Experimental Nuclear Structure
Part I
Filip G. Kondev
kondev@anl.gov
Workshop on “Nuclear Structure and Decay
Data: Theory and Evaluation”, Trieste, Italy
February 20th-March 3rd, 2006
Argonne National Laboratory
Office of Science
U.S. Department of Energy
A U.S. Department of Energy
Office of Science Laboratory
Operated by The University of Chicago
Outline
I) Lecture I: Experimental nuclear structure physics


reactions used to populate excited nuclear states
techniques used to measure the lifetime of a nuclear state
 Coulomb excitation, electronic, specific activity, indirect
 techniques used to deduce Jp

ICC, angular distributions, DCO ratios etc.
II) Lecture II: Contemporary Nuclear Structure Physics at the Extreme



spectroscopy of nuclear K-Isomers
physics with large g-ray arrays
gamma-ray tracking – the future of the g-ray spectroscopy
Have attempted to avoid formulas and jargon, and material
covered by other lecturers – will give many examples
2
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Some Useful Books
“Handbook of nuclear spectroscopy”, J. Kantele,1995
“Radiation detection and measurements”, G.F. Knoll, 1989
“In-beam gamma-ray spectroscopy”, H. Morinaga and T. Yamazaki, 1976
“Gamma-ray and electron spectroscopy in Nuclear Physics”, H. Ejiri and
M.J.A. de Voigt, 1989
“Techniques in Nuclear Structure Physics”, J.B.A. England, 1964
“Techniques for Nuclear and Particle Physics Experiments”, W.R. Leo, 1987
“Nuclear Spectroscopy and Reactions”, Ed. J. Cerny, Vol. A-C
“Alpha-, Beta- and Gamma-ray Spectroscopy”, Ed. K. Siegbahn, 1965
“The Electromagnetic Interaction in Nuclear Spectroscopy”, Ed. W.D.
Hamilton, 1975
Plenty of information on the Web
Pioneering
Science and
Technology
3
Office of Science
U.S. Department
of Energy
Input from many colleagues
C.J. Lister and I. Ahmad, Argonne National Laboratory, USA
M.A. Riley, Florida State University, USA
I.Y. Lee, Lawrence Berkeley National Laboratory, USA
D. Radford, Oak Ridge National Laboratory, USA
A. Heinz, Yale University, USA
C. Svensson, University of Guelph, Canada
G.D. Dracoulis and T. Kibedi, Australian National University, Australia
J. Simpson, Daresbury Laboratory, UK
E. Paul, University of Liverpool, UK
P. Reagan, University of Surrey, UK
and many others …
4
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
~6000 nuclei
are predicted
to exist
~3000
~3000 the
knowledge is very
limited!
5
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Introduction
 The nucleus is one of nature’s most interesting quantal fewbody systems
 It brings together many types of behaviour, almost all of
which are found in other systems
 The major elementary excitations in nuclei can be associated
with single-particle and collective modes.
 While these modes can exist in isolation, it is the interaction
between them that gives nuclear spectroscopy its rich
diversity
6
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
The Nucleus is Unique!
 Its uniqueness arises on the one hand because all forces of the
nature are presented in the nucleus - strong, electromagnetic,
weak, and even gravity if one considered condensed stellar
objects as a huge number of nuclei held together by the
gravitational attraction, in contrast to all other known physical
objects.
 On the other hand, the small number of nucleons leads to
specific finite-system effects, where even a few particles can
change the “face” of the whole system.
7
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
The Nucleus and other many-body systems
 The physics of the nucleus is not completely secluded from
the other many-body systems known in the nature.
A variety of nuclear properties can be described by the
shell model, where nucleons move independently in their
average potential, in close analogy with the atomic shell
model.
The nucleus often behaves collectively, like a fluid even a superfluid, in fact the smallest superfluid object
known in the nature and there are close analogies both to
condensed matter physics and to familiar macroscopic
systems, such as the liquid drop.
8
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
So to summarize …
NUCLEAR PHYSICS IS A BIG CHALLENGE
(because of complicated forces, energy scale, and sizes involved)
The challenge is to understand how nucleon-nucleon interactions
build to create the mean field or how single-particle motions build
collective effects like pairing, vibrations and shapes
NUCLEAR PHYSICS IS IMPORTANT
(intellectually, astrophysics, energy production, and security)
THIS IS A GREAT TIME IN NUCLEAR PHYSICS
(with new facilities just around the corner we have a chance to
make major contributions to the knowledge - with advances in
theory we have a great chance to understand it all - by compiling
& evaluating data we have a chance to support various
9
applications and to preserve the knowledge for future
generations!)
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
To learn many of the
secrets of the nucleus we have to put it at
extreme conditions and
study how it survives
such a stress!
10
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
11
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Nuclear Reactions – very schematic!
p
t
CN
r
a multi-step process
 Gamma-ray induced
no Coulomb barrier
 Neutron induced
low-spin states
no Coulomb barrier
 Light charged particles,
e.g. p, d, t, a
Coulomb barrier
low-spin states
Pioneering
Science and
Technology
 Heavy Ions (1970 - ????)
 high-spin phenomena
 nuclei away from the line of stability
Office of Science
U.S. Department
of Energy
12
Reactions with Heavy Ions – Classical Picture
R, Rt, Rp – half-density radii
INELASTIC SCATTERING
DIRECT REACTIONS
b – impact parameter
“SOFT” GRAZING
COMPOUND NUCLEUS
Rp
b<R=Rp+Rt
FUSION
b
R
“HARD” GRAZING
Rt
FRAGMENTATION
DEEP INELASTC REACTIONS
DISTANT COLLISION
b>R
E<Vc
ELASTIC SCATTERING
COULOMB EXCITATION
13
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
14
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Heavy Ions at the Coulomb barrier
Many properties of the collision can be quite well estimated by just using conservation
of momentum and energy.
Ecm = Mt / (Mb + Mt) Elab
Energy scale on which fusion starts is determined by Coulomb barrier, Vcb
Vcb = (4pe)-1 ZbZte2 / R = 1.44 ZbZt / 1.16 [(Ab 1/3+At 1/3) + 2] MeV
Lmax = 0.22 R [ m (Ecm – Vcb) ]1/2

