2603.8
2779.8
12.22 ± 1.63
3190.0
37.45 ± 7.47
3535.9
1.48 ± 0.17
2608.0
3194.9
43.26 ± 10.58
2440.9
31.28 ± 6.84
2619.3
2796.7
17.85 ± 3.00
2635.9
5.52 ± 1.04
3539.0
3551.2
3567.8
3572.9
I
out of level
I out of level
Ey(T)
17.23 ± 1.75
3.20 ± 0.45
56.74 ± 25.90
50.87 ± 4.11
2811.9
5.83 ± 0.64
3223.6
88.65 ± 16.43
2462.7
19.68 ± 3.94
80.32 ± 15.82
3228.8
Ey (A)
3574.6
3229.5
3574.6 100.00 ± 12.49
3589.4
3245.1
100.00 ± 27.83
3596.1
3251.8
100.00 ± 22.88
3620.9
3276.6
100.00 ± 20.01
3628.1
3283.9 100.00 ± 20.34
3655.7
3311.5 100.00 ± 39.03
3703.4
2772.5 100.00 ± 21.92
3709.4
3365.1
100.00 ± 23.05
3572.5
2
119
6.3.3
Upper limits on unseen transitions
The following 53 transitions were published in Adam's paper35, but not seen in
this work, or were placed elsewhere in the level scheme. Upper limits were calculated
using the intensity of the smallest observable nearby peak in the gate of interest. In
cases where the peak density was too high to defmitely eliminate a particular peak, the
uncertainty in the surrounding peak areas was used as an upper limit.
Table 6-5 Upper limits on transitions seen in Adam et
is the initial level assigned by Adam et al.
Ey (keV)
L
Ey (keV)
UL
al.
but not seen in this work.
L
UL
603.2
930.6
0.15
1714.7
1274.3
0.13
1047.9
2989.0
2989.0
0.13
658.8
855.3
1470.6
0.09
1732.4
3006.7
0.13
0.1
687.6
1915.2
0.05
1096.6
3012.1
0.09
1776.3
2121.0
0.09
1000.4
3012.1
0.02
947.1
2264.8
0.11
810.4
3012.1
0.01
1040.6
2267.7
0.04
1944.8
0.03
2103.5
2447.8
0.07
1965.4
3067.4
3074.9
880.3
2523.8
0.04
1792.7
3074.9
0.02
684.1
2523.8
0.15
500.2
3099.0
0.01
1983.4
0.05
805.8
0.21
1171.2
3105.5
3112.5
0.04
2744.1
2598.7
2744.0
1215.2
2749.2
0.1
583
3112.5
0.01
1016.6
2772.4
2772.4
0.12
874.9
0.05
1199.0
3140.2
3140.2
0.01
2772.4
2525.4
2869.8
0.4
2020.7
3144.0
0.01
2254.4
2869.8
0.05
1022.7
3144.0
0.01
1258.5
2729.2
0.02
887.3
0.01
998.4
2914.2
0.1
1045.3
1004.2
2920.1
0.04
2004.9
3214.2
3214.2
3232.0
1457.3
2927.8
0.04
1626.4
3232.0
0.04
1610.1
2928.7
0.1
911.7
3236.9
0.01
638.4
2964.33
0.01
788.9
3236.9
0.07
1155.5
2964.33
0.1
2217.4
3340.6
0.6
860.8
2981.4
0.01
1075.9
3340.6
0.01
2644.7
2989.0
0.1
2602.9
3358.3
0.03
0.07
0.1
0.02
0.02
0.03
L1
120
Angular correlation
6.4
6.4.1
Determination of correlation coefficients
The original data files were resorted to create a separate matrix of coincidence
data for each of the five angles: 42°, 71°, 109°, 138°, and 180°. The product of the
two relative efficiencies for each detector that recorded a 7ray in a coincidence event
was used to adjust each event to represent the true number of events. The matrices
were sliced at a particular energy in the same manner as the combined coincidence
files to produce five separate coincidence projection spectra. The peak of interest was
fit in the spectrum corresponding to each of the five angles.
For a given transition, the procedure was performed twice. For example, the
586 keV peak was fit in each angle spectra gated by the 344 keV transition, and then
the 344 peak was fit in each 586 keV gated angle spectrum. An average weighted by
uncertainty was used to produce the fmal accepted values. Since the process is
actually two fits of the same data, and not two unique experiments, the uncertainties
were averaged. In a small number of cases, the correlation from above or below only
was used due to the potential for doublets in a particular gate.
The uncertainty in the number of counts used for each angle is shown in 6-7. The
value
°Rad
is the uncertainty calculated by the Radware program and
aeff
is a random
efficiency uncertainty, estimated as 1.3% of the peak area.
6-7
Since the angular distribution function includes only even terms in
cos2
9 and
121
cos4
9, supplementary angles are redundant. The counts from supplementary angles
were averaged, e.g. the average of counts in a peak for the angles 42° and 138° was
used; also with the angles 71° and 109°.
6.4.2
Matrix solution of distribution coefficients
Values of N A22, and A were calculated by solving a matrix of simultaneous
equations. Each of the three average count values from each unique angle is to be fit
to the following equation
x=A0+A22+AP.
6-8
6-8 can be related to 2-39 by setting A0 = N and noting that A
Two matrices are created with the elements:
C =
WiPr(9i)P2(Oi), and
6-9
S2=wx1f(O1).
The x are the number of counts at the angle O. The
w1 = ---,
6-10
w1
are the weight parameters
where o is the uncertainty in a measurement x,. Last, the P2 are the
cr1
ordinary Legendre polynomials, evaluated at each of the three unique angles. Since
only even terms are used in the angular correlation function, the values of % and yare
0, 2 and 4, which correspond respectively to row or colunm 1, 2, and 3 in the matrix C.
The Akk are calculated from C inverse times S,
122
A=CSr.
6-11
7
The uncertainty in each value A
A
is
=.
6-12
A0
This method gave similar results as an algebraic solution for a few simple tests.
A sample result is seen in Figure 6-8, using the data from the 586 keV - 344 keV
correlation. A summary of the angular correlation results is presented in Table 6-6.
3E+05
586 keV -344 keY Correlation
1
\
2.E1-05
\
\
2.B-05
/
Theoretical
rxdata
-
x
.
1.EO5
0
30
60
90
Theta (degrees)
Figure 6-8 Sample angular distribution fit.
120
150
180
123
Table 6-6 Angular correlation results. In some cases there is more than one
acceptable solution. Where a measurement was made for the same yray in more than
one cascade, the result is listed separately, and then as a weighted average.
Ey-ET
Spin seq.
117 - 586
0+ -*
2+
170-1348
2+-*
2+-*
3+
175 - 411
195 - 778
2+ -+
3-
195 - 367
1----+
32-
271 -344
2+-*
2+-+
0+-*
315 - 271
2+ -+
325 - 1109
325 - 765
3+-+
3+-*
336 - 990
2+ -'
336 - 1261
2+ -*
336 - 990
2+-*
336 - avg
2+ -*
336 - avg
2+ -+
352 - 586
4+-*
2+-*
219 - 1299
249-1348
4+
368 - 586
3--*
388 - 586
411 - 344
2+-*
4+-*
428 - 1089
2+ -.+
441 -1109
4+-+
3+
2+
0+
2+
2+
2+
2+
2+
2+
2+
2+
4+
4+
2+
2+
3+
2+
457 - 1314
2+ -+
1-
472 - 411
6+-*
2+-*
2+-+
2+-*
2+-*
4+
354 - 411
482 - 778
491 - 1411
494 - 271
496 - 1109
504 - 930
504
3i----*
586
3+ -*
504 - avg.
3+ -*
31-
0+
2+
2+
2+
2+
520 - 778
2---+
3-
527 -411
4+-+
534 - 765
2---+
534 - 1109
2---'
4+
2+
2+
2+
558 - 703
2+-+
2+-*
3+-+
4+-*
558 - 271
2+--+
563 - 411
2+-*
544 - 974
547 - 1314
558 - 527
1-
4+
0+
0+
4+
-+2+
-+2+
-+2+
-+2+
-+4+
-+2+
-+2+
-+0+
-+2+
-+0+
-*2+
-+0+
-+2+
-+0+
A2
A4
-0.460 61
0.275 55
0.07171
-0.125 74
1.08 18
1.5631
0.159 24
0.077 25
0.18276
0.0811
0.84 12
0.91 11
0.16138
0.33415
0.006 40
0.004 21
-0.01921
-0.03 10
-0.27499
-0.061 75
-0.014 89
-0.324 86
-1.581 +1.0-3.4
-0.265 88
0.184 85
-0.112 99
0.06 10
0.136 36
0.110 +26-20
0.114 61
1.06020
0.7480
0.630 +43-22
4.421 7
6.344 8
0.684 496
-+2+
-+2+
-*0+
-+2+
-*0+
-*2+
-+0+
-+0+
-+2+
-*2+
-+2+
-+0+
-+0+
-*0+
-+2+
-0.07428
0.18074
-0.11222
0.02927
0.13075
0.041 21
0.060 19
-0.284 25
0.061 24
-1.418 12
0.11015
0.00716
-0.100 80
0.399 81
0.10193
-0.060 95
0.048
0.062 91
0.01 14
-0.11 14
0.15060
0.01859
0.08031
0.06264
0.14660
0.13831
0.29945
0.005
-0.18 ii
-0.13 11
0.108 63
-0.180 64
-0.092 83
0.107 +3.59-2.03
-1.342 +1.093-.
-9.736 +3.6-11.6
-0.05023
0.074 79
-0.040 51
-+2+
-*2+
-*2+
-*0+
-+0+
-+0+
-*0+
-*2+
-+4+
-*2+
0.18545
0.114 29
-0.00948
0.11330
0.114 +3.3-2.1
-1.51922
0.17686
0.24270
-0.09787
0.212 39
0.005 40
0.048 41
0.04895
-0.05786
0.01550
0.10 10
-0.050 ii
-0.051 85
-0.291 10
-0.00571
-0.08349
0.13 10
0.08 10
0.20547
0.07853
-0.12628
0.00974
124
Table 6-6 Angular correlation results. (Continued)
Ey-Ey
578 - 1089
587 - 344
623 - 974
623 - 1318
Spin seq.
2,3+-*
2+-p
2+-*
2+-*
641 - 1261
2+ -*
2+ -*
641 -990
2+-
641 - avg.
649 - 778
2+ -*
659 -527
2+-
675
930
2+ -+
675 - 344
675 -586
2+ 2+-+
675
2+ -*
623
avg.
avg.
2+ -p
679 - 411
679 344
3+-
679 - avg.
684 - 778
3+ (4-)_*
694 -974
2,3+-
3+ -+
700 - 271
703 - 271
704 - 344
709 - 1348
1- --*
2+ --*
709- 2nd
2+-p
713
0+-*
2+-*
586
2---+
713 -930
2+-f
715 - 411
731 - 1109
739 - 344
739 - 778
751 - 586
765 - 344
779 - 344
5(-)_*
788
1314
793 -778
3+-.-4
3+
2+
2+
2+
2+
2+
2+
2+
34+
2+
2+
2+
2+
4
4+
4+
32+
0+
0+
2+
3+
3+
2+
2+
4+
2+-
2+
332+
2+
3----+
2+
----
1-
2+-*
2+-*
0+ --*
3+-*
0+-*
34+
4+
795 - 344
795 - 411
813 - 344
813 - 1089
814 - 703
818 - 778
2-
2+-
3+
0+
3-
819-1314
2+-*
1-
4+-
A2
-+2+
-*0+
-*2+
-*0+
-*2+
0.34 ii
0.005 99
-+0+
0.57480
0.22890
-+2+
-0.032 41
-+2+
0.160 40
-0.22 12
-0.350 45
0.063 21
-*2+
0.23322
-*0+
-3+
0.022 19
0.05946
-2.91817
0.52721
0.47870
0.523 45
-0.649 52
-0.891 26
-0.843 39
0.047 54
-0.0313
0.349 41
0.070 22
0.091 23
2.450 48
2.358 +2.3-0.9
1.911 53
2.203 182
-*2+
0.00427
-0.16927
-0.05023
-+2+
0.054 29
-0.043 30
-0.194 29
-0.106 26
-+2+
-+0+
0.28389
0.07694
-0.0411
0.79938
--*0+
-+2+
-*0+
-+2+
-p2+
-+2+
-*0+
-p2+
--*0+
-+4+
-*2+
-42+
-*0+
-*0+
-*0+
-+2+
-+2+
-0+
2+ -* (3+-2+) -*0+
2+-p
A4
0.2811
0.27521
0.0010
0.18314
-0.17220
-0.09547
-42+
-+2+
-*2+
-*0+
0.31 10
0.054 99
0.017 22
0.248 19
0.24573
-0.018 97
-0.018 22
0.75622
0.00872
-2.699 184
0.302 161
1.684 562
0.04638
0.08448
-0.16938
0.16992
-0.05773
0.19779
-0.17240
0.12327
-0.03970
-0.05980
-0.05741
-0.00627
0.02 29
-0.214 16
-0.062 15
0.179 85
0.07 48
0.285 15
-0.005 15
-0.150 89
0.07795
-0.15738
-0.12530
0.04439
0.00975
0.12352
-0.37086
0.19337
0.15329
0.03439
0.16936
-0.01275
0.01857
0.044 84
0.144 86
0.178 3-4
-0.01 10
0.183 108
0.00076
1.581 414
0.00635
4.02440
0.007 14
-0.02827
6.452 +15.2 -3.2
78.254 +oo41.3
-0.24310
-0.99813
0.02077
-0.089 99
125
Table 6-6 Angular correlation results. (Continued)
Ey-Ey
832
1109
841
586
850 411
855
1314
866 - 1089
894
903
703
1109
909 - 586
Spin seq.
2+
2+ --+
2+2+-*
2+
4+
-*2+
-*2+
2---*
1-
-+0+
2- -+
3+
0+
2+
2+
22+
-*2+
1-
4+
4+
2+
13+
3+
3+
2+
2+
4+
2+ -*
2,3+-*
3+ -*
915-1299
2+-
929
2+-+
2+ -*
974
932 - 1314
937 - 411
937
344
940 - 974
952 - 1314
3+-.
0+-p
-- -*
2(+/-)--+
344
2+-*
966 - 411
2+ -*
2+-+
966
966
970
1160
344
974 - 344
980 - 794
985
1314
990 -271
1011 - 586
1011 -344
1011
930
1011 -avg.
