(n,n'y,) Reactions in 63 ,65 Cu and
Background in Ov,/ Experiments
by
Dennis V. Perepelitsa
Submitted to the Department of Physics in partial fulfillment of the Requirements
for the Degree of
BACHELOR OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2008
@2008 DENNIS V. PEREPELITSA
All Rights Reserved
The author hereby grants to MIT permission to reproduce and to distribute publicly
paper and electronic copies of this thesis document in whole or in part.
Signature of Author
Department of Physics
15 May 2008
Certified by
Joseph F. Formaggio
Thesis Supervisor, Department of Physics
Accepted by
Professor David E. Pritchard
Senior Thesis Coordinator, Department of Physics
MASSACHUSETTS INSTMTUTE
OF TEC-lINOLOGY
JUN 13 2008
LIBRARIES
Acknowledgments
Compiling a full list of everybody who has helped me along the last four years at
MIT is daunting if not impossible.
First and foremost, I would like to thank my thesis advisor Joseph Formaggio for
his guidance and support during the writing of this manuscript.
I am grateful to the Weak Interactions Team at the Los Alamos National Laboratory for introducing me to experimental science at a national laboratory. Their
instruction, mentorship and friendship was pivotal in my education as a scientist.
I am indebted to my mentor Steve Elliott, to my friend Vince Guiseppe, to Team
Leader Andrew Hime and to Vic Gehman. This one's for you.
I would like to thank Matt Devlin, Ron Nelson and other members of LANSCENS for their help and technical instruction during the course of this experiment at
LANSCE. This experiment was done in collaboration with Dong-Ming Mei and others
at the University of South Dakota, and members of the MAJORANA collaboration.
I would like to acknowledge my academic advisor, Peter Shor, and the competent
and warm staff in MIT's Physics and Mathematics Departments, for their support
during my time at MIT.
Along the way, certain professors and individuals have inspired me to add physics
as a major and, later, choose experimental physics as an academic career goal. My
junior year was crucial to this development. I want to single out Professors Krishna
Rajagopal for teaching me 8.05, Isaac Chuang for 8.13, Gerald Sussman for 6.946,
Edmund Bertschinger for 8.224, Ulrich Becker for 8.14 and Eric Jonas for mentoring
me in an undergraduate research position.
I would like to thank the many friends who stuck by me through MIT. I cannot
do justice to all of them here. I will always remember the kind words and sometimes
stern encouragements of BJP, JTM, CTS and NLH. I am indebted to you beyond my
ability to express. You showed me that no man is an island, but that no man need
be one, either.
Last but most important, I would like to thank my parents MLC and GCC, my
brother CVP and my sisters CNC and PAC. You taught me that the only benchmark
we must hold ourselves to are our own high standards. Your unwavering belief was a
stronger encouragement than grades or personal achievement.
With my family, I could climb any mountain. I would like to dedicate this
manuscript to them.
(n,n'y) Reactions in 63 '65 Cu and
Background in OvPP Experiments
by
Dennis V. Perepelitsa
Submitted to the Department of Physics
on May 16, 2008, in partial fulfillment of the
requirements for the Degree of
Bachelor of Science in Physics
Abstract
Measurements of (n, xn'y) reactions in Cu are important for understanding neutroninduced background for certain underground double beta decay experiments. Neutroninduced gammas are a contribution to background for the next generation of double
beta decay experiments, which are designed to reach the sensitivity of the atmospheric
neutrino mass scale (45 meV). Measuring and understanding the high-energy neutron
excitations of shielding materials such as natCu are crucial for establishing shielding
requirements and understanding background. In particular, the regions around the
Q-values of candidate OvP// decay isotopes must be investigated. Partial 'y-ray cross
sections for a natural copper target were measured using the GEANIE spectrometer
in a broad-spectrum neutron beam at LANSCE. The experimental apparatus, and
sources of systematic and statistical error are discussed. The results provide useful
data for benchmarking Monte Carlo simulation of background events in future experiments. Furthermore, measuring specific (n, n') excited state transitions in this
material represents a nuclear structure contribution.
Thesis Supervisor: Joseph Formaggio
Title: Thesis Supervisor, Department of Physics
Contents
1 Introduction
2 Theory of the Experiment
2.1 Background in Neutrinoless Double-beta Decay
2.2 Neutron-Induced Excitations .
2.3 Quantum Scattering .....
2.4 Nuclear Database Crosschecks
.. . . . .
3 Experimental Facility
3.1 GEANIE ............
3.2 WNR Beamline ........
3.3
4
Target Runs ..........
Calibration and Data Analysis
4.1 Analysis Overview . . . . . .
4.2 Energy and Time Alignment .
4.3 Neutron Flux . . . . . . ...
4.4 Efficiency Calibration . . . . .
4.5 Gamma-ray Attenuation . . .
4.6
4.7
Neutron-induced Copper Spectrum . . .
Gamma-ray Yields and Sensitivity Limits
25
27
30
35
38
42
4.8
Constructing the Integral Cross Section .