Excitation energy is usually lowered by Q-value and K.E. of evaporated particles
E*residue = Ecm + Q – K.E.
Velocity of center-of-mass frame, which is ~ velocity of fused residues
br2 = 2 Mbc2 Elab / [ (Mb + Mt)c2]2
Pioneering
Science and
Technology
15
Office of Science
U.S. Department
of Energy
HI Fusion-Evaporation Reactions
 R  p
l max
2
 (2l  1)T
l 0
l
 p 2 (l max 1) 2
A1 A2
   / 2mECM , m 
A1  A2
2
lmax
Pioneering
Science and
Technology
 2mR 2 
  2 ECM - VC )
  
16
Office of Science
U.S. Department
of Energy
Decay of the Compound Nucleus
 In a typical HI fusionevaporation reaction the final
nucleus is often left with L~6080 hbar and Ex~30-50 MeV
 The excited nucleus cools off
by emitting g-rays - their
typical number is quite large,
usually 30-40 and the average
energy is ~1-2 MeV – it is not a
trivial task to detect all of them
- the big advantage came with
the large g-ray arrays
17
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Channel Selection for g-ray spectroscopy
Detection of Light Charged Particles (a,p,n)
PLUS Efficient, flexible, powerful.....inexpensive.
MINUS Count-rate limited, Contaminant (Carbon etc, isotopic impurities) makes
absolute identification of new nuclei difficult.
CROSS SECTION LOWER LIMIT ~100 mb
~10-4
that is,
Detection of Residues in Vacuum Mass Separator
PLUS True M/q, even true M measurement. With suitable focal plane detector can be
ULTRA sensitive. Suppresses contaminants.
MINUS Low Efficiency
CROSS SECTION LOWER LIMIT ~100 nb
that is
~10-7
Detection of Residues in Gas Filled Separator
Improves efficiency of vacuum separators, at cost of mass information and cleanliness.
In some cases (heavy nuclei) focal plane counters clean up the data for good sensitivity.
18
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Some Channel Selection Detectors
Argonne FMA
USA
Light charged-particle detector
Microball – 96 CsI with photo diodes
USA
Jyvaskyla
RITU
Europe
19
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Calculate Reaction Rates
Reaction Yield/sec.
Y = N b Nt 
Nb = ib/e q
with ib = electric current in amps, q = charge state, e = 1.6 10-19 c
Nt = [Na /A] rx
with Na = Avagadros #, A = Mass # of tgt, r = density in g/cc, x = thickness (cm).
= Cross Section in cm2 .... note 1 barn is 10-24 cm
Accumulated data:
D = Y x TIME x Efficiency
Typical not “far from stability” experiment may have:
ib = 100 nA, q=10, A=100, rx= 10-3 & =1 barn - produces 3x105 reactions/sec
BUT
If partial cross section is 100 nb and efficiency is 10%...... rate is 10 /hour, 10 pb gives
~ 1 every 10 weeks!!!.....the present situation for producing the heavies elements.
20
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
The basic knowledge
What we want to know
Jp,K
 Excitation energy
Ex
excited state
a,b-,b,
EC,p,
fission,
g, ICC
 Quantum numbers
and their projections
 Lifetime
 Branching ratios
T1/2,es
Jp,K
How
T1/2,gs
Eg
00
ground state
stable or,
a, b-, b, EC, p, cluster, fission
 By measuring properties of
signature radiations
21
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
What is Stable?
A surprisingly difficult question with a somewhat arbitrary answer!
CAN’T Decay to something else, BUT