1016 -411
1037-1348
1052
411
1070 - 778
1084
1084
1086
1087
1090
1093
1107
1107
1109
411
1299
1314
344
1109
411
344
0+
1--2+ 3(+) 2---+
1-
2+-p
0+
2+
2+
2+
2+
4+
3+
4+
32+
4+
2-
2+2+-+
2+-+
2+-p
2+-+
2+--*
(4-)-_*
-- -+
----p
3+2+-*
2+-*
3+ -+
2+2+-+
5+-+
0.25266
A4
-0.068 si
0.06869
0.0210
-0.09377
-*2+
-*2+
0.22 10
-0.051 76
-0.052 74
0.002 21
0.23441
0.287 45
0.148 55
--+2+
0.66233
0.07939
-*0+
0.005 51
-+2+
-+2+
-0.14732
2.02683
-+2+
-+0+
-0.076 68
0.000 21
-0.235 72
1.736 +1.69-075
0.115 169
0.02342
-0.116 48
0.049M
-5.842 +1.97 -4.77
0.016 74
-0.664 166
0.098 44
-+0+
-p4+
-+0+
-0.067 62
-0.025 45
0.04831
-0.01381
-0.06 10
-0.3211
0.071 79
0.006 61
-*0+
-*0+
0.05575
-0.22827
0.05773
0.02525
-0.01518
--+0+
-0.082 16
0.094 90
0.327 86
-0.004 19
0.059 16
-0.087 96
0.453 25
-0.050 164
-0.16580
-0.23980
-0.11026
-0.01828
0.28258
-0.00425
0.02727
0.1666.4
0.104 45
0.204 56
0.16 12
0.06 12
0.185 68
0.058 so
-0.001 53
0.25 12
0.13 12
-0.25964
-0.00361
0.12944
0.04699
-0.083 22
-0.0613
0.08426
-0+
-+4+
-+0
-+2+
-*2+
-+2+
-+tj+
-+2+
-+2+
-*2+
--*2+
-p0+
-+2+
-*2+
1-
-+0+
2+
2+
4+
4+
32+
-*0+
-+0+
-+2+
-42+
-+2+
-+0+
1124-778
2+-i
1131 -344
0+-*
1138 - 344
2+ -+ (2+ - 2+) 0+
1138-1109
2+-p
2+
A2
0.440 50
-*0+
-0.029 96
0.54 10
-0.11680
0.22841
-0.0511
-0.168 23
-0.4512
0.19524
0.19932
0.119 65
0.333 68
-0.097 25
0.350 23
-0.02028
-0.11876
-0.02776
-0.078 63
0.797 +5.82 -0.87
-0.011 19
-0.121 62
0.091 34
0.022 68
0.12832
0.36444
0.03662
0.18246
0.034 75
-0.051 181
0.151 62
-0.222 105
0.16663
19.289 +10.31 -4.63
1.001 288
0.023 97
0.81763
-0.079 26
0.027 26
-0.166 34
126
Table 6-6 Angular correlation results. (Continued)
Ey-ET
1142 - 778
1149 - 1109
1160 - 411
Spin seq.
2(+I-)--+
3-
----*
2---'
- 586
2+--+
2+
- 778
- 344
2,3+ -*
3-
--+2+
0.193 83
0.021 85
4+-*
2+
-*0+
0.01272
-0.101 77
1-
--+0+
0.022 36
0.063 36
-0.010 43
-*2+
-*0+
-0.079 41
0.035 41
-0.050 164
2-*
2+-*
0.21752
-0.08553
-+0+
-+2+
0.24828
-0.00531
1-,2-3- -.
4+
4+
2+
3-
0.074 60
-0.026 59
2+-*
2-
-2+
0.115 56
-0.016 62
2---*
2+
-p0+
0.236 16
2+ --+
2+ --+
2+ --+
3-
-*2+
-p2+
0.248
61
-0.021 66
-0.032 45
0.038 39
0.321 56
-0+
0.071 38
0.072 39
0.206 44
-*0+
0.017 19
-0.027 19
-+0+
0.08894
-0.32 10
-*0+
-p0+
-*0+
-+2+
0.31635
1.15840
1160 - avg.
3+-*
1186 -344
1186 -411
2+--*
1191 - 1109
- 1314
- 351
1247 - 527
-344
1264 - 778
1285-1299
1299 - 344
1314
1316
1316
1316
1319
1327
1337
1348
A4
0.01 10
-+2+
-+2+
-+0+
-+2+
3i---+
1261
0.03795
-0.47978
-0.07729
-0.05438
2+
4+
4+
4+
4+
4+
2+
3+-*
1160 -344
1203
1204
1205
1209
1247
A2
-*2+
-*0+
- 778
- 586
- 930
- avg.
- 271
- 1314
- 344
- 344
2+-*
2+ 3(4.) -+
2+-*
2+-*
2,3--*
0+-*
3+ --+
1360 -371
1366 - 344
2+-*
1366 - 411
1369 - 586
1372-778
4+-*
-- --+
2---*
2+
2+
2+
0+
12+
2+
0+
4+
4+
2+
-+2+
-+2+
-0.021 43
0.18632
0.040
0.194 25
0.048 27
0.25829
0.051 31
-0.29 10
0.34 10
0.01318
-0.04735
-1.713 687
0.019 102
-0.021 27
0.011 20
0.246 125
0.25050
-,2+
-*2+
1401 -778
1401 -974
2+--*
3-
2+--*
2+
1406 - 778
1411 - 974
3(+)-*
3-
-2+
2+-*
1413 -344
1---+
2+
2+
-,
3-
3-
-0.08525
-0.06834
-+2+
-+2+
-+2+
1-,2--*
-0.04269
0.02230
-0.03937
-p2+
-0.063 20
0.021 20
-0.141 69
-0.09767
-0.188
0.054 52
-0.15852
-0.11042
0.05052
-0.03942
0.199 61
0.101 70
0.172 42
0.140 45
-0.20078
0.06976
-0.082 39
-0.011
0.025 20
2.472 +4.1 -1.1
1.285 +1.02-0.34
0.11057
0.210 75
36
-0.00640
-0.0148
-0.06536
-+0+
-p2+
0.39035
0.08587
-0.027 67
-0.073 69
-0.258 84
-p0+
0.41976
0.07891
-0.360 155
-+0+
-+0+
0.02674
-0.00571
0.214 74
-0.033 81
1447 -344
-+2+
2+-+(3)-2+-0+
0.24562
-0.01732
0.011 33
1447 - 1089
2+ -+
3+
-+2+
-0.008 37
-0.013 37
1481 - 778
2(-)-*
3-
-p2+
0.07357
-0.01758
1421 - 778
1427 -344
1431 -974
1442 - 1109
1446 - 411
(2+)
2+-*
3-i---+
2+
2+
--*
2+
2+-p
4+
-0.172 43
0.08259
-0.117 122
-0.096 121
127
Table 6-6 Angular correlation results. (Continued)
Ey-Ey
1489
1109
1492 -344
1492
411
1495 - 344
1503 - 411
1519
1532
3+ --+
-- -*
778
2,3----
411
---+
1536 - 411
1563 - 974
1566 - 1314
1575
1582
Spin seq.
2+
2+-* 4+
2+-+ 4+
(2+)-
411
1109
----+
2+-+
2+-+
3,4,5-9
2+
4+
34+
4+
2+
1-
2,3+ --+
4+
2+
32+
32+
2+
30+
2+
1727-1314
(2+)-+
1-
1739 - 778
1757 - 344
2,3---+
3-
1757 -778
1757 -367
2+2+-
1757 - avg.
2+--+
2+ -+
1+,2+ -*
1586 - 778
2+-+
1593
586
2+ -+
1596 - 778
1597 - 344
2+-
1606 - 778
1631 -271
2+-+
3(+)-+
2+-+
2+-+
1667
1599
1771
586
344
1109
1779 -586
1785 - 411
1789 - 344
1792 - 1109
1799 - 586
1802 - 344
2+-+
3+-+
2+ -+
----+
2+ -+
---+
1903 -344
344
----+
1921 - 344
1956 - 344
2(+I-)-+
1970-1314
1983 -344
1994 -344
1-,2-+
2,3+-+
1825
344
1857 - 344
1913
--+2+
-2+
--+0+
--+2+
-p2+
-+2+
-+2+
-+2+
-+0+
--+2+
--+0+
-+2+
-+2+
-+2+
-+0+
-+2+
-+2+
-+2+
-+0+
-+0+
-+2+
2--
---+
3332+
2+
4+
2+
2+
2+
4+
4+
32+
2+
2+
2+
2+
2+
1-
2+
4+
A2
0.17278
0.158 83
0.24 10
0.089 47
0.387 79
0.126
0.40 10
0.18 12
0.20 10
0.06272
-0.196 59
0.277 86
0.147 18
0.152 68
0.10329
0.30561
0.09738
0.14832
0.001 34
0.230 24
-0.072 74
A4
-0.083
0.012 84
0.04 10
-0.022 48
-0.078
-0.021 35
0.00 10
-0.3711
-0.06 10
-0.061 69
-0.196 59
0.025 88
-0.059
-0.018 68
-0.04030
0.08259
0.00837
0.02933
-0.04338
0.255 69
0.05773
0.04425
0.665 173
-0.05037
-0.15772
0.07843
-0.024 25
0.014 72
0.07539
-0.04239
-0.011 21
-+2+
-+4+
-0.150 22
0.12221
0.12221
-+0+
-+2+
-+2+
0.288 36
-0.019 38
-0.01 14
-0.040 42
-0.24892
0.37372
0.08277
-0.874 299
-0.248 47
2+ -(3- - 2+)- 0+
2+-+
2+-+
2--+
2+-p
2+-+
1802 -411
1810 -778
-O+
--+0+
-p0+
-p2+
-+2+
-+2+
-+2+
-+0+
-+0+
-+0+
-+0+
-0+
-+0+
-+0+
-+0+
-+2+
0.363 24
0.335 86
-0.365 97
0.137 82
0.253 58
-0.011 52
0.23637
-0.52731
0.211 18
-0.211 81
0.36025
0.21331
0.0116
0.23850
-0.19562
-0.00422
-0.00422
0.076 27
0.081 87
0.10 14
0.089 68
0.233 62
-0.023 17
0.011 28
0.00009
-0.01345
-0.148 ii
-0.662 457
-0.02650
0.041 40
-0.07828
0.23021
0.22389
-0.01429
-0.00433
-0.18 17
-0.021 53
-0.11766
0.01346
0.99055
-2.664 203
-0.14736
0.05233
128
Table 6-6 Angular correlation results. (Continued)
Ey-Ey
1994 -411
2034
2043
2069
586
344
586
2079 -586
2093 -344
2094 - 271
2114
2151
2159
2159
271
344
344
411
2169 -344
2180
2185
344
344
2196 -344
2217 - 778
2251 - 411
Spin seq.
4+
3(+) -* 2+
1-,2-3- -* 2+
2+-* 2+
(2+)- 2+
2+-p 2+
0+
2+-* 0+
1-,2 -* 2+
-- - 4+
2+-* 4+
2+,3+- 2+
2+- 2+
3-*
2-*
3(+)_*
3+--*
(2+)--*
(3-)--
2255 -344
(2)-*
2260
344
2(-)--*
2265 -271
2342 - 344
2+-
344
344
1,2+2+ 2+-*
2384 - 344
2+ --*
2405
344
3+ -*
2518 - 344
2,3--*
2365
2375
2536
344
2i----+
2570 -344
2i---+
2+ -p
2584
2588
2602
344
344
344
2619 - 344
2655 -344
2681
344
2698 - 344
2703
344
2722 -344
2744 -344
2+-*
-- -+
3(+)-+
2+-+
2+,3,4+-+
(2+) -+
1-f,2,3--+
2,3-+
(2+)-*
344
344
2+,3+ -*
2861 -344
2i--+
2+,3--*
2755
2795
2889 - 344
2+-
2+
2+
34+
2+
2+
0+
2+
2+
2+
2+
2+
2+
2+
2+
2+
2+
2+
2+
2+
2+
2+
2
2+
2+
2+
2+
2+
2+
--*2+
-*0+
--*0+
-p2+
-*2+
-*0+
-p2+
-p2+
A2
-0.134 43
0.088 47
0.080 64
-0.021 56
0.01591
0.12515
-0.06445
0.0536
A4
-0.01441
-0.059 48
0.107 62
-0.06554
-0.031 90
-0.03216
0.02245
0.0619
-*0+
0.164 43
0.012 39
-p2+
-0.17663
--*2+
-0.071 47
-+2+
-+0+
-*2+
-0.11494
-0.10535
-0.05045
-0.49690
-0.07663
-0.01664
-0.03645
-0.13576
0.22035
-+2+
-0.251 51
-0.011 52
-*0+
-*0+
0.11528
0.07928
0.27 10
-0.02 1-i
-+2+
-*0+
0.01855
0.283 3I
0.01757
-0.14236
-+0+
0.239 21
0.018 23
-0.04221
-*0+
--*0+
-+
0.15320
0.018
-0.17863
0.200 41
-0.060 23
-0.074 w
-+0+
0.31237
0.47027
-0.05529
-0.09540
0.06631
0.06329
0.208 i
-+0+
-+0+
-+0+
-+0+
-*0+
-+0+
-*0+
-*0+
-+0+
0.044 56
0.29423
0.578 +5.4 -2.4
0.00727
-1.355 192
-0.002 25
0.15821
0.102 37
0.003 24
0.276 52
0.031 25
-0.017 45
0.27225
0.51460
-0.16873
-0.01927
0.30969
0.05872
0.209 54
-0.026 59
0.20954
-0.12951
-0.02659
0.05356
-0.1410
-*0+
-*0+
-*0+
-*0+
0.19249
-0.13854
-0.11949
-0.06255
-+0+
-0.02 12
0.14 12
0.32 13
0.316 65
0.00938
-0.00860
-*0+
-*0+
-*0+
-*0+
6.014 +4.11 -1.80
-0.006 63
-0.566 123
-0.02030
129
Table 6-6 Angular correlation results. (Continued)
Ey-Ey
2893 - 344
2907 - 344
2941 - 344
2981 - 344
2995 - 344
3043 - 344
3165 - 344
3224 - 344
6.5
Spin seq.
2+
2i-,3,4+--+ 2+
1-,2 -* 2+
2+ -* 2+
(2+) -+
2+
2+-*
2+,2,4+(2+) -*
2i-,3,4+-
Mixing ratio
2+
2+
2+
-p0
A2
-0.03 10
-+0+
0.12792
-0.00392
0.06781
-*0+
0.248 81
-0.49 45
-0.18 39
-0.020 74
0.04 23
0.16 20
-+0+
--*0+
-0+
-*0+
-+0+
A4
0.2633
-0.0419
0.333 40
0.151 55
0.069 44
-0.04557
() calculation
In cases where the spin of the initial and final level could be unambiguously
determined, the 8value for a transition was found by a
minimization procedure.
The expected number of counts W(9) in 2-39 can be written as a function of the
mixing ratio £ For a number of counts in a given angle n(8),
n(e)_W(9)J2
6-13
The value of 5and the value of N were adjusted until the deepest minimum ofj was
found. The solver routine in Microsoft Excel was used to minimize this function. The
uncertainty in Sis the range that produces a change inj of one unit. Figure 6-9
shows the uncertainty range graphically.
The measured övalues are contained in Table 6-6. In cases where it was
possible to extract a 8value from more than one correlation, the weighted average of
delta is presented below the values it is comprised of.
130
586 keV x2
6.0
5.0
4.0
3.0
2.0
1.0
0.0
-3.2
-3.1
-3
I
I
-2.9
-2.8
-2.7
Figure 6-9 Sample of X2 reduction method. The uncertainty range in Sdue to the
variation of one unit inj is indicated.
6.5.1
Previous mixing ratio measurements
Several publications have previously reported Svalues for transitions in 152Gd
as described in 4.5. These mixing ratios are compared to this experiment in Table 6-7.
The enhanced quality of the coincidence data produced by the 8ic allows precision
measurement of previously published övalues and calculation of multipole mixing for
many more weak transitions.
131
Table 6-7 Previously measured Svalues compared to this work. The table is not a
complete report of all previously measured övalues: only the values measured for y
rays assigned to the same spin and parity as this were are shown.
This Work
y
Tagziria
NDS
Ferencei
0.035 195 M3/E2
-0.3<c<-
411
Kalfas
Lipas
0.032
543.7
0.048 41
586
622.8
-2.95 20
0.523 45
675.1
2.20 35
I-
678.6
764.9
3.82 35
794.8
50.6 +°-41.2
778
0.009 15
937
-0.03580
970.4
-0.018 18
0.45 9
0.18 8
-3.27 +7.76-
-5.4+1.5-2.6
0.018+4218 or 2.13
.i.