43
5 Error Analysis
5.1 Approximations and Systematic Error.
5.2 Statistical Error . . . . . . ...
5.3 Error Propagation . . . . . ..
5.4 Future Error Reduction . . . . .
6
24
24
Experimental Results
6.1
6.2
natCu
6.1.1
6.1.2
0v3/
6.2.1
(n,xn'y) Cross Sections
63 ,65 Cu (n,xn'7) 65 Cu
.
65 Cu (n,n'Hy) 65 CU
.
Regions of Interest . .
76 Ge
...........
44
44
47
48
49
6.2.2
6.2.3
6.2.4
6.2.5
6.2.6
6.2.7
82 Se
1 0Mo
0
116 C d
130 Te
136 Xe
150Nd
.....
..........
. . . . . .
.................
.................
.
....
....................
. . . . . . . . . . . . . ..
. . . . . . . .
..............
.............
. . . . ...
. . . . .
57
58
58
59
60
61
7
Conclusion
63
8
Appendix I: geanie.py Source Code
67
List of Tables
1
2
0O3/3 isotopes and Q-values .............
GEANIE detectors ...................
3
4
5
6
7
8
152Eu
9
.........
.......
and calibration source lines ...................
226 Ra and calibration source lines ...................
Coaxial detector attenuation coefficients . ...............
Neutron-induced 6 3 '65 Cu Spectrum Identification, 0-1MeV
Neutron-induced 63,65 Cu Spectrum Identification, 1-2MeV
Neutron-induced 63,65 Cu Spectrum Identification, 2-3MeV
Experimental Ov/3 Region of Interest Results . ............
16
22
..
.
.
....
......
......
..
32
33
36
39
40
41
55
List of Figures
LANSCE Experimental Facility Diagram ......
GEANIE Detector Position Diagram .........
Typical TDC Spectrum .
................
FC TOF: Time Axis ..
.................
FC PH: Energy Axis .
Neutron Flux Source .
.................
.................
.
.
Radium-226 Calibration Source Spectrum . . . . . .
.
Europium-152 Calibration Source Spectrum . . . . .
.
GEANIE Array Absolute Energy Efficiency Fit . . .
.
Detector Attenuation Correction ............
.
Neutron-Induced Natural Copper Spectrum, 3 < E, < 30 MeV
Contributions to Error in the 962-keV Cross-Section .
. .
63
Calculated and Simulated Cu 670-keV cross-section
. .
Calculated and Simulated 63 Cu 962-keV cross-section
. .
63
Calculated and Simulated Cu 1327-keV cross-section
. .
Calculated and Simulated 63 Cu 1412-keV cross-section
. .
65
Calculated and Simulated Cu 1115-keV cross-section
. .
Calculated and Simulated 65 Cu 1481-keV cross-section
. .
76 Ge 0,33 Q-value ROI and sensitivity
limit.....
.
76 Ge Ovo,3
Q-value DEP ROI and sensitivity limit.
. .
82Se OvP0P Q-value ROI
and cross-section . . . . . .
.
82Se Ov,/3 Q-value DEP ROI and
sensitivity limits.
. .
100Mo OvI/3 Q-value ROI and cross-section .
. . . .
116 Cd Ov3/3 Q-value ROI and cross-section .
.....
6
11 Cd Ov0/ Q-value DEP ROI and sensitivity limit.
. .
13 0 Te
0•O,3 Q-value ROI and cross-section .
. . . .
30
' Te Ov03 Q-value DEP ROI and sensitivity limit.
. .
136 Xe OvI3f3 Q-value ROI and sensitivity
limit.
1 36
Xe Ov/3/3 Q-value DEP ROI and sensitivity limit.
. .
150 Nd Ov/3/3 Q-value
ROI and sensitivity limit .
. .
. .
.
.
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1
Introduction
Several crucial questions in high-energy physics surround properties of neutrinos. The
electron neutrino, postulated by Pauli in 1930 to carry away missing linear momentum and conserve lepton number in beta decay [26], was later confirmed in 1956 [12].
Thought to be massless for decades, recent experiments such as ones at the Sudbury Neutrino Observatory (SNO) [6], Kamioka Liquid Scintillator Anti-Neutrino
Detector (KamLAND) [5] and Super-Kamiokande (Super-K) [7] have confirmed the
phenomenon of neutrino oscillation, implying that at least two of the neutrino flavors
have mass. It is a fascinating and elusive particle: it has a miniscule mass, different
mass and flavor eigenstates, interacts only weakly (through the only CP-violating
interaction) and presents serious technical challenges in its detection. Importantly
for this experiment, it may also be a massive Majorana fermion.
Besides trying to measure the neutrino masses and their mixing angles, scientists
are interested in questions relating to the chirality of observed neutrinos. It seems
that the only observed neutrinos are left-handed and the only anti-neutrinos are righthanded. Because the neutrino is not massless, there are reference frames in which the
chirality appears flipped. But since right-handed neutrinos and left-handed antineutrinos are not observed, could this mean that left-handed neutrinos are just righthanded neutrinos in another frame? In other words, could the neutrino be its own
antiparticle?