CAN’T Decay is a Philosophical Issue
 Violation of some quantity which we believe is conserved such as
Energy, Spin, Parity, Charge, Baryon or Lepton number, etc.
DOESN’T Decay is an Experimental Issue that backs up the beliefs
Specific Activity: A=dN/dt = lN
Activity of 1 mole of material (6.02 x 1023 atoms) with T1/2=109 y (l2.2 x
10-17 s) is ~0.4 mCi (1 Ci=3.7 x 1010 dps) (or 13 MBq) .... a blazing source, so
it is quite easy to set VERY long limits on stability.
Current limit on proton half-life, based on just counting a tank of water is
T1/2> 1.5 x 1025 yr.
22
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Stable Nuclei: Segre’s Chart
~ 280 Nuclei have Half-lives >106 years
So are (quite) stable against
Decay of their constituents (p,n,e)
N
Weak Decay (b+ b– and E.C.)
a,p,n decays
More complex cluster emission
Fission
(Mostly because of energy conservation)
Pioneering
Science and
Technology
Atomic Number, Z
Office of Science
U.S. Department
of Energy
23
Mean Lifetime
f decay (t ) 
Ae - lt
 le

- lt
- lt
Ae
dt

t
P n (t )   le -lt 'dt '
0
0
Probability for decay of a nuclear state
(normalized distribution function); l decay constant
t
1 - P n (t )  1 -  le

-lt '
dt ' e
-lt
0
Probability that a nucleus will remain at time t
Pioneering
Science and
Technology
Probability that a nucleus will decay within time t
 t     te dt 
0
-lt
1
l
The average survival time (mean lifetime - ) is then the
mean value of this probability
24
Office of Science
U.S. Department
of Energy
Half-life & Decay Width
T1/2: the time required for half the atoms in
a radioactive substance to disintegrate
relation between ,T1/2 and l

T 1/ 2 1

ln 2 l
6.58 10-16
 

 [ s]

[eV]
 |  1 | M | 2 |2
Determine the matrix element
describing the mode of decay
between the initial and final state
25
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
log ft values
log ft  log f  log t
t  T1b/ 2i 
T1/ 2
BRi
partial half-life of a given b(b+,EC) decay branch
f  f b  f n , n  0,1,2...
statistical rate function (phase-space
factor): the energy & nuclear structure
dependences of the decay transition
Decay
Mode
Type
b-
allowed
b-
1st-forb
EC+b allowed
f 0- , f1- , etc.
Pioneering
Science and
Technology
log ft
log f 0log f 0-  log( f1- / f 0- )
log( f 0EC  f 0 )
N.B. Gove and M. Martin, Nuclear Data Tables 10 (1971) 205
26
Office of Science
U.S. Department
of Energy
Hindrance Factor in a-decay
| I i - I f | L | I i  I f |
p ip f  (-1) L
Strong dependence on L
L=0 - unhindered decay (fast)
Exp
T1Exp
(
a
)
T
/ BR
HFi  / 2Theoryi  1/ 2 Theory i
T1/ 2
T1/ 2
T1Theory
/2
M.A. Preston, Phys. Rev. 71 (1947) 865
I. Ahmad et al., Phys. Rev. C68 (2003) 044306
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
27
g-ray decay
I ip i
| I i - I f | L | I i  I f |
p ( EL)  (-1) L
p ( ML)  (-1) L 1
electric multipole
magnetic multipole
Ei
L
pf
If
Ef
Eg  Ei - E f
dipole
quadrupole
octupole
E1:L=1,yes
E2:L=2,no
E3:L=3,yes
E4:L=4,no
E5:L=5,yes
M1:L=1,no
M2:L=2,yes
M3:L=3,no
M4:L=4,yes
M5:L=5,no
2-
0
L  0!
0
E0
1
hexadecapole
8
L  1,2 & 3
E1( M 2, E 3)
6
1
L  2...14
E 2( M 3, E 4...)
L 1
0
M1
28
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Partial lifetime & Transition Probability
exp
T1g/ 2  T1exp
/
BR