2.2 4
3.8 6
-4.9 1.2
-3.05 14
+1.0 5
1.0450
0.2<ö<1.5
+2.2 4
+4.1+17-11
1.84 66
-19 16
+3.8 6
3.47 +1.70-0.91
-0.4 +7-12
-0.4 +7-12
19 16
4.3 +0.7-
3.47+1.7-0.91
0.6
974
1010.7
0.033
0.18 +17-14
1.47 60
1.88 +1.93-1.06
0.23<ö1.41
0.03 +3-10
tor2.15
1086.3
1089.7
0.06 6
-0.18 14
-0.18 14
17+10-4
0.225
20+23-8
44<5<-7.1
1137.6
1185.6
0.32 6
-92
-92
-0.69 +O.46oO
1190.5
0.285
+0.064
+0.285
+0.064
1261
-0.041 35
-0.009 43
-0.016 30
1275
-0.2519
0.33 8or
1299.1
0.01620
<0.10
+0.043 17
1348.1
0.026 20
-13 +4-7
1369.2
-1.2 1-0.3
-0.5835
-13 +4-7
0.35 6
+4.3 +9-13
+4.3 +9-13
-0.285
-0.285
-0.31 29M3/E2
1209.1
0.28+0.17-0.21
-0.2014
2.592.10-0.95
<0.10
13.5 +-6.5
.1.
1411.5
1517.8
T
I.
-0.11 6
1586.23] 0.042 26
1596.9
1596.9
1667.4
1771
]
1789.1
-0.034 40
-0.235 45
+0.19+3-
+0.19+314
+0.259
+0.25 9
-0.28 12
+0.26+9-6
1797
>14.3
1802
<0.18
-0.1 8
-.030 25 M3/E2
+0.356
14
-0.28 12
0.26 3
+0.263
+0.26+9-6
1
-4.69 +2.66-1.28
or -0.21 8
-.3421
0.29 +9-8 E3/M2
1.1161
-0.1310
+0.9-1.6
1902.4
-2.7020
-0.114
0.4 +0.7-1.2
0.011 63
-11 2
-0.114
0.36 +25-18
0.58.07
1.47 0.60
-44<S<-7.1
I
132
Table 6-7 Previously measured övalues. (Continued.)
This Work
Taaziria
NOS
Ferer
+0.274
0.30 +9-8
-0.19 l2or
1915
4.3 +4.8-1.6
-0.074
1920
0.056 33
6.04 +4.1-1.8
1955.3
2033.8
2150.9
0.27 4
I
<5.9
<+5.9
-0.75<5<-
-0.62
0.41
2185
0.009 28
<-0.15
0.200r2.1
2342
9
2365
2375.3
2384
2495.6
0.003 26
0.16 2
0.10638
too weak
0.31 +-38
multiple
+0.158
+0.158
2518.5
0.10 +0.27-0.18
0.31 +-52
multiple
-2.7 <5<-
-1.7 10
0.06
multiple,
including
+0.21 6
+.216
2536
2619.7
-0.53 11
-0.01530
-0.098
2663
too weak
Tentative
<0.05
2697.9
0.38 34
I.
0.22
-0.098
0.22
1.
spin
I
6.6
Determination of level spin
The combination of angular correlation and an analysis of the spins of the fmal
levels have led to many new spin assignments. Those levels with significant
difference from the published values or those that have major relevance to the band
structure are described here. In all cases, level assignments have been made on the
basis of coincidence.
6.6.1
1475.2 keY O level
New O levels are particularly significant as a likely bandhead for a previously
133
unidentified band. The 1130 - 344 keV correlation has A44 = 0.93. only the 0-2-0
spin cascade has such a high value for the A44 coefficient. This level also matches a
recently
discovered4
new O state in '50Sm. The 1475 keV level was not established in
Adam's paper; the TORI68 does not list an 1130 keV yray. Some evidence for this
level was seen in the 152Eu decay.69 Transitions feeding from levels 2438, 2513, and
3360 keV above that feed the 1475 keV level have been identified. Most importantly,
the 296 keV transition seen is identified as originating from the 1771 keV 2 level.
The feeding helps support the assignment of these two levels to a new band as
described in Chapter 7. The coincidence gate for 1130 keV showing the strong 344
coincidence is shown in Figure 6-10.
3443
Figure 6-10 1130 keV gated coincidence spectrum showing 344 keV coincidence and
feeding transitions.
134
6.6.2
1681.1 keY 0 level
The A44 = 1.1 for the 1337 - 344 keV correlation, a strong indication of Ot
This is a new level, consisting of the previously unassigned 1337 keV yray and a 750
keV yray feeding the 930 keV level. The expected E0 component at 1680.8 keV
would likely be below detection limits of previous conversion electron studies.
6.6.3
1839.9 keV 3 level
Both Adam's paper and the TORI list this level as 2t Several of the angular
distribution measurements indicate spin 3. For example, the 909 586 keV correlation
and the 2084 422 keV correlations both indicate spin 3, with spin 2 far outside the
uncertainty. Furthermore, the lack of a 0 feeding, common to almost all of the other
2 levels favors the 3 assignment. The large E2 component in the 909 keV transition
indicates positive parity.
6.6.4
1915.5 keY 3 level
The fof3, 4f in the TORI data comes from
d,d'
measurements, which have
a lower confidence for spin determination. The 1160 411 keV correlation has a
negative A22, which eliminates spin 2, and the 1160 344 keV crossover measurement
eliminates all choices but spin 3. The choice of positive parity is consistent with
feeding from above and is supported by the lack of a feeding to the 1 level at 1314
keV.
135
6.6.5
Other spin assignments
Unambiguous spin and parity assignments have been made for several other
previously undetermined levels. These include 2133.3 keV, 2299.6 keV, 2401.4 keV,
1961.7 keV, 1975.5 keV, 2437.4 keV, 2539.9 keV, 2544.2 keV, 2880.4 keY, 2927.7
keV, 2999.4 keV, and 3139.4 keV. Table 6-3 shows the spins of these levels in
comparison to previous publications, the transitions that depopulate them can be found
in Table 6-2.
6.7
EO transition strength calculation
The E0 strengths reported in this study are all calculated using the method
described in 2.1.5. That method used the published conversion coefficients (a) and
the measured mixing ratio values (8) to calculate the E0 intensity. In certain cases it
is also possible to extract the E0 intensity from the angular correlation measurements
using de-orientation coefficients. For example, correlations with the 930 keV yray
and the 344 keY 7-ray can be used to find the E0 strength in the 586 keV 7-ray. The
Akk
for the 675 keV transition in coincidence with the 930 keV transition from the 930
keV level is the product of the relevant Ak and Bk as defined in 2-46.
A (675-930) = Ak (930) Bk (675)
6-14
The Akk for the 675 keV crossover correlation with the 344 keV 7-ray depends
on three factors:
A (675-344) = Ak
(344)Bk (675)Uk
(586)
6-15
136
Since the 930 keY and 344 keY transitions both connect spin and parity 2 to
0, the
Ak
(344) = Ak (930). The ratio of both Akk leaves oniy the de-orientation
coefficient.
A (675-344)
Uk(586)
A (675-930)
6-16
The de-orientation coefficient defined in 2-51 depends on a sum of the effects
from each multipolarity present. Since transitions that use E0 only connect levels of
the same spin and parity, the dominant mulipolarities in such a transition are E0, Mi
andE2,
Uk
=U°
+u
+U.
6-17
The coefficients in 6-17 depend on the intensity of each multipolarity,
IEOU
(2,2,0) + IMIU (2,2,1) + 1E2U (2,2,2)
k
6-18
JEO+JMI+1E2
6-18 can be solved to determine the E0 strength for the 586 keV transition.
The calculations to fmd the
Uk factors
7-rays feeding the 930 keV level.
using this method were performed using several
A similar calculation has been performed for the
same feeding yray in correlation with the 586 keV 7-ray in addition to correlations
with the 930 keV 7-ray. The results can be seen in Table 6-8. The
Uk
values in the
columns on the right are expected to be equal for the same k. Poor agreement among
the calculated numbers is due to the relatively large uncertainties in the angular
correlations.
Since the E0 intensity is only a small fraction of the Uk, as indicated in 6-18,
137
Table 6-8 Calculation of Uk factors using ratios of angular correlation factors.
I 586
corr.
A22
344 corr. I 930
corr I
344-930
A22
A22
A
A
A(586)
6751 0.234 22
0.064 22
-0.350 45
0.446 15
0.091 24
0.071 23
0.349 42
3871-0.28525
-0.024 27
0.20743
0.061 24
0.008 27
0.110 46
10101-0.11026
1-0.00525
-0.01928
0.28259
0.027 28
28
0.030 28
E
i
I
I
351I0.075
I
713! -0.16939
0.046 39
586-344
U2(586)
U4(586)
U2(586)
unc
U4(586)
0.122 0584
-0.182
0067
0.203
0069
-0.212
0.145
-0.117
0.131
0.038
5779
-0.274 3
0.077
0249
-0.038
6420
-0.067
0.100
0.076
3.874
1-0.121 63
0.44415
-0.2743
-0.224
0255
1.537
0261
0.055 43
0.243 63
0.444 15
0.226
0187
-0.325
0.527
0.140 45
!-o.o6o 66
-2.311
2649
-1.284
0057
-0.456
0497
0.203
9.624
75375
0.737
!-0.077
-o.125 79
-0.273 3
0.444 15
!
0.17093
-o.013 101 :
-0.274 3
0.444 15
-0.2743
0107
the angular correlation error will produce a large uncertainty in the calculated E0
strength. The resulting uncertainty is much larger than the error provided by
published conversion electron measurements. Therefore this method will not be
sensitive enough to produce a useful value of E0 strength. The 586 keV transition is
the strongest 7-ray that this method can be applied to; Uk calculations with weaker
transitions, such as the 765 keV 7-ray showed even less consistent results. The
calculation of electric monopole intensities in this work uses the method described in
2.1.5.
138
Chapter 7 Band Structure
The location of the N = 88 isotones in the transition between spherical
and deformed nuclei creates a difficult system to model. No current structure model
describes the '52Gd band structure completely, though various models can be used to
explain different parts of the complicated band structure. Due to the possible presence
of competing types of structures, the failure of a particular model to explain the whole
structure does not necessarily make that model entirely invalid.
The low-energy
positive-parity excited states in '52Gd can be organized into six quasirotational bands
and one potential bandhead, shown in Figure 7-1. The ground-state band (g.s.b.)
2691
io
2300
2307
(7
)
1098
(6
2139
8
1860
3
f747(
S
1915
15506
I3
1226
+
2
y-band
1282
1941
i )'
1605
2
1434
2
1771
2
1668
4+
4
+
1475
o
J
2
1318
1109
2
930
0
1047
755
615
2
344
/3 - band
0
152 Gd g.s.b
Figure 7-1 Positive parity band structure diagram for some low-lying states in '52Gd.
139
yband, flband, flyband, and i band have been established previously, though the 1915
keV .P = 3 member of the fiband has replaced the previously suggested 1839 keV
= 3 level. This replacement better matches the spacing of the 3 member of the
yband with respect to the g.s. band.
The j band starting with the new 0 state at 1475 keV is previously
unpublished. The 1941 keV level is indicated as a possible bandhead of a band
associated with the i band, due to its spin and parity and the energy spacing relative to
the O state in the i band. Higher members of this band are thus far elusive. A 3 level
is expected at around 2200 keV, there are several choices with undetermined spin
listed in Table 6-2. The parent decay spin of 2 means that higher energy 4 levels are
likely to be very weakly populated. Other assignments have been made based on
applicability to particular models and systematic trends seen in neighboring nuclei.
Some of the possible model explanations are explored in 7.1.2 through 7.1.5.
7.1
Nuclear structure model applications to '52Gd
7.1.1
Quasirotational bands
The pattern of low energy excited levels seen in '52Gd can be separated into
bands based on the models described in Chapter 3. However, the transitional nature of
this nucleus demands a combination of these models. Much of the band description
has been described previously, though the structure is still open to interpretation. In
140
general, the bands in Figure 7-1 are organized as rotational levels built on underlying
vibrations. The energies of the ground-state, yand fibands are plotted versus the
expected rotational spacing in Figure 7-2. If the '52Gd excited states in these bands
arose from a true deformed rotor, Figure 7-2 would show a linear relationship with
slope
as predicted by 3-13.
Though the plots are somewhat linear, the character of these bands is not well
explained by a pure rotor since the moment of inertia (inversely proportional to the
slope of Figure 7-2) is not constant. The relative moment of inertia implied by the
rotor model for each level in the band is plotted in Figure 7-3. The g.s. and flbands
have some similar though nonlinear behavior and the relative moment for the yband
3000
Rotational band spacing
-
2S00
'1500
ig.sT
1000
T
5001
0
20
40
J(.J+1)
60
80
100
120
Figure 7-2 Energy levels for selected bands showing deviation from rotational
spacing.
141
Relative moment of inertia
5
4.5
4
3.5
3
0.5
0
0
2
1
3
Band member
4
5
6
Figure 7-3 The moment of inertia implied by a pure rotor for selected bands. The
ordinate has units of inverse energy.
fluctuates as spin increases. Although the rotor model provides a basis for organizing
the excited states, the rotational limit is not a good match for '52Gd.
7.1.2
Ground state band
The vibrational model can also be applied to the '52Gd structure. The ground
state band has spacing near the expected R4 = 2.00 of a vibrator, as shown in Figure
7-4:
R
_E(4)=219
E(2)
7-1
Some of the measured B(E2) values match the vibrator predictions as well.
The lifetimes of five states have been measured by Johnson et al. ;70 most of these are
142
4
4
2
0
'52Gd gs.b.
Figure 7-4 Low-lying members of the ground-state band of '52Gd.
for transitions among low-lying members of the ground-state band. The absolute
B(E2)
values calculated from the lifetimes measured by Johnson et
al.
are shown in
Table 7-1.
The ratio of some of the observed B(E2) values in Table 7-1 also match the
Table 7-1 Lifetimes and absolute
B(E2)
Transition
values, as reported by Johnson et
t112
Ji-*Jf
(keV)
2; -o;
344.i
(j,$)
34.2±I.
al.
B(E2)
(e b2)
U.33±CJ.02
2;,
411.1
7.2±0.4
0.64±0.04
6, *4,
471.9
2.5±0.5
0.95±0.19
586.3
7.3±0.6
0.077±0.006
271.1
37±8
0.85+0.19
4
2 2
O*2
143
prediction of 3-7, which further indicates the possible vibrational nature of the 152Gd
nucleus.
2)
B(E2;2 O)
B(E2;4
=1.94.
(6-12)
However, if '52Gd is a vibrator, then we expect a 2 phonon triplet (Ok, 2, 4) at
twice the energy of the first 2 (Figure
3-2).
Such a triplet of states is not observed.
The presence of EO transitions is an additional argument against a spherical
vibrational structure. The form of the EO operator as described by Wood
= 0, ±2. Thus E0 transitions between, for example, the 2fl and 2
et al.7
g.s. b..,
has
would
not be observed in a vibrational nucleus. Table 7-2 shows that such forbidden E0
transitions are observed.
7.1.3
Variable moment of inertia model
Though the rotational description predicts R4
= 3.33,
the rotational prescription
can be modified to explain the adjustment in spacing. The Variable Moment of Inertia
(VMI) model has some success by describing the nucleus as a "soft" rotor. If the
moment of inertia in 3-13 is allowed to grow as the spin of the band increases, the
spacing of the levels decreases. A qualitative depiction of the shift is shown in Figure
7-5. Mariscotti et al.7' use a linear approximation of the moment of inertia to achieve
a good fit of ground state rotational band spacing across a large range of nuclei. While
the VMI model helps explain the ground state quasirotational spacing, it does not
explain other band structures observed, such as the band with low energy spins 0, 2,
144
6+
42A
\
4+
20A
\
2+
6A
2+
0+
0
0+
Figure 7-5 Change in ground state band spacing due to VMI. The adjustment to
ground-state band level spacing is caused by allowing the moment of inertia to vary
with spin.
and 4 starting at 615 keV. Furthermore, the change in moment of inertia is not
consistent for increase of spin between different bands, as seen in Figure 7-3.