In other words, is it a Majorana, instead of a Dirac, fermion? If this is the
case, then observing (and later measuring) processes which rely on the neutrino to
act as its own antiparticle would confirm the Majorana nature of the neutrino (and
help constrain other parameters, like neutrino mass). Some experiments to measure
one of these theoretical processes, double-beta decay, are taking data and others are
in development. In fact, a recent experimental result from the Heidelberg-Moscow
Experiment claims to have observed 0V/3 [13]. Before this (rare) process can be confirmed and measured in future experiments, scientists must undertake an investigation
of auxiliary issues such as background.
In the present work, we investigate an important background measurement in
preparation for these experiments, and construct several nuclear physics database
cross-checks. The motivation for this is to supplement the MAJORANA collaboration
and other neutrino researchers with necessary data. Data for this undergraduate
thesis was taken during a summer internship at the Los Alamos National Laboratory.
In effect, this is a nuclear physics measurement taken in the context of neutrino
science. Though inspired by members of the MAJORANA collaboration, its results
are applicable and important to other neutrinoless double-beta decay experiments as
well.
2
2.1
Theory of the Experiment
Background in Neutrinoless Double-beta Decay
Observation of neutrinoless double-beta decay would show that the neutrino is Majorana in nature. Since the rate of this hypothetical process is related to the effective
Majorana mass, measuring it will give an experimental constraint on neutrino parameters. Unfortunately, current experimental limits on the neutrino masses indicate
that the next generation of experiments will have to be sensitive to the atmospheric
mass scale (- 45 meV) and suppress background by an order of magnitude more than
is currently possible.
Only a handful of nuclear isotopes have the energetics to be Ov/3 candidates.
Scientists will be looking for a specific single-site, two-electron signal with an energy
equal to the Ov/ Q-value (e.g. for 76 Ge, this is 2039-keV). Again, as the process
is rare, every source of background radiation that falls within this region of interest
must be understood. Without a handle on the contribution from background, experimenters cannot claim one way or the other that they have measured this process
or put limits on their apparatus sensitivity. There are other powerful backgroundrejection technologies to signal from background, each appropriate for a different set of
experiments. For example, multi-site rejection and pulse shape analysis to distinguish
gammas from electrons in MAJORANA and the GERDA experiments [9]. However, in
solid-state detectors, a double escape peak from a higher-energy gamma can become
an electron overlapping the Q-value. Thus, the area of the spectrum 1022-keV above
the Q-value is also a region of interest (ROI).
To minimize background radiation, experimental sites deep underground are being
investigated for their sources of radiation. [21] Although many forms of background
radiation are suppressed or lessened under the earth's surface, it is important to
quantitatively understand the ones that do exist. Two of these sources of background
are thermal and fast neutrons. These neutrons are created by spallation processes
caused by high-energy cosmic rays, and can contaminate an experimental site. The
free neutrons are likely to interact with material likely to be around the experimental
site: enriched germanium in the detectors, natural lead and copper shielding, and
other detector and shielding materials.
Thus, inelastic neutron scattering measurements are important for the next generation of neutrinoless double-beta decay experiments. [20] By measuring the gammaray production cross-sections of overlapping lines in shielding and detector materials,
scientists can provide benchmarks for background simulations and analyses. Though
the current effort is related to the MAJORANA experiment, which uses enriched 76 Ge
as the double-beta decay candidate, examining the regions of interest for any Q-value
is important.
Experimental attempts to measure Ov03 in a variety of isotopes are underway
in underground laboratories around the world [4]. Some of these isotopes (and their
Q-values) taken from [35] are given below in Table 1, updated with recent results
from [29], [1] and [30].
Table 1: 0/33 isotopes and Q-values
Transition
Q-value (keV)
7Ge
82
Se
_ 76Se
-
1oMo
16-Cd
2995.5(1.9)
86Kr
-- 10
2039.00(0.05)
Ru
3034.40(.17)
116 SSn
2809(4)
13OTe
1 0 Xe
2530.3(2.0)
136 Xe
1366 Ba
2457.83(.37)
3367.7(2.2)
1oNd -•15 Sm
This table lists eight isotopes that could undergo neutrinoless double-beta decay,
along with a recent measurement of the Q-value.
2.2
Neutron-Induced Excitations
To investigate the potential contaminating background radiation in double-beta decay
experiments, data for this experiment was taken using the broad-spectrum neutron
beam of a linear accelerator. Therefore, it is important to understand how neutrons
over a wide energy range hitting a target cause gamma radiation.
In this experiment, we chose to study (n, xn'T) reactions. Specifically, reactions
activated by an incident neutron which produced one more (x) neutrons and one or
more photons. In x = 1 reactions, the neutron excites the nucleus and leaves the
target area while the nucleus decays. In x > 1 reactions, the neutron is so energetic
that it knocks out additional neutrons, leaving the nucleus an isotope with lower A
number in an excited state. Of course, other interactions take place (for example, an
63
(n, py) reaction on 63 Cu would convert this isotope to an excited state of Zn, and
a (n, n'c-y) reaction on 65 Cu would convert this isotope to an excited state of 60 Co)
but (n, xn'l) interactions are very likely to happen and do not change the identity of
the decaying element.