T
/2
g
1/ 2 
 Ig i  (1  aTi )
T1exp
/2
Ei
Ig 1
Ig
Ig 2
Ig 3
partial half-life
ln 2
8p ( L  1)  Eg 
 
Pg ( XL : I i  I f )  g 
2 
T1/ 2 L2 L  1)!!  c 
partial g-ray Transition Probability
B ( XL : I i  I f ) 
2 L 1
B( XL : I i  I f )
reduced Transition Probability
I i M ( XL) I f
2
2Ii  1
contains the nuclear structure information
Pioneering
Science and
Technology
29
Office of Science
U.S. Department
of Energy
Hindrance Factor in g-ray decay
FW ( N ) 
B( XL)Theory
B( XL) Exp

T1g/ 2 ( XL) Exp
T1g/ 2 ( XL)Theory
Hindrance Factor: Weisskopf (W): based on spherical
shell model potential
Nilsson (N): based on deformed
Nilsson model potential
… usually an upper limit, but …
T1g/ 2 ( EL)W , sec
ML B ( ML )W , m N fm
2
2 L-2
T1g/ 2 ( ML )W , sec
EL
B ( EL)W , e 2 fm2 L
E1
0.06446 A2 / 3
6.762 A-2 / 3 Eg-3 10-15 M1
1.7905
E2
0.0594 A4 / 3
9.523 A-4 / 3 Eg-5 10-9 M2
1.6501A2 / 3
3.100 A-2 / 3 Eg-5 10-8
E3
0.0594 A2
2.044 A-2 Eg-7 10-2
M3
1.6501A4 / 3
6.655 A-4 / 3 Eg-7 10-2
E4
0.06285 A8 / 3
6.499 A-8 / 3 Eg-9 104
M4
1.7458 A2
2.116 A-2 Eg-9 105
E5
0.06929 A10 / 3
2.893 A-10/ 3 Eg-11 1011 M5
1.9247 A8 / 3
9.419 A-8 / 3 Eg-11 1011
2.202Eg-3 10-14
30
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Quadrupole Deformation
12+
deformed nucleus
10+
I
8+
6+
4+
I=Jw
2+
0+
156Dy
EI=2/2J I(I+1)
B(E2) ~ 200 W.U.
8.16  1013
B ( E 2)  5
[e 2b 2 ]
Eg [keV ] g [ ps ]
5
B( E 2; KI i  KI f ) 
Q02 I i K 20 I f K
16p
(from collective models)
b 2  -7
p
80

7pQ0
49p

80 6eZr02 A2 / 3
 g [ ps ]  (1.58  0.28) 1014E2-4 [keV ]Z -2A2 / 3

1
b2 
466  41
A  E2 [keV ]
1
31
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
2
Octupole Deformation
 E 3[ s]  0.012264  E3-7  [ B( E 3) ]-1
1
E3- [ MeV ]; B( E 3)  [e 2 fm6 ]
1
b3 
4p
ZR 3
B( E 3) 
e2
32
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
K-forbidden decay
w
Deformed, axially symmetric nuclei
K is approximately a good quantum number
each state has not only
Jp but also K
W1
W2 K=W1+W2
 The solid line shows the dependence
of FW on ΔK for some E1 transitions
according to an empirical rule: log FW
= 2{|ΔK| - λ} = 2ν
 i.e. FW values increase approximately
by a factor of 100 per degree of K
forbiddenness
 fn=(Fw)1/n – reduced hindrance per
degree of K forbiddenness
33
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Experimental techniques
 Direct width measurements
 Inelastic electron scattering
 Blocking technique
 Mossbauer technique
34
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Specific Activity
Time Range: a few seconds up to several years
A  lN  A0 e
- t /
 Statistical uncertainties are usually small
 Systematic uncertainties (dead time, geometry, etc.)
dominate
usually want to follow at least 5 x T1/2
Tag on specific signature radiations (a, b, ce or g) in a “singles” mode
Clock
Detector
Source
35
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Specific Activity: Example 1
198
Hg (g , n)197Hg
 More than 270 spectra were measured
 Followed 4 x T1/2
191.4
36
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Specific Activity: Example 2
Si det
C foil
1 GeV pulsed proton beam on 51 g/cm2 ThCx target
on-line mass separation (ISOLDE)/CERN
37
Pioneering
Science and
Technology
H. De Witte et al., EPJ A23 (2005) 243
Office of Science
U.S. Department
of Energy
Very long-lived cases – Example 1
Time Range: longer than 102 yr
A  lN
T1/ 2  ln 2
N
A
the number of atoms estimated by other
means, e.g. mass spectrometry
38
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Very long-lived cases – Example 2
Ap (t )
Ad (t )