7.1.4
Soft rotor
The VMI can be extended to explain rotational bands as well as the ground
state band. The model can be called a "soft" rotor model. The deformed rotational
model described in 3.3.3 can also be described as a soft rotor. Such a combination of
quasi-rotational bands built on vibrational band heads can extend across much of the
observed pattern of bands seen in '52Gd. The 615 keV level has been described as a /3
145
vibration with rotational levels 930 keV, 1282 keV , etc. (Figure 7-1) built on it. The
1109 keV level can be described as a yvibration with 1434 keV, 1550 keV, etc as
rotational states in this band. The two-phonon 0
/3/3
vibration should be at
approximately twice the first 0 energy at 1230 keV. The 1048 keV level along with
the 1318 keV spin 2 are near enough to this energy to be considered a /3/3 band. The
flyvibration is expected near the sum of the /3(615 keV) and y (1109 keV) vibrations,
indeed there is an identifiable band starting at 1606 keV.
The soft rotor predictions begin to deviate substantially from the observed
levels after about 1.7 MeV. Continuing the prescription predicts a
'vibration at 2218
keV. This is quite high in energy to be populated at either of the possible couplings: 0
or 4, so its existence cannot be detected in this experiment. A triple phonon J8/3,8
vibration would be expected at 1845 keV. The 0 at 1475 might be the 0 combination
of three phonons, but the energy difference between experiment and model is rapidly
growing. The predicted energies from combinations of many vibrational phonons
produce energies far from the levels in the experimental data.
7.1.5
Anharmonic vibrator
The vibrator predicts the spins observed in some bands such as the /3 band seen
in Figure 3-2, but the energy spacings are inconsistent with the predictions of the
harmonic vibrator model. The energies can be adjusted by adding additional terms to
the vibrator Hamiltonian to produce an anharmonic vibrator. The energy of the
146
vibrational model 3-4 results from the Hamiltonian 3-3. That Hamiltonian contains
one of each
b
and
bt,
the creation and annihilation operators for vibrational phonons.
Adding terms with multiple operators can cause levels to mix and changes the
energies. One example is the following Hamiltonian:
HVIb
a{bb+J+B(b +b)
7-2
Adjusting the parameter B can reproduce some of the observed level spacing.
However, this form of the operator allows transitions of AN> 1. In the case of the
'52Gd band labeled ,8 this would indicate that the transition from the
2
930 keV level
to the 0 ground state is allowed. In the vibrational model, the 930 keV level would be
a two-phonon level; the 586 keV transition would be a one-phonon transition while the
930 keV to ground state 0 transition would be a two-phonon change. The relative
B(E2)
value for the 930 keV transition is two orders of magnitude smaller than the 586
keV transition, indicating that it is basically forbidden, as shown in Figure 7-6.
While the adjusted anharmonic vibrator can explain the
fi band or other single
bands, different bands require different adjustments to fit the model. For example, the
930 keV 2 level of the flband would be a two-phonon vibrator, expected at 1230 keV
(Figure 3-2), or twice the one phonon 615 keV level. If the B parameter is adjusted to
make the two-phonon level at 930 keV, then what would be the two-phonon bandhead
of the yband at 1109 keV is now far outside the model. The band labeled /Jyis also
not predicted by the anharmonic vibrator. Other parameters or different models are
required to explain other bands or encompass all the band structure simultaneously.
147
R
6'
D
g930
2+
N=1
I
2+
LN2
344_k.
0+
Figure 7-6 Partial level diagram showing B(E2) values that differ from the
anharmonic vibrator.
7.1.6
Interacting boson model (IBM)
A second form of the anharmonic vibrator is based on the concept of nucleon
pairs with total angular momentum J = 0 (s bosons) or J = 2
(d bosons)
dominating
low-energy structure. The basis of the Interacting Boson Model (IBM) is an
anharmonic vibrator. Assuming the ground state has all
can be predicted as the energy
Ed
s
bosons, the energy of a state
of all d bosons plus an interaction between boson
pairs:
c
= 6dd +
7-3
. (d2)
JO,2,4
The C are proportional to the energy shift of the 0,
and
dt
2
and 4 levels. The d
are creation and annihilation operators for d bosons. The superscript (J)
148
indicates that the d bosons are coupled to produce the proper total angular momentum:
0, 2, or 4. The additional parameters allow the energies to be more closely matched to
the level energies determined by experiment.
The Hamiltonian 7-3 is a simplified version of the IBM Hamiltonian. This
form preserves the AN = 1 rule of the vibrator model. Some higher order terms that
can be added mix states with different numbers of bosons and account for interaction
between s and d boson pairs. The Hamiltonian 7-3 accounts for all valence particles
indiscriminately, some IBM models include terms that account for the difference
between neutrons and protons. Several of the models mentioned in 4.6 use the IBM or
similar variants.
Many IBM calculations accurately predict much of the observed energy
spacing. Adam et
al.35
achieve and average deviation for 13 predicted level energies
of only 53 keV with an IBM calculation. Tagziria
et al.53
predict the lowest five levels
almost exactly, the match at higher energies is worse.
The major benefit to the IBM model is the ability to predict transition
strengths. The model as used by Lipas et
al.55
is able to predict collective Mi
transitions. Several of the experimentally measured 8 values indicate substantial Mi
admixture in collective states. For example, the 8= -2.9 of the 2fl* 2 g.s. 586 keV
transition indicates approximately 10% Mi admixture. The Lipas et
al.
model predicts
8 -6.1. Tagziria et al. also predict three Svalues; the match between experiment and
calculation may indicate the underlying reasons for the structure.
Unfortunately, since the model parameters are generally based on the
149
experimental data, the IBM generally lacks predictive power. The success of the IBM
rarely extends far outside the model space, and thus thrther model extensions are
required to describe the remaining bands. For the case of '52Gd, Adam et al. conclude
that "None of the models explain the data in a completely satisfactory way."
7.2
Multipole transition strengths
7.2.1
Monopole transition intensity
As described in 2.1.5, strong monopole transitions can indicate mixing of
different shapes between levels. The
1:0
calculated from 2-32 are shown in Table
7-2.
Table 7-2 Electric monopole intensities IAE for selected transitions and relevant
conversion coefficients.
Ey
M1
*1O3
cNaK iü
387.8 420.00
110.00
K
10
41.93
3
E2
3
lv
tXK
22.31
TEQ
,E0
1K
2.86
0.82
Band Desc
-+
2+
P
I_i
.1+
526.9
82.00
9.00
19.15
9.90
3.16
fi
0.44
-p
'3+
586.3
20.20
2.10
14.67
7.66
0.94
0.17
"/3
'3+
-*
'3+
622.8
675.0
10.90
6.00
1.70
1.50
12.59
10.31
6.61
5.48
-0.01
-0.01
0.03
0.03
"ir
'3+
'3+
"fir
"P
'3+
764.9
5.70
1.30
7.58
4.12
0.07
'3+
-+
0.07
3.70
1.80
4.75
2.71
0.00
0.01
'I2
-4
'3+
974.1
5.00
0.60
2.40
4.23
0.12
0.03
1010.6
5.70
1.40
3.87
2.27
0.02
0.01
"ir
"17
'3+
-+
'3+
"ir
g.s.
'3+
'3+
928.4
g.s.
'3+
'3+
-
"P
150
Table 7-3 Electric monopole intensities. (Continued)
M1*
aK
Ey
a*1O3
1137.6
3.00
0.60
2.93
1261.3
2.20
0.40
1596.9
1.01
1771.4
3
lu
aK
2*
1EO
1E0
1K
CIK Band Desc.
1.79
0.00
0.01
12
-*
2.30
1.46
0.00
0.01
/Jy
-*
g.s.
0.23
0.99
3.16
0.00
0.00
'ir
-+
g.s.
1.41
0.27
0.88
3.16
0.01
0.00
L20
1778.8
1.60
0.40
0.87
3.16
0.00
0.00
b17
1857.5
0.76
0.28
0.82
3.16
-0.07
0.02
2093.2
1.25
0.24
0.67
3.16
0.02
0.01
2365.1
1.20
0.30
0.50
3.16
0.02
0.01
Wood et
square radius
al.7
(r2).
Z.103
ii
L4
ii
2+
7
-+
-*
g.s.
-
g.s.
-
describe how E0 transition rates are correlated to the root-mean
In that model, the E0 transitions could be caused by mixing of a
spherical ground state band with a deformed shape in the fi band. It could be said that
the strong monopole transitions in Table 7-2 are between bands with different intrinsic
shapes.
The observed monopole intensities in these transition nuclei are consistent
with a mixing of spherical and deformed shapes, a reflection of the transitional nature
of '52Gd.
All of the measured monopole strengths above 1 MeV are not significantly
different from zero. The decline in the probability of internal conversion relative to y
emission with increase in energy is one reason. Furthermore, the high-energy states
have less distinct shapes so that changing the shape without changing the angular
momentum becomes less probable.
151
7.2.2
Relative B(E2) values in positive parity bands
The vibrational and rotational models make strong predictions about the
expected relative B(E2) values. The transitional nature of 52Gd results in
quasirotational bands that do not always follow these predictions well. However,
selected relative B(E2) values support much of the band structure and help clarify the
assignments that have been made. Figure 7-7 and Figure 7-8 show some relative
B(E2)
values relevant to the band structure. The values are calculated as described in
2.1.2 and are normalized out of a given level. Since decay to the ground state band
requires the annihilation of only one phonon, decays to the g.s. band from one-phonon
bands are relatively strong. Decays into other bands require the simultaneous
annihilation and creation of vibrational phonons; these dual step processes are
hindered. Decays within the band should generally be strongest, since the change of
rotation involves the whole nucleus. However, these quasirotational bands do not
always follow these prescriptions.
In the yband, the largest B(E2) values for the 2 and 3 states feed into the
ground state rotational band. Electric quadrupole transitions within the band are
strongest from the 4 state and the second strongest for the
325
keV yray from the 3
level. The 116 keV difference between the 4 and 3 levels of the yband is probably
suppressed due to the E5 energy dependence for E2 transitions. The observation of
even a weak 116 keV tray would result in a large
from the yband to the
2
B(E2). E2
strengths for transitions
and O members of the flband are generally smaller, though
152
not weak. The wavefunctions that describe these bands are probably not as pure as the
band designation implies; mixing between bands is likely the cause of these enhanced
interband transitions.
A similar pattern of enhanced transition strength to the g.s. band and strong
inter-band transitions is seen in the fi band. None of the measured values from this
experiment are high enough to show B(E2) values for transitions into the yband from
r
I
4
±_____
1915
-1860
-1605
-1550
2
-f
- 1434
- 1318
4-
1282
1226
2
-1109
-1047
c4N
-930
-755
-- -615
-344
-0
0
152
Gd g.s.b
y-band
f3-band
13y-band
Figure 7-7 Band structure diagram showing B(E2) values. The values from a given
level are normalized to highlight particular features of the structure.
153
the /1 band, but it is expected that they are somewhat restricted in the manner
described above for y* /ltransitions. In this band, the
B(E2) values
to the g.s. are
about equal to the intraband B(E2) values.
The more weakly populated and higher energy bands have fewer calculable
intraband B(E2) values. The i band shown in Figure 7-8 has a strong preference to
decay by intraband transitions and then decays strongly into the 'band. There are not
--1941
2
1860
1771
1692
'7-
___f_
1550
-
-1475
0
1318
1282
1226
-1109
-1047
II-
930
- 755
-615
.
j-band
i-band
iy-baacl
Figure 7-8 Selected B(E2) values for additional bands in '52Gd.
0
154
enough measured B(E2) values for thej band to make a defmite judgment about
feeding preferences. The B(E2) values for the iyband are shown only to indicate the
possible relationships with other bands. Since the
2
state at 1941 is only a suggested
band head and has no other band members, so no mtraband transitions are available.
7.3
Other bands and excited states
73.1
Octupole states
Two negative parity bands, seen in Figure 7-9, can be established from the
observed levels. In this study, the spin parity assignments were confirmed for the 3,
1, and 5 levels in the K = 0 band, and the 2, 3 and tentative (4) in the K
= 1
band.
The angular correlation data for transitions from the 1807 keV level agree with 4, but
none of the evidence is strong enough to make a defmite assignment.
The inverted order of the 3 and 1 members of the K = 0 band is thought to be
due to mixing with other negative parity states33. The Coriolis force distortion in a
rotational band can mix odd states with iK = 1. The mixed 3 states are pushed apart
in energy leading to reversed spin order in the K
= 0 band
but normal ordering in the K
= 1 band.
7.3.2
Promoted pair basis states
It has been suggested69' 72 that some of the observed levels can be explained in terms
of proton pair promotion across the subshell gap at Z = 64 (see section 3.1).
155
11
2814
(6
9
2331
7
1880
2713
)
(4
-'---_-----1807
3
- _ -l692
- -/----'- 1644
1
1471
1314
3
1123
K=l
0 keV
152
Gdg.s
Figure 7-9 Negative parity bands in '52Gd.
The pair excitation energy for this gap is roughly 1 MeV. The 615 keV level
could be explained as the result of promoting a proton pair across the subshell gap. In
this picture of the band structure, the 1109 keV and 1047 keV levels are one-phonon y
- and fl-vibrations as in the soft rotor. Soft rotor states similar the first two can be
built upon the pair excitation at
615
keV. If the 615 keV is called g', then the 1475
keV level could be considered a fi' excitation and the
1606
a
bandhead. Further
systematic investigation of this pattern is necessary to assess its validity.
7.3.3
Shell model excitations
Above approximately 1.8 MeV, the level density becomes increasingly large,
156
and the models presented so far fail to accurately predict spins and energies. At this
energy, it becomes possible to separate a pair of protons or neutrons and excite one of
them to a new subshell. Empirically, the energy required for such an excitation is near
2
MeV. The possible configurations are large in number and give rise to a multitude
of possible states. For example, if a valence proton is promoted to 2d312, the angular
momentum of the pair can couple with the remaining 2d512 hole to produce excitations
with integer spin from 1 to 4. The multitude of2 levels seen in '52Gd above
2
MeV is
an indication of broken pair states.
7.4
Band structure systematics
Patterns of excites states observed in many of the isotones with 88 neutrons
h1112
S112
3(2
d312
Z=64
d512 _
5/2
Figure 7-10 Example of a single nucleon excitation across the Z = 64 subshell gap.
The resulting d512 hole can couple to the d312 excited particle to produce spin 1 to 4.
157
show much similarity. Figure 4-2 shows a comparison of the ground-state andy'
bands of several N = 88 isotones. Similarities can also be seen in other bands in
several of these nuclei. The flbands of even proton number isotopes for Z = 60
through Z = 66 are shown in Figure 7-11. The increase in deformation as protons are
added decreases the y-band energies from left to right in the figure, but the energy
spacing is very consistent.
A comparison of the ybands for the same isotones is shown in Figure 7-12.
The same general decrease in the band member energies is seen as the number of
protons increases.
10
8
8
2726
6
2149
I 0
2300
1602
4
1227
2139
8-'-
2163
6
1668
6
1658
1822
1747
4
6
S"
1448
'i
2
1171
0
917_
1282 -_±
1252
1045
4
765
930 ._2
905
0
661
'48Nd f3'-.p±iLi4o
615
Sin
'52Gd /3
2
'54Dy
/3
344
0- 0
152 Gd g.s.
Figure 7-11 Comparison offlquasirotational bands for some N= 88 isotones. The
152Gd ground-state band has been included for scale.
158
10
2304
72 183
6
2099
6 ') 2107
5
2020
)
'.'
8
6
5
1990
1862(-
1748
1227
4
1683
4+1643
3
1512
3
2
148
+
)
1886
5' 1740
1504
1550
31434
4i443
3+
1334
1248
Nd y
1194
150
Sm y152
Gd y
1027
Dyy
4+ 755
2
344
0- 0
'
Gd g.s
Figure 7-12 Comparison of ybands for some N = 88 isotones. The '52Gd ground-state
band has been included for scale.