Instead of decaying to a lower-state by gamma emission, an excited nucleus can
decay by releasing a conversion electron and a characteristic X-ray. When measuring
gamma ray production cross sections, the possibility of missed events because of
internal conversion should be considered. The TOI 2003 [17] described how likely
this was for a given transition.
Additionally, a high-energy incident neutron is likely to impart much of its kinetic
energy to the nucleus and excite it to a high level. Rather than decay immediately to
the ground state (which is sometimes not feasible due to angular momentum conservation or other reasons), the nucleus will often give off a gamma cascade and transition
in steps down to the ground state. For example, an observed (les -4 gs) event could
have come from the nucleus excited to the first excited state decaying, or part of a
cascade from a much higher level. The relationship between a high-energy excited
state and probable gamma cascades can be reconstructed if the branching ratios from
each level are known. In principle, we could choose to measure the level cross sections
for a given excited state (that is, how likely is a neutron to put the nucleus into a
certain state). In practice, however, we are interested in the gamma ray production
cross sections for a given transition. One of the reasons is that we are interested in
the end result of what gamma radiation is produced by a neutron and not the exact
decay schemes by which it is produced.
Finally, to correlate which decay events are activated by which incident neutrons,
the gamma ray production must be prompt. That is, the decay should occur within
the timing resolution of the experimental apparatus. In practice, this meant that the
half-life of any excited state reached should be under 15ns to give meaningful results
about how this depends on neutron energy.
2.3
Quantum Scattering
In a decay event, photons carry away units of angular momentum. Since this is a
conserved quantity, given the angular momentum quantum numbers of the initial
and final state, and current spin of the nucleus, the gamma will tend to head in
some directions over others. In the normal decay of a radioisotope with nuclear spin,
the nuclear spins of the sample point in all directions with equal probability, so any
angular dependence in the decay event is averaged out.
Thus, the cross-section of a transition could display some angular distribution
u(0, 4). In our setup, the azimuthal 0-symmetry is not broken, but the presence of
the neutron beam breaks the 0-symmetry in (n,n'y) reactions. It is known that when
a sample is placed in the flight path of an active neutron beam, the nuclear spins
tend to point in the plane anti-parallel to the direction of the beam. Any azimuthal
dependence in the cross-section will be averaged out, but there is some theoretical
dependence on 0, the angle of incidence with the beam.
Quantum scattering theory says that the differential cross-section can be expressed
as the weighted sum of even Legendre polynomials in sin 0 [10]:
do(0)
dO
4r
4w
aP,(sinO)
(1)
n=0,2,4
Above, o0 is the integral cross section, which can be obtained by integrating the
differential cross-section over the range of sin 0. Roughly, the weights of the different
polynomials measure the "anisotropy" of the event. ao measures how isotropic the
decay is, a2 measures any overall dipole moment, a4 measures any overall quadrupole
moment, etc. Since the sense of absolute scale is set by o0 ,ao - 1 by definition, and
the weights of the other polynomials are expressed as unitless ratios to the weight of
the isotropic term.
A key mathematical property of even Legendre polynomials is that for every n > 2,
they integrate out to zero. This means that even though there may be a contribution
from the quadrupole at a given angle 0, the net addition to the integral cross-section
over all angles will be zero. In practice, since no apparatus can sample continuously at
all angles, approximations are used to connect the differential cross section sampled
at certain angles to the integral cross section. Some researchers reason that the
contribution from a 4 and higher terms is negligible and sample at an angle which is a
zero of P2 to eliminate the a2 term and measure ao directly [32]. Another possibility
is to find optimal sampling angles 0 and then use numerical quadrature to estimate
ao from measurements of d [22]. Still, other researchers measure the cross-section as
if their array had complete coverage, calculate the theoretical paramters an and then
correct their measurement for this.
Although GEANIE allows the experimenter to sample the differential cross-section
at multiple values of sin 0, in this paper, we circumvent a full treatment of the angular
problem by treating our detector as having close to complete coverage.
2.4
Nuclear Database Crosschecks
Finally, data obtained from the experiment is useful for measuring other quantities directly comparable with the literature. Of the published (n, xn'y) data, cross-sections
against neutron energy tend to be well-measured only for specific transitions, or in
common isotopes, or at single energy values, or with low statistics or with significantly small amounts of angular coverage. Constructing cross-section measurements
at this apparatus serves two purposes. The comparison with established results gives
us confidence in results using the same analysis process or provides an overall normalization for the same data. The other purpose is to contribute not well-measured
results to the nuclear physics community.
In addition, nuclear reaction simulation packages such as TALYS [15] or GNASH
[34] are usually only accurate in modeling prominent or low-level transitions. Nuclear
(n, xn') data is useful for providing benchmarks for further development. In addition
to cross-sections, other calculated values such as branching ratios, level-production
cross-sections and other measurements can be.