ld
ld - l p
Ap , l p
(1 - e
- ( ld - l p ) t
T1/2(250Cf)=13.05 (9) y
daughter
)
250Cf
a
13 y
246Cm
parent
Ad , ld
a
4747 y
242Pu
a
5105 y
mass-separated source
alpha-decay counting technique
T1/2 = 4747 (46) years / Compared to values ranging from
T1/2=2300 up to 6620 years
Pioneering
Science and
Technology
39
Office of Science
U.S. Department
of Energy
Electronic techniques
Time Range: tens of ps up to a few seconds
The “Clock” - TAC, TDC (START/STOP); Digital Clock

START
“singles” – Eg-time, Ea-time

START
“coincidence” – Eg1-Eg2-t ; Ea1-Eg1-t
Ea1-Ea2-t
Difficulties at the boundaries: e.g. for very short– and very long-lived cases!
40
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Prompt Response Function
 all detectors and auxiliary electronics show statistical fluctuations in the
time necessary to develop an appropriate pulse for the “clock”
 depend on the characteristics of the detectors: e.g. light output for
scintillators, bias voltage, detector geometry, etc.
 instrumental imperfections in the electronics – e.g. noise in the
preamplifiers
Some typical values
Detector
FWHM, ps
plastic scintillators
~100
BaF2
~100
Si
~200
Na(I)
~500
Ge
0.6-9 ns
41
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Prompt Response Function: Ge detectors
F ( x, l ) 

 f (t , l ) P( x - t )dt
-
f (t , l )  le -lt (t  0)or  0(t  0)
PRF
decay
1
- ( z /  )2
1
P( z ) 
e 2
 2p
a schematic illustration
PRF depends on:
 the size of the detector
 the energy of the g-ray
42
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Recoil-shadow technique
the shortest lifetime that can be measured is limited by the TOF
thin production target
43
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
One example: 140Dy experiment at ANL
54Fe
+ 92Mo @ 245 MeV
a2n channel, mass 140 only 5% from the total CS
44
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Some of the equipments used …
1 70% Gammasphere HpGe detector
4 25% Golf-club style HPGe detectors
2 LEPS detectors
1 2"x2" Large Area Si detector
2"x2" Si Detector
Pioneering
Science and
Technology
45
Office of Science
U.S. Department
of Energy
140Dy:
Experimental Results
T1/2=7.3 (15) ms
Similar results by the ORNL group, Krolas et al., PRC 65, 2002
Pioneering
Science and
Technology
D.M. Cullen et al., Phys. Lett. B529 (2002)
46
Office of Science
U.S. Department
of Energy
Recoil-decay tagging
47
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
The Heart of RDT: the DSSD
208Pb(48Ca,2n)254No
80 x 80 detector 300 mm strips,
Each with high, low, and delay line
amplifiers, for implant, decay, and
fast-decay recognition.
Data from DSSD showing implant
pattern 40 cm beyond the focal plane
48
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
a-a (parent-daughter) correlations
177Au
Implantation->Decay 1->Decay 2
within a single pixel
Implant
Timescale of Events
a1: 6.12 MeV
0
T1st
a2: 5.7 MeV
Time
T2nd decay
decay
49
Pioneering
Science and
Technology
F.G. Kondev et al. Phys. Lett. B528 (2002) 221
Office of Science
U.S. Department
of Energy
Neutron deficient nuclei
50
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Odd-Z Au (Z=79) isotopes
51
Pioneering
Science and
Technology
F.G. Kondev et al. Phys. Lett. B528 (2002) 221
Office of Science
U.S. Department
of Energy
Odd-Z Au (Z=79) isotopes –sample spectra
52
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
a-g correlations
53
Pioneering
Science and
Technology
I. Ahmad et al., Phys. Rev. C68 (2003) 044306
Office of Science
U.S. Department
of Energy
Pulsed beam technique
the shortest lifetime that can be measured is limited
by the width of the pulsed beam
 Less effective, but …
 well defined “clock”
sensitive to in-beam and
decay events
“singles”: g-time
 coincidence: g-g-time
the longest lifetime that can be measured is limited
by the time interval between the beam pulses
54
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Pulsed beam: g-time
178Ta
176Yb(7Li,5n)
reveals the time history of levels above the
58 ms isomer !
55
Pioneering
Science and
Technology
F.G. Kondev et al. Phys. Rev. C54 (1996) R459
Office of Science
U.S. Department
of Energy
Pulsed beam: g-time (short-lived)
The importance of PRF
In g-time measurements PRF
depends on Eg for a single transition
175Ta
170Er(10B,5n)
56
Pioneering
Science and
Technology
F.G. Kondev et al. Nucl. Phys. A601 (1996) 195
Office of Science
U.S. Department
of Energy
Limitations: Pulsed beam g-time
 Complicated when more than one isomer is presented
 2  1
 Complicated because of contaminations
 Limited time range – e.g. TAC (Ortec 567) – 3 ms
 Rate dependent time distortions
2
prompt
1
Gate 220 keV
1
Gate 350 keV
1
1
I sf
Gate 580 keV
2
prompt
Gate 600 keV
57
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Pulsed beam: g-g-time technique