The bands labeled as "i" are shown for '50Sm '52Gd, and '54Dy in Figure 7-13.
The match here is less impressive, though still readily apparent. Mixing with other
states as the energy increases is the likely case of the energy differences of excited
states in the i bands.
7.5
Conclusions
7.5.1
Summary
The improved ability of the 8it spectrometer and other newer multi-detector
159
10
2300
S
1747
2'
1417
-
6
1227
0
15Oc
7c
2
1255
mi
2
\o
2
1390
0
1058
1318,'
1048
"2Gdi
Dyi
344
0
152
Gdg.s.
Figure 7-13 Comparison of the "i" rotational bands in some N= 88 isotones. The
152Gd ground-state band has been included for scale.
arrays to record high-quality coincidence data provides good reason for repeating and
the ability to improve upon previous work. The linkage of excited states and the
strength of the transitions that connect those states have been clarified beyond
presently published data in many cases. 54 new levels are postulated and 266 new
transitions have been identified as produced by the '52Gd. Angular correlation of the
radiations from more than 250 different cascades has provided
spin
and parity
assignments for many of these levels. Mixing ratios for 144 transitions have been
reported. This new information serves as a basis for further model development.
The low-energy excited states of '52Gd can be organized into related bands to
highlight possible underlying structures. These bands can be described by various
models with a range of success. While no model sufficiently explains all bands, the
160
soft-rotor model described the widest range of structures in a qualitative manner.
Improvements on the IBM and other quantitative models have been able to describe
the some of the transitional behavior of the N = 88 region.
The similarity of band structure seen in the N = 88 isotones even within a
region of rapid shape change suggests the possibility of a relatively uncomplicated
model description that encompasses several nuclei in this region. Newly discovered
excited states in 152Gd that are analogous to those in '50Sm, support the development
of a common structure description including and extending beyond these nuclei.
7.5.2
Further work
Although minor refmements might be made in the level scheme and the
spectroscopy, the level energies and transitions listed in this work are complete to an
uncertainty that is beyond what is needed to compare the data to current models.
Further study of tray energies and level relationships is of limited value. Lifetime
measurements of more excited states would be helpful to compare absolute B(E2)
values. However, due to the difficulty in obtaining these measurements, coulomb
excitation, while still hindered by the complexity of the level scheme is preferred for
further measurement of transition strengths.
The systematic patterns found in neighboring nuclei may be the foundation of
a new type of band description. The 148Nd and '54Dy spectroscopy should be
investigated with the higher power of a detector such as the 8it to look for new
states and bands similar to the "i" and '' bands in '52Gd.
161
8.
Appendix
162
Appendix 1 Energy sorted tray list. Energies are in keV, LI is the initial level, LF is
the fmal level populated by a transition. The intensities are normalized so that the 344
keV transition has intensity 1000.
Ey
Abs I
L1
117.2
1.56 ± 0.09
1048.1
158.4
0.59 ± 0.04
1282.4
160.4
0.31 ± 0.03
1475.2
169.5
0.48 ± 0.03
1862.2
175.2
0.78 ± 0.05
930.8
178.6
0.22 ± 0.05
1109.4
195.1
7.99 ± 0.43
1318.6
208.9
0.65 ± 0.05
1318.6
J"
Lf
J'f
930.8
2+
1123.4
3-
0+
4+
0+
2+
2+
2+
2+
2+
1123.4
1109.4
1314.7
1-
1692.5
3+
4+
2+
755.5
930.8
211.6
0.12 ± 0.03
1643.9
2-
1434.1
218.5
0.29 ± 0.02
1862.2
248.8
1.43 ± 0.09
1941.5
1643.9
1692.5
270.3
9.79 ± 6.87
1318.6
2+
2+
2+
271.2
128.76 ± 6.87
615.5
296.1
<.01
1771.7
297.8
0.13 ± 0.01
1941.5
311.7
0.19 ± 0.01
1862.2
315.2
13.64 ± 0.69
930.8
324.7
0.64 ± 0.05
1434.1
335.6
1.05 ± 0.17
337.6
0+
2+
2+
3-
2+
3+
2-
1475.2
3+
0+
2+
0+
1048.1
344.3
1643.9
2-
1550.2
1941.5
2+
2+
3+
2+
1605.8
4+
0+
2+
2+
0.31 ± 0.05
1808.0
(4-)
1470.7
5(-)
344.3
1000.00 ± 0.00
344.3
0.0
351.7
4.41 ± 0.22
1282.4
353.7
0.40 ± 0.02
1109.4
2+
4+
2+
367.8
5.66 ± 0.30
1123.4
3-
755.5
387.7
7.14 ± 0.36
1318.6
930.8
391.1
0.41 ± 0.03
407.0
0.75 ± 0.04
1941.5
2247.0
411.2
63.86 ± 3.20
755.5
428.0
0.38 ± 0.02
1862.2
0+
2+
4+
4+
2+
4+
3+
2+
3+
0+
2+
2265.5
1314.7
755.5
1123.4
2(+/-)
2+
615.5
1109.4
930.8
755.5
441.0
0.64 ± 0.05
1550.2
454.7
0.03 ± 0.02
2719.6
456.8
0.83 ± 0.07
1771.7
471.7
0.31 ± 0.03
1227.1
482.5
0.98 ± 0.05
1605.8
2+
2+
2+
4+
2+
0+
4+
2+
2+
6+
2+
490.2
0.29 ± 0.03
1808.0
(4-)
1318.6
490.8
1.31 ± 0.10
2247.0
2+
1757.1
1-
492.2
0.11 ± 0.01
2300.0
2-
1808.0
(4-)
494.0
2.51 ± 0.13
1109.4
2.51 ± 0.15
1605.8
1109.4
503.6
1.33 ± 0.07
1434.1
2+
2+
3+
615.5
496.4
930.8
0+
2+
2+
520.4
1.27 ± 0.07
1643.9
2-
1123.4
3-
432.6
E0
1048.1
1550.2
1839.9
344.3
1434.1
615.5
1109.4
1-
4+
3-
163
Appendix 1 Energy Sorted tray list. (Continued)
Ey
Abs I
L
J1
527.0
4.18 ± 0.22
1282.4
4+
755.5
534.4
0.92 ± 0.06
1643.9
2-
1109.4
544.0
3.04 ± 0.17
1862.2
1318.6
547.4
0.83 ± 0.07
1862.2
557.7
0.49 ± 0.03
1839.9
557.9
1.50 ± 0.08
1605.8
563.2
1.02 ± 0.06
1318.6
566.3
0.14 ± 0.08
2247.0
2+
2+
3+
2+
2+
2+
577.7
0.61 ± 0.04
2011.8
2,3+
1434.1
579.9
0.65 ± 0.04
1862.2
1282.4
586.7
147.00 ± 7.35
595.8
0.10 ± 0.06
2729.3
2+
2+
2+
597.8
0.14 ± 0.02
1915.5
930.8
J
4+
2+
2+
1314.7
1-
1282.4
1605.8
4+
0+
4+
0+
3+
4+
2+
2+
2+
0+
2+
4+
6+
2+
2+
1123.4
3-
1048.1
755.5
1681.1
344.3
2133.6
623.0
14.88 ± 0.77
1941.5
633.5
0.11 ± 0.01
1915.5
633.6
0.03 ± 0.01
1860.8
634.0
0.03 ± 0.01
2880.9
641.5
0.95 ± 0.10
648.5
1.99 ± 0.11
2247.0
1771.7
3+
0+
2+
3+
5+
2+
2+
2+
656.4
0.62 ± 0.04
2300.0
2-
1643.9
2-
659.2
0.37 ± 0.02
1941.5
1282.4
662.7
0.22 ± 0.03
1771.7
675.2
9.65 ± 0.49
1605.8
678.8
4.13 ± 0.22
1434.1
2+
2+
2+
3+
4+
2+
2+
4+
681.6
<.03 ± 0.01
3012.1
2+,3,4+
684.3
0.36 ± 0.02
1808.0
(4-)
693.6
0.56 ± 0.04
2011.8
2,3+
2330.7
1123.4
1318.6
697.2
0.27 ± 0.03
2011.8
2,3+
698.0
0.11 ± 0.01
2709.7
2+
615.5
E0
615.5
1318.6
0.0
1318.6
1282.4
1227.1
2247.0
1109.4
930.8
755.5
1314.7
2011.8
615.5
699.6
1.50 ± 0.08
1314.7
1-
703.3
14.71 ± 1.26
1318.6
703.9
25.74 ± 2.21
2+
0+
2+
1692.5
930.8
3,4,5
3-
2+
1-
2,3+
709.5
0.78 ± 0.05
2401.8
713.1
2.22 ± 0.12
1643.9
2-
715.3
0.98 ± 0.06
1470.7
5(-)
755.5
0+
0+
2+
3+
2+
4+
721.8
0.06 ± 0.01
2529.6
3(+)
1808.0
(4-)
723.9
0.47 ± 0.04
1771.7
2+
1048.1
730.8
0.76 ± 0.06
1839.9
1109.4
0+
2+
738.9
4.32 ± 0.23
1862.2
747.4
0.12 ± 0.07
2880.9
750.5
0.40 ± 0.03
1681.1
753.0
0.41 ± 0.04
1862.2
3+
2+
2+
0+
2+
1048.1
615.5
344.3
1123.4
3-
2133.6
2+
2+
2+
930.8
1109.4
164
Appendix 1 Energy Sorted tray list. (Continued)
Ey
Abs I
756.8
0.16 ± 0.09
2437.8
762.0
0.21 ± 0.02
1692.5
765.2
47.84 ± 2.40
1109.4
768.1
0.38 ± 0.04
779.1
L
Jf
1681.1
0+
2+
2+
2524.1
2+
3+
2+
2+
1757.1
1-
90.66 ± 4.61
1123.4
3-
344.3
2+
788.3
0.74 ± 0.06
2103.0
--
1314.7
1-
792.6
0.51 ± 0.03
1915.5
1123.4
3-
794.9
3.10 ± 0.17
1550.2
755.5
4+
804.5
0.24 ± 0.02
2719.6
1915.5
806.6
0.40 ± 0.04
1915.5
813.0
3.58 ± 0.21
2247.0
813.9
0.42 ± 0.04
2729.3
814.3
0.65 ± 0.04
1862.2
1048.1
3+
2+
3+
3+
0+
818.1
1.35 ± 0.08
1941.5
1123.4
3-
818.9
0.75 ± 0.07
2133.6
1314.7
1-
830.0
0.04 ± 0.03
2999.8
832.3
1.85 ± 0.12
1941.5
930.8
344.3
834.2
0.40 ± 0.03
2749.2
3+
4+
2+
3+
2+
2+
2+
2+
2+
2+
2+
3+
837.2
0.32 ± 0.03
2529.6
3(+)
1692.5
837.4
0.09 ± 0.05
3006.5
(3-)
2169.8
2-
839.2
0.05 ± 0.01
2121.1
1282.4
841.2
0.69 ± 0.04
1771.7
850.4
0.33 ± 0.02
1605.8
4+
2+
2+
4+
2+
4+
855.3
0.71 ± 0.07
2169.8
2-
1314.7
1-
857.5
1.00 ± 0.08
2773.1
2+,3
1915.5
1109.4
1434.1
1915.5
2169.8
2-
1109.4
2+
3+
3+
1915.5
930.8
755.5
857.9
0.72 ± 0.08
2719.6
2+
1862.2
865.8
0.75 ± 0.05
2300.0
2-
1434.1
3+
2+
3+
869.1
0.16 ± 0.02
2+
2011.8
2,3+
877.8
0.32 ± 0.02
(4-)
930.8
887.5
0.82 ± 0.09
2880.9
1808.0
2749.2
3+
1862.2
893.6
12.84 ± 0.66
1941.5
2+
1048.1
902.7
2.87 ± 0.18
2011.8
2,3+
1109.4
909.2
2.50 ± 0.13
1839.9
930.8
912.7
0.06 ± 0.02
1668.2
914.6
1.07 ± 0.07
2558.1
928.6
5.46 ± 0.29
2247.0
930.2
23.36 ± 0.47
930.8
931.5
1.68 ± 0.10
1862.2
932.1
3.50 ± 0.24
2247.0
937.3
2.96 ± 0.16
1692.5
3+
6+
2+
2+
2+
2+
2+
3+
2+
2+
0+
2+
2+
4+
940.3
0.56 ± 0.05
2258.2
--
952.5
0.70 ± 0.06
2265.5
2(+I-)
953.6
0.77 ± 0.06
2709.7
2+
965.6
1.18 ± 0.09
2880.9
2+
755.5
1643.9
2-
1318.6
2+
0+
2+
0.0
930.8
1314.7
1-
755.5
1318.6
4+
2+
1314.7
1-
1757.1
1-
1915.5
3+
165
Appendix 1 Energy Sorted ray list. (Continued)
E'
Abs I
L
J'j
Jf
970.5
13.29 ± 0.68
1314.7
1-
344.3
974.3
52.15 ± 2.63
1318.6
2+
344.3
2+
2+
3+
4+
975.1
0.75 ± 0.06
2667.7
l+,2+
1692.5
979.6
1.22 ± 0.06
2529.6
3(+)
1550.2
985.3
1.07 ± 0.09
2300.0
2-
1314.7
1-
990.4
13.50 ± 0.69
1605.8
2+
615.5
1605.8
0+
2+
2+
3+
4+
3+
993.3
0.91 ± 0.10
2599.0
(2+)
1010.8
6.77 ± 0.35
1941.5
1013.0
0.49 ± 0.04
2928.1
1016.1
0.98 ± 0.06
1771.7
1017.2
0.85 ± 0.06
2709.7
2+
2+
2+
2+
930.8
1915.5
755.5
1692.5
1021.6
0.64 ± 0.04
3309.7
2+,3,4+
2287.8
--
1027.3
0.18 ± 0.02