3
Experimental Facility
Data for this experiment was taken at the linear accelerator at the Los Alamos Neutron Science CEnter (LANSCE), a major experimental science facility at Los Alamos
National Laboratory. Some references which describe these facilities in more detail
are given below. Similar experiments have been taking place at this facility for over
a decade, and the specific apparatus used in this experiment is well-documented.
The LASNCE experimental facility is shown in Figure 1. The LANSCE linac is
an 800 MeV proton beam, which is converted using a spallation target to a neutron
beam in the Weapons Neutron Research (WNR) Facility, and the 200 beam flight
path was used in this experiment. The flight path runs through GEANIE, a high-
resolution gamma ray spectrometer used in previous (n, xn'^y) reaction measurements,
fission studies and experiments concerning nuclear spectroscopy, nuclear reactions and
nuclear structure. GEANIE is operated by LANSCE-NS, the "Neutron and Nuclear
Science" group of Los Alamos National Laboratory.
Established literature describes the operation and calibration of the experimental
facility, including addressing the angular distribution problem and performing benchmarking measurements of the 5"Fe (n,xn'y) 846-keV 2+ --+ gs line [19]. Another
excellent reference that discusses GEANIE, the WNR and calculates 2 38 u (n,xZ7Y)
production cross sections is [8]. A more involved description of how the fission chamber functions is given in [33]. During the summer of 2007, I visited the WNR facility
at least once a week to actively oversee the experiment while data was being taken.
I
I
Figure 1: LANSCE Experimental Facility Diagram
This is a diagram showing the proton beam, spallation target, neutron beam flight
path, collimation, fission chamber, detector array and lead beam stop. Adapted
from [8].
3.1
GEANIE
The detector array used in this experiment is the GErmanium Array for NeutronInduced Excitations (GEANIE). GEANIE normally consists of 26 high-purity, highresolution germanium detectors. Sixteen of these detectors are coaxial with an energy
range up to roughly 4 MeV (8000 channels, 2 channels per keV), and ten are planar
with an energy range up to roughly 1 MeV (8000 channels, 8 channels per keV). Since
most of the examined gamma ray energies of interest were greater than 1 MeV, the
planar detectors were seldom used. For the rest of this analysis, we focus on the
coaxial detectors.
6, 12, 15, 24
~EZIZIXIZZIZI-zz~
14, 17. 22
7, 16, 19, 25
Figure 2: GEANIE Detector Position Diagram
The figure on the left is a top-down view showing the values of 0 that correspond to
active coaxial detectors. The figure on the right is a side-view showing the three
halos (q = -29', 00, 290) which have active coaxial detectors.
The detector array was arranged in a set of four "halos" (mounted rings). Each
ring is defined by a value of q, which is the angle that the cone between the target
and the ring makes with the plane parallel to the ground. Historically, the first three
halos (at q = -29", 00, +290) were installed first and contain seven, six and seven
detectors at equally spaced locations along the ring. The fourth halo at q = +550
consisting of six detectors was installed later. Since all of the detectors in this last
halo were planar detectors, only detectors from the first three halos were primarily
used in this analysis. Along each ring, a detector position is also defined by 0, the
angle of incidence with the vertical plane of the beam, with 0 = 0 corresponding to
directly behind the target. Looking down on the array from above, the positive values
of theta go counter-clockwise.
Det #
1
2
Type
P1
P1
P1
P1
P1
Activre?
Table 2: GEAN\JIE detectors
0
0
Distance
cos Ob
Comments
29.00 -152.8' 14.415 cm 0.778
Yes
Yess
-29.00 -154.00 14.442 cm 0.786
Yes s 29.00
3
157.00 14.379 cm 0.805
4
Yess
-29.00 157.90 14.318 cm 0.810
Yess
56.50
27.00
5
16.535 cm -0.492
Yess
6
29.00
102.00 14.237 cm 0.182
Cx
7
Cx
Yes
-29.00 102.50 14.288 cm 0.189
P1
Yess
8
55.00
77.00
18 cm
-0.129
0
P1
No
9
55.00 -129.0'
18 cm
0.361
No data
P1
No
10
55.00
-77.00 0
18 cm
-0.129 Poor statistics
0
11
No
Cx
26.50 14.308 cm -0.895 Poor resolution
0.00
1.00
Yess
29.00
12
Cx
14.379 cm -0.874
Cx
No
-29.00
1.20
13
14.773 cm -0.874
Low statistics
Yess
14
Cx
0.00
-25.20 14.392 cm -0.905
Yess
29.00
-51.10 14.392 cm -0.549
15
Cx
Yess
Cx
-29.00 -51.00 13.846 cm -0.550
16
Yess
17
Cx
0.00
-76.90 14.442 cm -0.227
Yess
P1
56.50
-25.00 16.378 cm -0.500
18
Yess
-29.00 -102.0 0 14.308 cm 0.182
19
Cx
P1
No
20
0.00
-128.0
14.161 cm 0.616
Unstable gain
No
55.50
129.0c 17.089 cm 0.356
21
Cx
No data
Yess
22
14.917 cm -0.199
Cx
0.00
78.50
Cx
Nc
23
0.00
129.5c 14.237 cm 0.636
Poor statistics
0
Yess
29.00 -101.7
24
14.176 cm 0.177
Cx
Ye•s
Cx
-29.00
53.50 14.435 cm -0.520
25
Nc
29.00
53.00
Cx
26
14.455 cm -0.526
No data
This table lists each of the 26 detectors and indicates if it is planar or coaxial,
whether or not it was included in the final analysis, its position (0, phi), its distance
to the detector, which values of cos Ob it is sampling and any reasons for it not being
included in the analysis.