START
“coincidence” – Eg1-Eg2-t ; Ea1-Eg1-t
Ea1-Ea2-t
58
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
g-g-time: decay of the 9/2- isomer in 175Ta
175Ta
170Er(10B,5n)
59
Pioneering
Science and
Technology
F.G. Kondev et al. Nucl. Phys. A601 (1996) 195
Office of Science
U.S. Department
of Energy
g-g-time: decay of the 21/2- isomer in 179Ta
179Ta
176Yb(7Li,4n)
Why there is a prompt component?
290
60
Pioneering
Science and
Technology
F.G. Kondev et al. Nucl. Phys. A617 (1997) 91
Office of Science
U.S. Department
of Energy
Centroid-shift technique: g-time
Time Range: near PRF
F ( x, l ) 


-

f (t , l ) P ( x - t )dt
M r ( F (t ))   t r F (t )dt
  M1 ( F (t )) - M1 ( P(t ))
-
Introduced by Z. Bay, Phys. Rev. 77 (1950) 419
6 ch x 92 ps = 552 ps
179W
P.M. Walker et al. Nucl. Phys. A (1996)
Pioneering
Science and
Technology
61
Office of Science
U.S. Department
of Energy
Centroid-shift technique: g-g-time

Must be more careful!
The PRF depends on both Eg1 and Eg2
62
Pioneering
Science and
Technology
F.G. Kondev et al. Nucl. Phys. A632 (1998) 473
Office of Science
U.S. Department
of Energy
Coulomb excitations
Time Range: up to hundreds of ps
E  Vcb
Z1 Z 2 e 2

 1
v
19F(1
MeV) on 238U ~1.6
40Ar(152
MeV) on 238U ~130
63
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Intermediate energy Coulomb excitations
  1.5(3) ps
64
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Deduction of Transition Multipolarity
Basic techniques
 Internal conversion electrons
 Angular distributions
 Angular correlations (DCO ratios)
 Gamma-ray polarization
65
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Internal conversion electrons
a
tot
I ce
I ip

 a K  a L  a M  ...
Ig
p
If
Ei
i
f
L
Ef
Intensity ratio
Eg  Ei - E f
Ei  Eg - Bi , i  K , L,...
oo
E0
1
Low energy isomers
10-1 <
50< Z
10-2 - 10-3
10-4 - 10-5
30<Z < 50
Z < 30
 L  2me c

 L  1  E
a K ( EL)  Z 3 
Important for heavy
nuclei, where inner
electron shells are
closer to the nucleus
2



L 5 / 2
Important for lowenergy transitions
66
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Internal conversion electrons
Sensitive to L
allows deduction of the mixing ratios
5/ 2 -
Ei
M1 E2
3/ 2 -
Ef
1 L  4
2 
I g ( E 2)
I g ( M 1)
a M 1/ E 2
a M 1   2a E 2