2719.6
2+
1692.5
3+
1029.4
0.24 ± 0.02
2500.1
3-,4,5
1470.7
5(-)
1031.3
0.37 ± 0.03
1962.1
--
930.8
1036.9
2.04 ± 0.13
2729.3
1692.5
1048.1
2+
0+
2964.1
3(+)
1915.5
755.5
2+
3+
0+
3+
4+
3+
1048.1
1048.7
E0
0.51 ± 0.05
0.0
1052.4
1.99 ± 0.11
1808.0
(4-)
1057.0
0.42 ± 0.03
2749.2
0.13 ± 0.01
2709.7
3+
2+
1692.5
1066.3
1643.9
2-
1069.4
1069.6
0.53 ± 0.04
2503.6
2+,3,4+
1434.1
3+
0.35 ± 0.03
2193.3
--
1123.4
3-
1072.7
0.10 ± 0.01
2387.3
1-,2-3-
1314.7
1-
1076.2
0.58 ± 0.04
2719.6
2+
1643.9
2-
1081.4
0.20 ± 0.02
2011.8
2,3+
930.8
1083.8
0.16 ± 0.02
2401.8
2+
1318.6
1084.1
0.70 ± 0.05
0.82 ± 0.05
2.12 ± 0.14
1643.9
2-
1086.9
2.39 ± 0.21
2401.8
1314.7
1-
1089.8
15.73 ± 0.88
1434.1
3+
2+
2+
3+
1109.4
755.5
1085.9
2193.3
1839.9
2729.3
--
1084.3
2+
2+
2+
4+
344.3
1090.9
0.33 ± 0.03
3006.5
(3-)
1915.5
1109.4
2+
3+
2+
4+
0+
3+
1092.7
0.77 ± 0.07
1106.6
5.66 ± 0.30
2201.8
1862.2
1109.3
43.16 ± 2.18
1109.4
2+
2+
2+
1117.3
0.46 ± 0.03
2551.5
--
1434.1
1123.5
1.24 ± 0.08
2247.0
2+
1123.4
3-
1126.9
0.39 ± 0.03
3042.3
(2+)
1915.5
3+
1128.9
0.70 ± 0.06
2773.1
2+,3
1643.9
2-
1131 .0
2.39 ± 0.14
1475.2
344.3
1137.9
13.77 ± 0.85
2247.0
0+
2+
1109.4
2+
2+
1142.2
0.55 ± 0.04
2265.5
2(+I-)
1123.4
3-
1149.1
0.80 ± 0.06
2258.2
1109.4
2+
755.5
0.0
166
Appendix 1 Energy Sorted tray list. (Continued)
E'y
1155.5
1159.9
1164.1
1165.0
1168.3
1171.9
1176.5
1185.9
1188.2
Abs I
0.24 ± 0.02
4.40 ± 0.23
0.19 ± 0.03
0.20 ± 0.02
0.62 ± 0.19
0.95 ± 0.05
0.25 ± 0.02
3.60 ± 0.19
0.60 ± 0.05
1190.5
6.88 ± 0.40
1191.7
1199.4
1201.9
1203.0
1203,9
1205.5
0.16 ± 0.02
0.15 ± 0.02
1209.1
1218.2
1219.4
4.87 ± 0.32
1222.0
1235.5
1237.3
1246.7
1247.2
1253.1
1257.4
1261.4
1262.5
1263.8
1271.6
1275.2
1275.7
1278.2
1284.5
1289.3
1299.2
1307.8
1314.5
1314.7
1316.2
1318.6
1325.9
1327.3
0.36 ± 0.08
0.54 ± 0.04
0.60 ± 0.05
1.79 ± 0.11
0.27 ± 0.03
0.13 ± 0.02
0.32
0.77
0.26
0.38
2.24
0.35
0.53
15.54
0.39
1.35
0.23
1.27
0.32
0.53
1.34
0.33
33.84
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
0.03
0.06
0.02
0.03
0.14
0.03
0.04
0.79
0.03
0.08
0.02
0.13
0.03
0.04
0.09
0.05
1.69
0.03 ± 0.01
1.27 ± 0.08
22.66 ± 1.13
4.41 ± 0.23
4.86 ± 0.39
14.14 ± 0.72
0.78 ± 0.08
L1
2437.8
1915.5
3080.3
2599.0
3009.4
2928.1
2300.0
1941.5
2880.9
2300.0
2882.9
3006.5
2325.8
2133.6
2327.6
1550.2
2524.1
2327.6
1975.8
2540.3
2928.1
2880.9
1862.2
2529.6
3009.4
2691.8
1605.8
2193.3
2387.3
2201.8
2880.9
2709.7
2401.8
2928.1
2604.4
1643.9
3066.5
2437.8
1314.7
2247.0
1318.6
1941.5
2642.0
J"
L
1282.4
755.5
2+,3,4+ 1915.5
(2+)
1434.1
(2+)
1839.9
2+
1757.1
21123.4
2+
755.5
2+
1692.5
21109.4
2+
1692.5
(3-)
1808.0
I
1123.4
2+
930.8
2,3+
1123.4
4+
344.3
2+
1314.7
2,3+
1109.4
2+
755.5
3+
1318.6
2+
1692.5
2+
1643.9
2+
615.5
3(+)
1282.4
(2+)
1757.1
1+,2+
1434.1
2+
344.3
-930.8
1-,2-3- 1123.4
2+
930.8
2+
1605.8
2+
1434.1
2+
1123.4
2+
1643.9
2(-)
1314.7
344.3
22,3 1757.1
2+
1123.4
10.0
2+
930.8
2+
0.0
2+
615.5
2,31314.7
2+
3+
J'tf
4+
4+
3+
3+
3+
1-
3-
4+
3+
2+
3+
(4-)
32+
32+
1-
2+
4+
2+
3+
20+
4+
1-
3+
2+
2+
32+
2+
3+
321-
2+
130+
2+
0+
0+
1-
167
Appendix I Energy Sorted ray list. (Continued)
Ey
Abs I
L
'it
1331.2
1336.8
1338.4
1344.0
0.07 ± 0.01
2.27 ± 0.12
0.34 ± 0.03
0.32 ± 0.03
0.11 ± 0.01
15.33 ± 0.77
0.79 ± 0.08
0.58 ± 0.03
0.07 ± 0.08
0.76 ± 0.06
1.64 ± 0.10
2.31 ± 0.13
1.22 ± 0.08
0.16 ± 0.01
0.75 ± 0.09
0.15 ± 0.05
1.95 ± 0.12
3139.8
2+
0+
2+,3
1-,2
1347.1
1348.2
1352.9
1360.3
1364.1
1364.2
1365.6
1369.1
1372.0
1378.1
1394.1
1395.4
1400.6
1400.7
1406.4
1410.8
1412.9
1414.3
1417.5
1421.1
1424.6
1427.0
1430.9
1434.9
1437.1
1442.1
1446.4
1446.7
1454.2
1457.6
1470.9
1481.2
1484.5
1486.3
1489.4
1491.5
1495.4
1502.9
1507.0
3.31 ± 0.19
1.78 ± 0.10
4.39
0.24
7.11 ± 0.36
0.64 ± 0.06
0.38 ± 0.04
0.88 ± 0.06
0.19 ± 0.03
1.78 ± 0.11
1.46 ± 0.09
0.43 ± 0.04
0.78 ± 0.09
1.58 ± 0.12
1.05 ± 0.06
3.48 ± 0.20
0.46 ± 0.03
0.08 ± 0.04
0.23 ± 0.02
1.13 ± 0.07
0.10 ± 0.01
0.27 ± 0.02
1.10 ± 0.09
0.38 ± 0.03
1.72 ± 0.10
0.45 ± 0.03
0.84 ± 0.06
±
1681.1
2773.1
3285.2
3153.2
1692.5
2667.7
1975.8
3009.4
2914.2
2121.1
2300.0
2495.2
2133.6
2999.8
2325.8
L
Jf
1808.0
344.3
1434.1
1941.5
1808.0
(4-)
2+
3+
2+
(4-)
2+,3,4+
3+
344.3
1+,2+
1314.7
2+
615.5
(2+)
1643.9
2+
1550.2
4+
755.5
2930.8
1-,2
1123.4
2+
755.5
2+
1605.8
I
930.8
2524.1
2719.6
2+
1123.4
1318.6
2529.6
2729.3
3(+)
2+
1757.1
2964.1
2540.3
2544.6
3340.8
1771.7
2749.2
2558.1
3042.3
3(+)
3+
(2+)
(2+)
2+
3+
2+
(2+)
2551.5
2201.8
2880.9
2773.1
2387.3
2401.8
2604.4
3400.9
2919.9
2599.0
2247.0
1839.9
2258.2
2437.8
2+
1-
-2+
2+
2+,3
1-,2-32+
2(-)
2+,3
2,3(2+)
2+
3+
2+
1123.4
1318.6
344.3
1550.2
1123.4
1123.4
1915.5
344.3
1318.6
1123.4
1605.8
1109.4
755.5
1434.1
1318.6
930.8
930.8
1123.4
1915.5
1434.1
1109.4
755.5
344.3
755.5
930.8
2+
1-
0+
24+
4+
2+
34+
2+
2+
32+
32+
2+
4+
333+
2+
2+
3-
2
2+
4+
3+
2+
2+
2+
33+
3+
2+
4+
2+
4+
2+
168
Appendix 1 Energy Sorted tray list. (Continued)
Ey
1517.8
1518.2
1518.6
1521.2
1528.9
1530.3
1532.4
1536.0
1544.3
1544.3
1548.0
1554.8
1562.5
1564.7
1566.2
1570.8
1571.1
1575.2
1582.1
1586.3
1593.2
1596.5
1596.9
1599.0
1605.7
1605.8
1606.0
1609.1
1613.3
1613.5
1620.7
1631.5
1631.5
1633.5
1640.1
1642.4
1645.2
1646.1
1646.3
1646.5
1663.4
1667.5
Abs I
7.78 ± 0.43
0.37 ± 0.02
2.03 ± 0.11
0.36 ± 0.04
0.12 ± 0.02
0.14 ± 0.02
0.39 ± 0.03
0.28 ± 0.02
0.18 ± 0.02
0.60 ± 0.04
0.56 ± 0.06
0.09 ± 0.01
1.06 ± 0.07
0.31 ± 0.03
1.60 ± 0.12
0.24 ± 0.02
2.67 ± 0.14
1.05 ± 0.06
1.09 ± 0.10
16.81 ± 0.89
1.38 ± 0.09
3.28 ± 0.18
6.30 ± 0.35
4.30 ± 0.24
0.23 ± 0.04
3.31 ± 0.17
2.69 ± 0.15
0.10 ± 0.02
0.46 ± 0.03
0.35 ± 0.03
0.24 ± 0.02
2.73 ± 0.14
1.13 ± 0.06
0.40 ± 0.05
0.94 ± 0.08
0.20 ± 0.02
0.31 ± 0.04
0.62 ± 0.05
0.39 ± 0.03
0.14 ± 0.02
0.49 ± 0.07
11.24 ± 0.60
L1
1862.2
2133.6
2642.0
3212.9
3285.2
2964.1
2287.8
2291.5
3236.5
2667.7
2862.6
2169.8
2880.9
2495.2
2880.9
2325.8
1915.5
2330.7
2691.8
2709.7
2524.1
2719.6
1941.5
2529.6
2919.9
1605.8
2729.3
2540.3
2544.6
J
2+
2+
2,31+,2+
1-,2
3(+)
---
2+
1+,2+
2,322+
1-,2
2
I
3+
3,4,5
1+,2+
2+
2
2+
2+
3(+)
2,32+
2+
3+
(2+)
3047.1
1+,2,3-
2551.5
2247.0
1975.8
2742.4
2749.2
3335.3
3400.9
2964.1
3080.3
2401.8
-2+
2+
-3+
2773.1
2011.8
2+,3,4+
2+,3
3(+)
2+,3,4+
2+
2+,3
2,3+
L
Jf
344.3
615.5
2+
0+
1123.4
3-
1692.5
1757.1
1434.1
755.5
755.5
1692.5
1123.4
1314.7
615.5
1318.6
930.8
1314.7
755.5
344.3
755.5
1109.4
1123.4
930.8
1123.4
344.3
930.8
1314.7
0.0
1123.4
930.8
930.8
1434.1
930.8
615.5
344.3
1109.4
1109.4
1692.5
1757.1
1318.6
1434.1
755.5
1109.4
344.3
3+
13+
4+
4+
3+
31-
0+
2+
2+
1-
4+
2+
4+
2+
32+
32+
2+
1-
0+
32+
2+
3+
2+
0+
2+
2+
2+
3+
1-
2+
3+
4+
2+
2+
169
Appendix 1 Energy Sorted tray list. (Continued)
Ey
Abs I
L1
J1
1668.1
1681.6
1682.3
1684.8
1690.2
0.33 ± 0.03
0.48 ± 0.04
0.20 ± 0.02
0.27 ± 0.05
0.44 ± 0.07
0.51 ± 0.06
0.31 ± 0.06
0.30 ± 0.03
1.25 ± 0.16
0.15 ± 0.01
0.45 ± 0.07
0.80 ± 0.06
1.58 ± 0.09
0.12 ± 0.01
2599.0
2729.3
2964.1
2999.8
3006.5
3009.4
3009.4
(2+)
2+
3(+)
2+
(3-)
(2+)
(2+)
2,3-
1690.6
1694.5
1711.2
1727.4
1729.7
1732.3
1736.9
1739.5
1748.4
1757.5
1757.5
1758.2
1761.7
1769.3
1771.5
1772.1
1779.0
1784.7
1785.2
1786.8
1789.1
1789.3
1790.7
1792.5
1797.0
1798.5
1802.5
1805.2
1807.1
1809.5
1810.5
1812.6
1818.7
1821.5
1825.4
1836.0
1841.0
1841.8
1845.2
11.21 ± 0.61
0.21 ± 0.03
0.27 ± 0.03
0.71 ± 0.07
0.10 ± 0.01
5.34 ± 0.33
0.30 ± 0.24
1.56 ± 0.09
0.79 ± 0.05
0.20 ± 0.02
0.21 ± 0.02
1.31 ± 0.08
7.24 ± 0.37
0.18 ± 0.02
1.17 ± 0.08
1.22 ± 0.07
1.79 ± 0.10
1.15 ± 0.07
0.09 ± 0.01
0.11 ± 0.01
1.28 ± 0.07
0.38 ± 0.04
0.16 ± 0.02
0.90 ± 0.07
0.09 ± 0.01
2.15 ± 0.12
0.00 ± 0.00
0.97 ± 0.06
0.56 ± 0.05
0.22 ± 0.04
2642.0
3042.3
2345.2
3047.1
2667.7
2862.6
2503.6
2880.9
2687.1
J1tf
930.8
1048.1
1282.4
1314.7
1314.7
1318.6
1314.7
930.8
2+
0+
4+
11-
2+
12+
(2)
1-
1,2+
1+,2,3-
0+
1314.7
615.5
1314.7
1+,2 930.8
2,31123.4
2+,3,4+ 755.5
2+
1123.4
1,2+
930.8
3400.9
2+,3
3080.3
2524.1
2880.9
3205.8
2709.7
2540.3
3335.3
2401.8
2719.6
2133.6
2544.6
2901.9
2919.9
2729.3
2558.1
2853.3
3499.6
2932.6
2919.9
2742.4
2+,3,4+
1318.6
755.5
1109.4
1434.1
930.8
755.5
2+,3,4+ 1550.2
2+
615.5
2+
930.8
2+
344.3
(2+)
755.5
-1109.4
2,31123.4
2+
930.8
2+
755.5
1,2+
1048.1
2+,31692.5
2+
1123.4
2,31109.4
930.8
2928.1
2437.8
2169.8
2946.7
2964.1
2773.1
2776.4
2+
2+
2-3(+)
2+,3
2+,3,4+
1643.9
2+
2+
2+
2+
3+
1109.4
615.5
344.3
1109.4
1123.4
930.8
930.8
1-
2+
34+
32+
22+
4+
2+
3+
2+
4
4+
0+
2+
2+
4+
2+
32+
4+
0+
3
32+
2+
2+
0+
2+
2+
32+
2+
170
Appendix 1 Energy Sorted tray list. (Continued)
Ey
1857.5
1862.3
1870.9
1875.1
1876.4
1886.4
1890.4
1894.3
1896.9
1897.1
1901.9
1902.6
1908.4
1913.2
1916.1
1918.0
1921.1
1928.9
1932.2
1933.2
1941.3
1950.1
1951.5
1954.0
1955.8
1956.8
1965.5
1970.4
1970.8
1974.0
1975.8
1983.5
1993.8
1996.0
2004.1
2012.2
2015.3
2018.1
2021.4
2021.9
2033.9
2043.1
2043.8
Absi
L1
2.79 ± 0.15
6.83 ± 0.39
0.21 ± 0.02
0.25 ± 0.04
0.23 ± 0.02
0.65 ± 0.05
0.40 ± 0.05
0.38 ± 0.03
0.25 ± 0.04
0.41 ± 0.06
0.49 ± 0.06
28.27 ± 1.43
0.26 ± 0.02
0.98 ± 0.06
0.31 ± 0.04
0.40 ± 0.05
6.68 ± 0.34
0.24 ± 0.02
0.09 ± 0.02
0.62 ± 0.07
11.60 ± 0.58
0.20 ± 0.03
0.21 ± 0.03
0.14 ± 0.03
5.00 ± 0.27