These values of (0, 0) are different from the angle of incidence with the beam 0 b,
with the conversion given by cos Ob = - cos 0 cos 0. For various timing-, resolution- or
gain-related reasons, some detectors were not included in the analysis. Additionally,
a few offline detectors had their data acquisition channels used in other, unrelated
experiments. Table 2 lists the detectors, their type (coaxial or planar), reference
angles, distance to target and whether or not they were used in this analysis (along
with the reason if the detector is challenged).
3.2
WNR Beamline
To create a broad-spectrum neutron beam, the monoenergetic 800 MeV proton beam
is run through an unmoderated natW spallation source, resulting in neutrons with
energies ranging from about 0.1 MeV to 600 MeV. The beam delivers between 2 and
4 yA of current with a specific time structure. The beam is composed of 40 Hz
macropulses 625 ps wide, each of which is composed of micropulses spaced 1.8 Ps
apart.
The beam area on target was trimmed with lead collimaters after the spallation
source but before the fission chamber and detector array. For this experiment, the
area of the beam on target was reduced to 1.9 cm radius with lead collimators. This
ensures that the beam area would fall entirely within the copper target.
The GEANIE flight path runs through a fission chamber 18.495 m after the spallation target, consisting of 235 U and 23 8 U foils, at which fission reactions ((n, f), with
fission products f) are measured by the data acquisition system. Time of flight (TOF)
information, along with a pulse height proportional to the number of fission events,
was stored during each run.
The center of the array, where the target sits, is 184.5cm after the fission chamber.
Time-of-flight analysis was used to reconstruct neutron energies. A sharp gamma
flash at the beginning of the TOF spectrum signified the arrival of gammas from the
spallation chamber, followed by the fastest neutrons. Since the speed of light, the
distance between chamber and spallation source, and the neutron mass is known, the
velocity of any incident neutron is related to its energy by E, = Eo/V1 - v2/ 2 ,
where Eo = 939.6MeV is the neutron rest mass. The time resolution of the data
acquisition system is 15ns.
For a given neutron energy, the pulse height information in the fission chamber
can later be combined with the known fission cross-sections of isotopic uranium to
give a calculation of neutron flux.
3.3
Target Runs
In the summer of 2007, runs were taken with a natural copper target between 6/18/08
and 7/1/08. The target was composed of three half-millimeter sheets measuring four
square inches in area, which covered all of the beamspot. natCu is 69.15% 6 3 Cu (62.93
amu) and 30.85% 65 Cu (64.93 amu). At room temperature, natural copper has a
density of 8.96 grams per cubic centimeter. To convert recorded events to a cross
section, the thickness of a copper isotope seen by an incident neutron needs to be
determined.
The thickness in atoms per barn of the target is given by the following calculation:
(8.96 g/cm3 ) x (1.5 mm thick target) x (10-24 cm 2 /barn)
atoms
(6.022 x 1023 g/amu) x (.6915 x 62.93 + .3085 x 64.93 amu/atom)
barn
Two efficiency calibration runs using known-activity were performed, during which
the beam was turned off. An efficiency calibration run with 152 Eu was performed on
7/3/08 and one with 226 Ra from 7/3/08 to 7/5/08.
Both copper isotopes are stable, so there should be no background caused by
radioactive decay of the unactivated target. Still, to investigate sources of background
in the experiment that are not from (n, n') reactions on natCu, data was taken with
the neutron beam turned on and a blank capsule as the target.
4
Calibration and Data Analysis
The data acquisition system at LANSCE has the interesting property that it records
information from both the fission chamber and the array spectrometer. Interpreting
the experimental results requires an understanding of the beam structure and format
of the information output by the apparatus. While data is being taken, individual
events detected by the system are written to disk for later off-line processing and
analysis.
4.1
Analysis Overview
Data analysis for this experiment was done using a number of pieces of legacy software
written by GEANIE collaborators at LANL, in addition to a software suite developed
by the author for this experiment. To unpack the event files written to disk into a
more accessible format, code from the internal tscan analysis package was used. This
is the step at which time and energy gain-alignment occured and individual detectors
and information channels were turned on or off. Then, channels from the resulting
data could be extracted using the rgmt code from the tscan package. This includes
neutron flux data, calibration spectra and livetime spectra. The excite program was
used to obtain neutron-induced gamma spectra gated on netron energy bins.