1  2
M 1, E 2, M 3, E 4
a M 1 - a exp
  exp
a -aE2
2
67
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Direct ICC measurements
Nuclear reactions
Detector
Radioactive source
target
beam
b-rays
68
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Basic electron transporters
Superconducting solenoid
 Broad-range mode – 100 keV up to a few MeV
 Lens mode – finite transmitted momentum bandwidth
(p/p~15-25%) – high peak-to-total ratio
Mini-orange (looks like a peeled orange)
 transmission > 20%
 small size and portability, but
poorer quality
69
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Superconducting Solenoid Spectrometer
70
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Conversion electron measurements
a K (431)  0.056(7)
a L (431)  0.033(4)
a Kth (431)  0.008( E1);0.022( E 2);0.058( E 3);0.067( M 1);0.21( M 2)
K
(431)  1.7(2)
L
K
(431)  6.7( E1);3.9( E 2);1.9( E 3);6.5( M 1);5.2( M 2)
L
a Lth (431)  0.001( E1);0.006( E 2);0.032( E 3);0.010( M 1);0.040( M 2)
E3: L=3, p=yes
178Ta
176Yb(7Li,5n)
Pulsed-beam
technique
71
Pioneering
Science and
Technology
F.G. Kondev et al. Nucl. Phys. A632 (1998) 473
Office of Science
U.S. Department
of Energy
The SACRED Electron Spectrometer
University of Jyväskylä, Finland
72
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Recoil-gated CE spectrum from 208Pb(48Ca,2n)254No
73
Pioneering
Science and
Technology
P.A. Butler et al.,PRL 89 (2002) 202501
Office of Science
U.S. Department
of Energy
ICC from total intensity balances –example 1
Works well for g-rays with energies below about 250 keV

In out-of-beam (or decay) coincidence data
Igtoti  Ig i  (1  aitot )  Igtoto  Ig o  (1  a otot )
aotot  ( Ig e o / Ig e i )  (1  aitot ) -1
i
o
a tot (350)  0.05
a tot (99)  3.9
228/463
1085/463
i
o
74
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
ICC from total intensity balances –example 2
In-beam: only when gating from “above”
Igtoti  Ig i  (1  aitot )  Igtoto  Ig o  (1  a otot )
Igtoti  Igtoto  I sf
577/611
I sf
207/311
75
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Angular Distributions
The gamma-rays emitted from nuclear reactions exhibit angular distributions:
W ( )  1  A22 P2 (cos  )  A44 P4 (cos  )
A22  a 2 A2max ; A44  a 4 A4max
a k ( J i )  r k ( J i ) / Bk ( J i )
r k ( J )  (2 J  1)   (-1) J - m  J , m, J - m | k 0  Pm ( J )
m
The orientation of the nucleus will be
slightly attenuated by the emission of
evaporated particles (n,p,a) and g-rays.
Pm ( J ) 
exp( -m 2 / 2 2 )
J
2
2
exp(
m
/
2

)

m- J
76
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Angular Distributions: Experiment
Measure: the g-ray yield as a function of 
target
Beam direction

 using a single detector – “singles” mode – contaminants
 using a large gamma-ray array – “coincidence” mode - you must be careful!77
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
How to determine the mixing ratios?
I) If both A2 and A4 have been measured – see
E. Der Mateosian and A.W. Sunyar, ADNDT 13 (1974) 407
1) Determine the attenuation coefficient (a2)
for known E2 transitions depopulating levels
of known spin (gs band in even-even nuclei)
a 2  A2exp / A2max
/J
II) If only A2 has been measured (A4~0)
J
A2max  B2  F2
Tabulated in E. Der Mateosian and A.W. Sunyar, ADNDT 13 (1974) 391
2) For the transition of interest determine:
A2max  A2exp / a 2
3) From E. Der Mateosian and A.W. Sunyar, ADNDT 13 (1974)
407
get 
78
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Angular Distributions: Example 1
175Ta
MeV
W)
170Er(10B,5n)@64
cos2()
172g: (AD)=0.44 -13+17; (RM)=0.54 -/+5
CAESAR array/Canberra (AUS)
79
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy
Angular Distributions: Example 2
80
Pioneering
Science and
Technology
Office of Science
U.S. Department
of Energy