0.23 ± 0.02
0.27 ± 0.03
0.73 ± 0.08
0.13 ± 0.02
0.07 ± 0.01
1.13 ± 0.06
1.46 ± 0.09
1.75 ± 0.10
0.08 ± 0.01
0.13 ± 0.03
0.35 ± 0.11
0.30 ± 0.02
0.46 ± 0.04
0.14 ± 0.03
0.09 ± 0.01
2.59 ± 0.15
1.15 ± 0.07
0.41 ± 0.05
2201.8
1862.2
2+
2+
3153.2
2+,3,4+
3189.7
2999.8
3009.4
2999.8
3212.9
3212.9
3006.5
2+
(2+)
2+
1+,2+
1+,2+
(3-)
3012.1
2247.0
2524.1
2+,3,4+
2258.2
3025.3
3233.0
2265.5
2544.6
2862.6
3042.3
1941.5
2880.9
3265.5
2882.9
2300.0
3080.3
3088.3
3285.2
2901.9
2729.3
1975.8
2327.6
2749.2
-2+,3,4+
2928.1
2347.8
3325.2
2946.7
2773.1
2776.4
3340.8
2964.1
2387.3
3153.2
2+
2+
2+32(+I-)
(2+)
2,3(2+)
2+
2+
1-,2,32+
22+,3,4+
(2+)
1-,2
-2+
2+
2,3+
3+
2+
1,2+
2+
-2+,3
2+,3,4+
(2+)
3(+)
1-,2-32+,3,4+
L
Jf
344.3
0.0
1282.4
1314.7
1123.4
1123.4
1109.4
1318.6
1314.7
1109.4
1109.4
344.3
615.5
344.3
1109.4
1314.7
344.3
615.5
930.8
1109.4
0.0
930.8
1314.7
930.8
344.3
1123.4
1123.4
1314.7
930.8
755.5
0.0
344.3
755.5
930.8
344.3
1314.7
930.8
755.5
755.5
1318.6
930.8
344.3
1109.4
2+
0+
4+
1-
332+
2+
1-
2+
2+
2+
0+
2+
2+
1-
2+
0+
2+
2+
0+
2+
1-
2+
2+
331-
2+
4+
0+
2+
4+
2+
2
1-
2+
4+
4+
2+
2+
2+
2+
171
Appendix 1 Energy Sorted tray list. (Continued)
Ey
2044.2
2050.9
2051.9
2058.2
2059.2
2069.1
2075.5
2076.0
2078.8
2086.5
2092.7
2093.5
2094.0
2102.8
2104.1
2108.4
2111.7
2113.6
2118.6
2127.3
2128.2
2128.7
2140.3
2150.2
2150.9
2158.8
2161.7
2168.6
2168.9
2172.1
2176.0
2177.0
2180.0
2181.7
2181.9
2184.8
2185.0
2190.9
2195.9
2201.4
2201.8
2208.5
2209.1
Abs)
0.34 ± 0.07
0.37 ± 0.03
0.13 ± 0.01
0.23 ± 0.03
0.10 ± 0.01
1.58 ± 0.09
0.57 ± 0.08
0.74 ± 0.05
1.40 ± 0.10
0.42 ± 0.05
0.15 ± 0.02
1.90 ± 0.10
1.34 ± 0.09
0.31 ± 0.04
0.47 ± 0.03
0.20 ± 0.02
0.25 ± 0.05
1.51 ± 0.10
0.90 ± 0.06
0.14 ± 0.02
0.32 ± 0.04
0.30 ± 0.02
0.15 ± 0.02
0.34 ± 0.03
3.95 ± 0.23
1.34 ± 0.08
0.57 ± 0.04
0.59 ± 0.04
0.54 ± 0.06
0.59 ± 0.04
0.28 ± 0.04
0.45 ± 0.03
1.15 ± 0.18
0.28 ± 0.03
0.29 ± 0.03
0.29 ± 0.04
4.07 ± 0.25
0.42 ± 0.04
1.36 ± 0.12
0.22 ± 0.01
0.22 ± 0.02
0.30 ± 0.03
0.22 ± 0.02
L1
3359.3
2981.5
2667.7
2401.8
3182.5
2999.8
3006.5
2691.8
3009.4
2430.7
3139.8
2437.8
2709.7
3212.9
2719.6
3233.0
3042.3
2729.3
2734.3
3250.9
3236.5
2882.9
3265.5
3080.3
2495.2
2914.2
3285.2
3098.9
2513.3
2928.1
3285.2
2932.6
2524.1
3112.5
3305.3
3499.6
2529.6
3314.7
2540.3
2201.8
3132.4
3139.8
2964.1
L
Jf
1314.7
1-
2+,3,4+ 930.8
1+,2+
615.5
2+
344.3
2+,3,4+ 1123.4
2+
930.8
(3-)
930.8
1+,2+
615.5
(2+)
930.8
2+
0+
2+
32+
2+
0+
2+
1-,2,3-
--
344.3
2+
2+
2+
1048.1
2+
0+
344.3
615.5
1109.4
2+
0+
2+
2+
2+,3(2+)
615.5
1123.4
2+
1+
615.5
0+
32+
0+
615.5
1123.4
0+
3-
1,2+
2+,3,4+
930.8
1109.4
2+
755.5
1-,2,3- 1123.4
2+,3,4+ 930.8
1-,2
344.3
2+
755.5
1-,2
1123.4
2+,3+
930.8
4+
3-
344.3
2+
2+
2+
2+
2+
4+
32+
1,2+
2+
1-,2
755.5
4+
1109.4
2+
2+
2+
1.2+
755.5
344.3
930.8
4+
2+
2+
3-
--
1123.4
2+,3-
1314.7
1-
3(+)
-3+
2+
--
344.3
1123.4
2+
32+
0+
2+
2+
4+
2+
3(+)
344.3
0.0
930.8
930.8
755.5
172
Appendix 1 Energy Sorted tray list. (Continued)
Ey
Abs I
L.
L
Jf
2211.7
0.21 ± 0.03
3335.3
2+,3,4+
1123.4
3-
2213.2
0.17 ± 0.02
3143.8
2+, 3,4+
930.8
2+
3-
2217.4
0.93 ± 0.06
3340.8
(2+)
1123.4
2220.9
0.21 ± 0.03
3534.9
2+
1314.7
1-
2223.4
0.10 ± 0.01
3153.2
2+,3,4+
2225.9
2233.4
0.35 ± 0.02
2981.5
2+,3,4+
930.8
755.5
0.09 ± 0.01
3164.8
2236.1
0.21 ± 0.02
2580.4
--
344.3
2+
4+
2+
2+
2236.2
0.16 ± 0.02
3359.3
1-,2,3-
1123.4
3-
2246.4
0.33 ± 0.03
2247.0
2+
0.0
0+
4+
2+
2+
4+
2+
2+
930.8
2251.2
1.22 ± 0.09
3006.5
(3-)
755.5
2251.6
0.12 ± 0.02
3182.5
2+,3,4+
930.8
2254.7
1.78 ± 0.14
2599.0
(2+)
344.3
2256.6
0.28 ± 0.02
3012.1
2+,3,4+
755.5
2259.6
2259.9
0.18 ± 0.03
3189.7
1.15 ± 0.08
2604.4
2(-)
344.3
2262.4
0.25 ± 0.03
3386.4
2+2,4+
2265.1
1.21 ± 0.08
2880.9
2+
1123.4
615.5
2270.0
2275.4
0.09 ± 0.01
3025.3
2+,3,4+
0.20 ± 0.03
3205.8
2+
755.5
930.8
2276.7
0.35 ± 0.03
3400.9
2+,3
1123.4
3-
2281.3
0.29 ± 0.04
3212.9
1+,2+
930.8
2298.8
0.26 ± 0.02
2914.2
0.58 ± 0.07
3236.5
2+
2+
615.5
2306.0
2306.5
0.04 ± 0.01
2923.8
1,2+
2311.5
2313.0
0.33 ± 0.03
3066.5
2+,3
0.03 ± 0.01
2928.1
2317.5
0.17 ± 0.02
2932.6
2+
2+
2320.1
0.07 ± 0.02
3250.9
2+,3,4+
930.8
2324.4
2327.2
0.32 ± 0.03
24,3,4+
0.06 ± 0.01
3080.3
3450.0
24,3,4
755.5
1123.4
2+
0+
2+
0+
4+
0+
0+
2+
4+
2334.0
0.10 ± 0.01
3088.3
(2+)
755.5
2335.0
0.14 ± 0.02
3265.5
1-,2,3-
930.8
2342.5
2.28 ± 0.12
2687.1
1,2+
344.3
2347.7
0.86 ± 0.05
2347.8
1,2+
0.0
2348.5
2350.0
0.74 ± 0.05
2691.8
1,2+
344.3
0.20 ± 0.02
3106.6
2+
755.5
2354.3
0.38 ± 0.05
3285.2
1-,2
930.8
2360.3
0.29 ± 0.03
3484.1
2+,3,4+
1123.4
3-
2365.1
7.44 ± 0.39
2709.7
2+
344.3
2367.5
0.09 ± 0.01
3122.6
2+,3,4+
755.5
2375.2
14.32 ± 0.75
2719.6
2+
344.3
2+
4+
2+
2376.3
0.39 ± 0.04
3499.6
2+,3-
1123.4
3-
930.8
930.8
615.5
755.5
615.5
615.5
3-
0+
4+
2+
3-
4+
2+
2+
0+
2+
4+
2+
173
Appendix 1 Energy Sorted ray list. (Continued)
Ey
2378.7
2382.4
2384.3
2388.8
2397.2
2397.8
2404.8
2405.0
2411.9
2420.1
2426.0
2426.9
2428.5
2429.9
2436.3
2440.9
2449.9
2462.7
2471.9
2479.0
2482.2
2488.8
2495.4
2495.7
2497.0
2513.8
2518.2
2524.4
2525.1
2536.3
2551.1
2554.9
2557.7
2569.9
2570.8
2572.2
2575.1
2579.5
2583.9
2585.2
2588.2
2596.9
2598.9
Abs I
0.05 ± 0.02
0.36 ± 0.04
2.15 ± 0.12
0.32 ± 0.03
0.32 ± 0.03
1.42 ± 0.09
23.38 ± 1.22
0.22 ± 0.04
0.27 ± 0.03
0.25 ± 0.05
0.22
±
0.04
0.19 ± 0.02
0.19 ± 0.03
0.64 ± 0.11
0.14 ± 0.02
0.11 ± 0.02
0.14 ± 0.02
0.16
±
0.03
0.10 ± 0.01
0.26 ± 0.04
0.15 ± 0.03
1.02 ± 0.09
0.50 ± 0.05
0.82 ± 0.04
0.34 ± 0.05
0.08 ± 0.02
4.25 ± 0.27
1.77 ± 0.09
0.48 ± 0.08
5.18 ± 0.31
1.13 ± 0.10
0.23 ± 0.03
0.53 ± 0.03
6.63 ± 0.35
0.09
0.30
± 0.01
± 0.03
1.26 ± 0.11
1.31 ± 0.13
2.80 ± 0.21
0.55 ± 0.04
6.62 ± 0.34
0.33 ± 0.05
0.42 ± 0.03
L1
3134.6
3139.8
2729.3
3143.8
3153.2
2742.4
2749.2
3335.3
3534.9
3350.9
3534.9
3182.5
3359.3
2773.1
3367.3
3551.2
3205.8
3572.9
3226.3
3233.0
3236.5
2833.1
3250.9
2495.2
3112.5
2513.3
2862.6
2524.1
3139.8
2880.9
2895.4
3309.7
2558.1
2914.2
3325.2
3502.6
2919.9
2923.8
2928.1
3340.8
2932.6
3212.9
2599.0
J'
L
2+
2+
2+
755.5
755.5
344.3
755.5
755.5
344.3
344.3
930.8
1123.4
930.8
1109.4
755.5
930.8
344.3
930.8
1109.4
755.5
1109.4
755.5
755.5
755.5
344.3
755.5
0.0
615.5
0.0
344.3
0.0
615.5
344.3
344.3
755.5
0.0
344.3
755.5
930.8
344.3
344.3
344.3
755.5
344.3
615.5
0.0
2+, 3,4+
2+,3,4+
-3+
2+,3,4+
2+
-2+
2+,3,4+
1-,2,32+,3
--
2+,3,4+
2+
--
2+,3,4+
2+,32+
1,2+
2+,3,4+
1-,2
1.2+
1,2+
2,32+
2+
2+
--
2+,3,4
2+
2+
2+
--
2,31,2+
2+
(2+)
2+
1+,2+
(2+)
Jf
4+
4+
2+
4+
4+
2+
2+
2+
32+
2+
4+
2+
2+
2+
2+
4+
2+
4+
4+
4+
2+
4+
0+
0+
0+
2+
0+
0+
2+
2+
4+
0+
2+
4+
2+
2+
2+
2+
4+
2+
0+
0+
174
Appendix 1 Energy Sorted ray list. (Continued)
E1
Abs I
J1
L1
2602.5
3.20 ± 0.19
2946.7
--
344.3
2603.8
0.19 ± 0.03
3534.9
2+
930.8
2608.0
0.09 ± 0.02
3539.0
--
930.8
2619.1
4.68 ± 0.24
2964.1
3(+)
344.3
2619.3
2629.7
0.06 ± 0.01
3551.2
2+,3,4+
930.8
2+
2+
2+
2+
2+
0.15 ± 0.01
3386.4
2+,2,4+
755.5
4+
2635.9
2637.2
0.06 ± 0.01
3567.8
2+,3,4+
930.8
0.45 ± 0.04
2981.5
2+,3,4+
344.3
2644.5
0.38 ± 0.03
3400.9
2+,3
755.5
2655.0
0.17 ± 0.01
3269.9
1,2+
615.5
2655.1
2.33 ± 0.20
2999.8
2+
344.3
2662.3
3.04 ± 0.39
3006.5
(3-)
344.3
2665.0
2.88 ± 0.62
3009.4
(2+)
344.3
2668.0
2.34 ± 0.29
3012.1
2+,3,4+
344.3
2681.0
1.68 ± 0.19
3025.3
2+,3,4+
344.3
755.5
2+
2+
4+
0+
2+
2+
2+
2+
2+
4+
0+
4+
2+
2+
0+
0+
0+
2+
4+
0+
0+
2+
2+
4+
4+
2+
2+
2+
2+
4+
2+
2+
4+
2+
2+
4+
L1
2684.1
0.05 ± 0.01
3439.2
2+,3,4+
2687.9
0.65 ± 0.03
2687.1
1,2+
0.0
2694.3
0.12 ± 0.01
3450.0
2+,3,4
755.5
2697.8
2702.8
3.80 ± 0.29
1.46 ± 0.11
3042.3
(2+)
3047.1
1+,2,3-
344.3
344.3
2709.9
3.21 ± 0.16
2709.7
2710.7
0.20 ± 0.02
3325.2
615.5
2719.9
5.33 ± 0.27
2719.6
2+
2+
2+
2722.2
2.80 ± 0.22
3066.5
2+,3
344.3
0.0
0.0
2728.9
0.13 ± 0.02
3484.1
2+,3,4+
755.5
2728.9
0.29 ± 0.02
2729.3
2+
0.0
2734.4
1.42 ± 0.07
2734.3
1+
0.0
2740.8
2743.9
0.26 ± 0.11
3085.3
1,2+
344.3
1.52 ± 0.21
344.3
0.23 ± 0.02
3088.3
3499.6
(2+)
2744.1
2+,3-
755.5
2751.7
0.16 ± 0.02
3508.9
(2+)
755.5
2754.5
1.97 ± 0.24
3098.9
2+,3+
344.3
2768.3
0.58 ± 0.07
3112.5
1.2+
344.3
2772.5
2778.2
0.12 ± 0.03
3703.4
--
930.8
0.51 ± 0.06
3122.6
2+,3,4+
344.3
2779.8
0.05 ± 0.01
3534.9
2+
755.5
2787.9
0.46 ± 0.06
3132.4
--
344.3
2795.5
1.47 ± 0.19
3139.8
2+
344.3
2796.7
0.17 ± 0.01
3551.2
2+,3,4+
755.5
2799.2
0.70 ± 0.15
3143.8
2+, 3,4+
344.3
2808.8
0.89 ± 0.11
3153.2
2+,3,4+
344.3
2811.9
0.07 ± 0.01
3567.8
2+,3,4+
755.5
J'tf
175
Appendix 1 Energy Sorted ray list. (Continued)
E'y
Abs I
L
J'1
Lf
2820.6
2833.5
2838.2
0.49 ± 0.06
--
344.3
0.13 ± 0.01
3164.8
2833.1
1,2+
0.0
0.45 ± 0.06
3182.5
2+,3,4+
344.3
2844.6
0.16 ± 0.03
3189.7
--
344.3
2861.1
1.09 ± 0.07
3205.8
2+
344.3
2869.3
0.74 ± 0.05
3212.9
1+,2+
344.3
2882.0
2882.5
0.89 ± 0.08
3226.3
2+,3,4+
344.3
1.90 ± 0.10
2882.9
2+
0.0
2888.8
0.56 ± 0.06
3233.0
2+,3-
344.3
2892.7
2906.7
2915.1
0.86 ± 0.08
3236.5
2+
344.3
0.86 ± 0.06
3250.9
2+,3,4+
344.3
0.25 ± 0.01
2914.2
2+
0.0
2921.6
0.25 ± 0.03
3265.5
1-,2,3-
344.3
2927.6
2940.9
0.72 ± 0.04
2928.1
2+
0.0
2.94 ± 0.19
3285.2
1-,2
344.3
2961.0
0.65 ± 0.08
3305.3
--
344.3
2965.7
2971.2
0.31 ± 0.06
3309.7
2+,3,4+
344.3
0.22 ± 0.05
3314.7
--
344.3