To analyze the yields for a given gamma peak yield seen by a given detector
in a given neutron energy bin, the gf3 program from the RADWARE gamma-ray
analysis software was used [28]. After the yield, livetime, neutron flux and calibration
information was extracted, the author synthesized this data with a python module,
called geanie.py, written for this purpose, heavily relying on the popular pylab [18] and
scipy [31] Python packages. The commented source code is attached in the appendix
at the end of this manuscript. geanie.py is a library that defines useful functions for
analysis. It is imported at the start of any script which performs data analysis. At
various stages of the analysis bash and FORTRAN scripting were also used.
To construct the integral cross-section a for a given transition -y at a neutron
energy E,,several measurements have been synthesized in the expression:
or = N -I(y, En)/c(Y)
t 4(En)" F(-)
(3)
Equation 3 is the focus of this experiment. I is the corrected yield for the transition, E is the calibrated efficiency, ( is the corrected neutron flux, F is an attenuation
correction and N is an overall normalization. In the sections that follow, we describe
each of these in detail, as well as discuss errors that arise from each of its terms and
alternate formulations of it. We return to the equation in Section 4.8.
4.2
Energy and Time Alignment
After the event file is processed, two spectra are compiled for each detector. The
first of these is the 8192-channel ADC energy spectrum, in which events are sorted
by energy with a gain depending on whether the detector is planar or coaxial. In
addition to these ADC spectra, the data acquisition system records events measured
while the beam is off, but supresses them by a factor of 8, which will be important
later while performing an efficiency calibration. Similarly, the events are sorted by
time in a 8192-channel "TDC" time spectrum with a gain of 4.0 ns / channel (eight
times as compressed as other time of flight spectra), with each macropulse being
written from left to right (since the fastest neutrons arrive first, we later reverse the
spectrum so that the lower energy ones are on the left). Of course, the macropulse
has several micropulses as a substructure. Thus, the TDC spectrum looks like many
reversed time-of-flight spectra put together side by side.
Both types of spectra need to be calibrated. The energy spectrum for each detector
was aligned using a pair of known transitions as reference lines for a linear calibration.
For the coaxial detectors, a gain of 0.5 keV/channel was used with channel zero
coinciding with 0 keV by calibrating the 670-keV and 962-keV transitions in 63 Cu to
channels 1339 and 1924, respectively. Planar detectors were aligned using the same
lines with a gain of 0.125 keV/channel to channels 5357 and 7696.5, respectively.
In general, once calibrated individual detectors drifted only a few channels at most
during the time that data was being taken.
To combine the TDC spectra, the width between the individual micropulses was
measured to be 447 channels (1.788 ps using the TDC compression), and these individual spectra were added together to give a single time-of-flight spectrum compiled
from all the micropulses. A TDC spectrum before this operation is shown in Figure
3. The sharp peak, caused by prompt gammas from reactions in the spallation target,
must be aligned in each detector. The offset for each detector was calibrated so that
the tip of the gamma peak falls at channel 100.
ouu
I
II
TDC Counts I
I'-•
TDC'Counts
I
500
400
SIA
-C
o 200
U
100
9
LYJ' ~
4 600
YF·*LYR
4500
PI1·UI·
5000
1'IYI1~
5500
I
~ri·~rC1
6000
I
~liY
6500
iLl
ýý
I ~~ I~i~iT
7000
~rL·IY- I~
7500
·n
8000
Time channel
Figure 3: Typical TDC Spectrum
This is a typical time spectrum seen by a detector. Each peak is a "gamma-flash"
which ends a micropulse and signifies the arrival of gammas from the spallation
target. Since the fastest neutrons arrive first, the low-energy part of each micropulse
is on the right.
Once the energy and time axes are calibrated, the next stage of the analysis is
to gate the ADC spectra on the information in the TDC spectra, to give a neutroninduced energy spectrum for a given neutron energy bin. Since the distance between
the fission chamber and the array is known, time of flight analysis can be used to
produce gamma ray spectra gated on neutron energy. This is the basis for future
high-level analysis, and extracting peak yields from gated spectra is discussed in
Section 4.7.
4.3
Neutron Flux
After the event files are processed, information from both fission chambers are stored
in separate matrices for processing into a neutron flux. For neutron energies up to
2 - 3 MeV, the 235 U foil is used because the 23 8 U (n, f) cross-section is small and
the results unreliable. For higher neutron energies, the neutron flux is reconstructed
from the 238 U fission chamber instead. Since many of the regions of interest in this
experiment are higher than 2 MeV, the 23 8U fission chamber is used almost exclusively.
Fission chamber events are stored in a two-dimensional matrix sorted by time of
arrival and energy. Both axes must then be calibrated and processed. When summed
along the energy axis, the result is a time of flight (TOF) spectrum, which shows the
time distribution of all fission chamber events. An example is shown in Figure 4. A
small y-flash to the left of the large peak is caused by photons from the spallation
target arriving, and signals the start of the micropulse to the data acquisition system.
In the figure below, it occurs at channel 118.
0
oE
0
Time Axis (channels)
Figure 4: FC TOF: Time Axis
Each count is actually a fission event. This time of flight spectrum shows the temporal
distribution of fission events over the time span of a micropulse.
1200
o
1000
E
800
U
' 600
E
-
400
200
U
Energy Axis (channels)
Figure 5: FC PH: Energy Axis
Each count is actually a fission event. This energy spectrum shows the energy
distribution of measured fission events. The lower peak is from a-detection.