2980.5
2995.2
1.35 ± 0.24
3325.2
2+
344.3
1.62 ± 0.15
3340.8
(2+)
344.3
3001.2
0.40 ± 0.03
2999.8
2+
0.0
3008.4
3015.3
0.15 ± 0.01
3009.4
(2+)
0.0
0.51 ± 0.05
3359.3
1-,2,3-
344.3
3023.1
0.72 ± 0.13
3367.3
--
344.3
3042.5
0.84 ± 0.07
3386.4
2+,2,4+
344.3
3056.6
0.92 ± 0.09
3400.9
2+,3
344.3
3068.7
3085.7
0.44 ± 0.05
3413.1
1,2+
344.3
0.22 ± 0.04
3085.3
1,2+
0.0
3088.5
0.09 ± 0.03
3088.3
(2+)
0.0
3094.8
0.27 ± 0.02
3439.2
2+,3,4+
344.3
3107.1
0.46 ± 0.03
3106.6
3134.9
0.09 ± 0.01
3134.6
2+
2+
0.0
3139.9
0.52 ± 0.10
3484.1
2+,3,4+
344.3
3140.6
3158.3
0.38 ± 0.02
3139.8
2+
0.0
1.85 ± 0.35
3502.6
--
344.3
3164.7
3.62 ± 0.61
3508.9
(2+)
344.3
3174.5
1.14 ± 0.19
3518.8
3190.0
0.58 ± 0.12
3534.9
3194.9
0.12 ± 0.05
3539.0
3206.2
0.57 ± 0.03
3205.8
2+
0.0
3223.6
1.02 ± 0.19
3567.8
2+,3,4i-
344.3
3228.8
0.66 ± 0.13
3572.9
--
344.3
0.0
344.3
2+
344.3
344.3
Jf
2+
0+
2+
2+
2+
2+
2+
0+
2+
2+
2+
0+
2+
0+
2+
2+
2+
2+
2+
2+
0+
0+
2+
2+
2+
2+
2+
0+
0+
2+
0+
0+
2+
0+
2+
2+
2+
2+
2+
0+
2+
2+
176
Appendix 1 Energy Sorted
Ey
Abs I
ray list. (Continued)
L,
J
Lf
Jf
0.94 ± 0.10
3236.5
2+
0.0
3245.1
0.09 ± 0.03
3589.4
--
344.3
3251.8
0.12 ± 0.03
3596.1
--
344.3
3269.6
0.23 ± 0.02
3269.9
1,2+
0.0
3276.6
3283.9
3311.5
0.32 ± 0.06
3620.9
--
344.3
0.23 ± 0.05
3628.1
-
344.3
0.04 ± 0.01
3655.7
--
344.3
3324.9
0.64 ± 0.04
3325.2
2+
0.0
3329.0
0.18 ± 0.01
3329.0
1,2+
0.0
3338.4
0.07 ± 0.01
3340.8
(2+)
0.0
3365.1
0.10 ± 0.02
3709.4
--
344.3
3381.2
0.07 ± 0.00
3381.2
1,2+
0.0
3413.4
0.10 ± 0.01
3413.1
1,2+
0.0
3535.9
3574.6
0.02 ± 0.00
3534.9
2+
0.0
0.06 ± 0.01
3574.6
1,2+
0.0
0+
2+
2+
0+
2+
2+
2+
0+
0+
0+
2+
0+
0+
0+
0+
3235.3
177
9. References
R.M. Steffen and K. Alder in The Electromagnetic Interaction in Nuclear
Spectroscopy, edited by W.D. Hamilton (Amsterdam, Holland: North-Holland
Publishing Company, 1975, Ch. 1)
2
K.S.Krane and R.M. Steffen, Phys. Rev. C 2, 724 (1971)
K.E.G. Löbner, The Electromagnetic Interaction in Nuclear Spectroscopy edited by
W.D. Hamilton (Amsterdam, Holland: North-Holland Publishing Company, 1975, Ch.
5)
'I
P. Schmelzenbach, The Study of'505m Through the Beta Decay of'50Pm, '5OmEu and
Doctoral Thesis: Oregon State University (2003)
R.M. Steffen and K. Alder in The Electromagnetic Interaction in Nuclear
Spectroscopy, edited by W.D. Hamilton (Amsterdam, Holland: North-Holland
Publishing Company, 1975, Ch. 2)
6
K.S. Krane, Introductory Nuclear Physics (New York: John Wiley & Sons, Inc.,
1988)
J.L. Wood, E.F. Zganjar, C. De Coster, and K. Heyde, Nuci. Phys. A 651, 323
(1999)
8
j Kantele, Handbook of Nuclear Spectrometry (San Diego, CA: Academic Press
Inc., 1995)
HSICC online internal conversion coefficient calculator
http://iaeand.iaea.org/physco/ Accessed 4-2004.
10
D.A.Bell, C.E. Aveldo, M.G.Davidson, and J.P.Davidson, Can. J. Phys. 48, 2542
(1970)
"K. Siegbahn, Alpha, Beta, and Gamma-Ray Spec! roscopy (Amsterdam, North
Holland Publishing Company, 1965)
12
K. S. Krane, Table of Coefficients for Analysis ofAngular Distribution of Gamma
Radiation from Oriented Nuclei, Los Alamos Report LA-4677, 1971.
13
R.M. Steffen and K. Alder in The Electromagnetic Interaction in Nuclear
178
Spectroscopy, edited by W.D. Hamilton (Amsterdam. Holland: North-Holland
Publishing Company, 1975, Ch. 12).
14
A. R. Edmonds, Angular momentum in Quantum Mechanics (Princeton, N.J.,
Princeton University Press 1957)
15
KS. Krane, Nuci. Instr. Meth. 98, 205 (1972)
16
K.S. Krane, Nuci. Instr. Meth. 109, 401 (1973)
17
G. Audi and A. H. Wapstra, Nucl. Phys. A 565, 1 (1993)
18
M.A. Preston and R.K. Bhaduri, Structure of the Nucleus (Reading MA, AddisonWesley Publishing Company, Inc. 1975)
19
R. F. Casten, Nuclear Structure from a Simple Perspective (New York: Oxford
University Press, 1990)
20
D.G. Flemining, C. GUnther, G Hagemann, B. Herskind, and P. Tjøm, Phys. Rev. C
8, 806 (1973)
21
D.G. Flemming, C. GUnther, G Hagemann, B. Herskind, and P. Tjøm Phys Rev.
Lett. 27, 1235 (1971)
22
23
T.W. Elze, J.S. Boyno, and J.R. Huizenga, Nucl. Phys. A 187, 473 (1972)
R. Bloch, B. Elbek, and P.O. Tjøm, Nucl. Phys. A 91, 576 (1967)
24
K.Ya. Gromov, V.V.Kuznetsov, M.Ya.Kuzinetsova, M.Finger, J.Urbanec,
O.B.Nielsen, K.Wilsky, O.Skillbriet and M.Jorgensen, Nuci. Phys. A 99, 585 (1967)
25
j Kormicki, H. Niewodniczanski, Z. Stachura, K. Zuber, and A. Budziak, Acta
Phys.Polon. 31, 317 (1967)
26
B. Harmatz and T. Handley, Nuci. Phys. A 121, 481 (1968)
27
A. T. Strigachev, D. S. Novikov, A. A. Sorokin, V. A. Khalkin, N. B. Levetkova,
and V.S.Shpinel, Izvest. Akad. Nauk SSSR, Ser. Fiz. 25, 813 (1961)); Columbia
Tech. Transl. 25 824 (1962)
28
A. S. Basina, K. Y. Gromov, and B. S. Dzhelepov, Izvest. Akad. Nauk SSSR, Ser.
It'
Fiz. 24, 813 (1961)
29
30
j Frana, I. Rezanka, M. Vobecky, and V. Husak, Czech. J. Phys. 10, 692 (1960)
K.S.Toth, O.B.Nielsen, and O.Skilbreid, Nuci. Phys. 19, 389 (1960)
31
G. N. Flerov, S. A. Karamyan, G. S. Popeko, A. G. Popeko, and 1. A. Shelaev, Yad.
Fiz. 15, 1117 (1972); Soy. J. Nuci. Phys. 15, 618 (1972)
32
J. Adam, P. Galan, K. Y. Gromov, Z. T. Zhelev, V. V. Kuznetsov, M. Y.
Kuznetsova, N. A. Lebedev, 0. B. Nielsen, T. Pazmanova, J. Urbanec, and M. Finger,
Izv. Akad. Nauk SSSR, Ser. Fiz. 34, 813 (1970); Bull. Acad. Sci. USSR, Phys. Ser.
34, 722 (1971)
u
D. R. Zolnowski, E. G. Funk, and J. W. Mihelich, Nuci. Phys. A 177, 513 (1971)
' WWW Table of Radioactive Isotopes
http://nucleardata.nuclear. lu. se/nucleardataltoilnucSearch.asp, Accessed 4-2004.
u
Adam, J. Dobes, M. Honusek, V.G. Kalinnikov, J. Mrázek, V.5. Pronskikh, P.
Caloun, N. A. Lebedev, V. I. Stegailov, and V. M. Tsoupko-Sitnikov, The European
Physical Journal A 18, 605 (2003)
36
Agda Artna-Cohen, Nuc!. Data Sheets 79, 1 (1996)
N. M. Antoneva, A. A. Bashilov, B. S. Dzhelepov, and B. K. Preobrazhenskii,
Dokiady Akad. Nauk SSSR 119, 241 (1958); Soviet Phys. Dokiady 3, 289 (1958)
38
Y. Gono, M. Fujioka, and T. Toriyama, J. Phys. Soc. Jap. 29, 255 (1970)
R. A. Meyer, Fizika (Zagreb) 22, 153 (1990)
40N. M. Stewart, E. Eid, M. S. S. El-Daghmah, and J. K. Jabber, Z. Phys. A 335, 13
(1990)
41
D. Mehta, M. L. Garg, J. Singh, N. Singh, T. S. Cheema, and P. N. Trehan, Nucl.
Instrum. Methods Phys. Res. A 245, 447 (1986)
42y Yan, H. Sun, D.Hu, J. Huo, and Y. Liu, Z. Phys. A 344, 25 (1992)
Kawaldeep, V. Kumar, K. S. Dhillon, and K. Singh, J. Phys. Soc. Jpn. 62, 901
180
(1993)
'' A.K.Sharma, R. Kaur, H. R. Verma, and P. N. Trehan, J. Phys. Soc. Jpn. 48, 1407
(1980)
'
H.S.Pruys, E.A.Hermes, and H.R.Von Gunten, J. Inorg. Nuci. Chem. 37, 1587
(1975)
46
U.Schneider and U. Hauser, Z. Phys. A 273, 239 (1975)
'
J. Barrette, M. Barrette, A. Boutard, G. Lamoureux, S. Monaro, and S. Markiza,
Can. J. Phys. 49, 2462 (1971)
48
D. R. Zolnowski, M. B. Hughes, J. Hunt, and T. T. Sugihara, Phys. Rev. C 21, 2556
(1980)
w
z
W. Bowman, T. T. Sugihara, and F. R. Hamiter, Phys. Rev. C 3, 1275 (1971)
50
C.A. Kalfas, W. D. Hamilton, R.A. Fox, and M. Finger, Nuci. Phys. A 196, 615
(1972)
51
Ferencei, M. Finger, J. Dupák, A. Jankech, J. Koniek, F. A. Schus, J. Rikovská,
A. Machová, andD.W. Hamilton, Czech. J. Phys. B 31, 511 (1981)
52p 0. Lipas, J. Kumpulainen, E. Hammaren, T. Honkaranta, M. Finger, T. I.
Kracikova, I. Prochazka, and J. Ferencei, Phys. Scr. 27, 8 (1983)
53H. Tagziria, M. Elahrash, W. D. Hamilton, M. Finger, J. John, P. Malinsky, and
V.N. Pavlov, J. Phys.(London) G 16, 1323 (1990)
M. Asai, K. Kawade, H. Yamamoto, A. Osa, M. Koizumi, and T. Sekine, Nuci.
Instrum. Methods Phys. Res. A 398, 265 (1997)
P. 0. Lipas, P. Toivonen, and E. Hammarn, Nucl. Phys. A 469, 348 (1987)
56
D. S. Chuu, C. S. Han, S. T. Hsieh, and M. M. King Yen, Phys. Rev. C 30, 1300
(1984)
A Gómez and 0. CastinOs, Nuci. Phys. A 598, 267 (1995)
58
0. Engel, U. Hartmann, A. Richter and H. J. WOrtche, Nucl. Phys. A 515, 31(1990)
181
R. F. Casten, W. Frank, and P. von Brentano, Nuci. Phys. A 444, 133 (1985)
60
A. Armina and F. lachello, Ann. Phys. (N.Y.) 281, 2 (2000)
61
J. Kern, P. E. Garret, J. Jolie, and H. Lehinann, Nuc!. Phys. A 593, 21(1995)
62
C. S. Han, D. S. Chuu,., S. T Hsieh, and H. C. Chiang, Phys. Lett. B 163, 295
(1985)
63
A. M. Demidov, L. I. Govor, V. A. Kurkin, and I. V. Mikhailov, Yad. Fiz. 60, 581
(1997); Phys. At. Nuci. 60, 503 (1997)
64
Y.M.Zhao and Y. Chen, Phys. Rev. C 52, 1453 (1995)
65
M. Sambataro, 0. Scholten, A. B. L. Dieperink, and G. Piccitto, Nuci. Phys. A 423,
333 (1984)
66
W.D. Kuip Nuclear Structure of the N=90 isotones, Doctoral Thesis: Georgia
Institute of Technology (2001)
67
J. Wood, personal communication 4-2004
68
WWW Table of Radioactive Isotopes
h Up /Lp.çe ardata.nuc lea ru .. 7n ucleardataltoi/nuclide.asp?iZA= 650 152 Accessed 62003
69
John Wood, personal communication 5-2004
70N. R. Johnson, I. Y. Lee, F. K. McGowan, and T. T. Siguhara, Phys Rev. C 26,
1004 (1982)
71
72
M.A.J. Mariscotti, G. Scharff-Goldhaber, and B. Buck, Phys. Rev. 178, 1864 (1969)
J.L. Wood, K. Heyde, W. Nazarewicz, M. Huyse, and P. Van Duppen, Physics
Reports 215, 101 (1992)