When summed along the time axis, the result is a pulse height (PH) spectrum,
which shows the energy distribution of all events. An example is shown in Figure 5.
The small peak on the left comes from a-particle detection, which must be excluded
in the analysis, and the peak on the right comes from (n, f) events. To make a
corrected TOF spectrum which includes only counts from fission events, the left peak
is excluded with a cut. More detail is given in [33]. In the figure above, it was made
at channel 237.
The matrix is folded along the energy axis from the a-cut to the high end of the
energy spectrum. Using the distance between the spallation target and the fission
chamber, the time of arrival gives a measure of neutron energy as described above
in Section 3.2. Then, using experimentally measured 235,238 U fission cross-sections
from the literature, the number of counts, as well as the foil thickness, is turned
into a neutron flux. Since the apparatus resolution is 15ns, the flux for a given
neutron energy must be binned into an energy region that corresponds to that time
bin. Because of the functional form of energy depending on velocity, a 15ns time
bin corresponds to a larger energy bin at higher neutron energies than lower one. A
measurement of neutron flux derived in this manner is shown in Figure 6.
a)
C
0
L.
C
x
ULL
Neutron energy (MeV)
Figure 6: Neutron Flux Source
This shows the neutron flux on target as measured by the
during the natural copper runs.
238U
fission chamber
Due to limitations in the data acquisition system, not every measured fission event
is recorded in more detail. Every event detected by the system but not written in
detail to disk is recorded in a special scaler spectrum. By summing this spectrum
and comparing it with the number of recorded events, an apparatus livetime L can be
derived. With this in mind, the flux through a given neutron bin can be calculated
in the following manner:
I (E,) =
(Ets
(counts/MeV)
LB(E,)
(4)
In equation 4, Icts is the number of fission counts reported by the analysis software
for a particular neutron energy bin E, and L is the fractional livetime for the fission
chamber. To normalize the results per MeV, we divide by the size of the neutron
energy bin B(E,).
4.4
Efficiency Calibration
Two known-activity radioactive sources were used to calibrate the detector array.
A sealed 226 Ra source in secular equilibrium with some of its shorter-lived daughter
products provided for useful calibration points as high as 2.5MeV. The gamma emitters in this chain were used as calibration point sources. This source was calibrated
to 1.86 x 106 Bq (decays/second) on 1/2/02. The part of the decay chain in secular
equilibrium is
226Ra -
a -222
Rn,---
218
Po -- a
214
Pb -t3
-214
Bi
(5)
A 152Eu source with two decay modes (5 2 Eu --+ 1 2Sm by electron capture with
a branching ratio of .7210, 152Eu --- 152Gd by beta decay with a branching ratio of
.2790) provided for calibration points as low as 186-keV. This source was calibrated
in 1979 and calculated to have an activity of 1.49 x 105 Bq on 7/13/07.
The decay energies and conversion coefficients were taken from [17] and the
branching ratios for all isotopes were taken from [11] and [16]. The exact calibration lines and branching ratios used in this calibration are shown in Tables 4 and
3. Each active detector was calibrated separately, with the planar detectors only using calibration lines up to 1MeV, to investigate the spread in the absolute efficiency
between the detectors.
In addition, an efficiency calibration was derived treating the sum of the detector
spectra as a single spectrometer. Though we used the efficiency of the array in our
final calculations, the individual detector efficencies are needed in a later analysis
of systematic error. The following formula was used to derive the efficiency e of an
individual detector for an incident gamma ray of energy y:
c(-) = 47r-
r-t-L
(6)
Above, Iy is the measured intensity of the line, fit with gf3 (this piece of software
is introduced in Section 4.1 and discussed in detail in Section 4.7) from the calibration
spectra, in counts, r is the rate in decays per second, t is the runtime in seconds, and
L is the data acquisition system livetime. This is described in more detail below. The
major statistical uncertainty in the yield is a function of the intensity of background
around the calibration peaks. We did not estimate uncertainty in radioactivity rate
or recorded runtime, and the uncertainty reported in determining the livetime was
not significant.
Due to limitations in the data acquisition system, not every detector energy deposition is recorded in more detail. Every event detected by the system but not written
in detail to disk is recorded in a special scaler spectrum. By summing this spectrum
and comparing it with the number of recorded events, a livetime L for this specific
detector can be derived.
For the calibration runs, the runtime t is not simply equal to the logbook runtime.
During the 226 Ra and 152Eu calibration runs, the neutron beam was off. Instead of
the normal macro- and micropulse information, an artificial electronic system was fed
into the data acquisition system. A 37.9MHz pulser took the place of the micropulse
structure of the beam. When the pulsar is on, the daq records all events to the "beam
on" matrix, and supresses all "beam off" events with a 1:8 ratio. Thus, the actual
runtime must be adjusted for this.
Table 3: 152Eu and calibration source lines
Energy (keV)
121.7817 (3)
244.6975(8)
295.9392(17)
344.2785(12)
Decay
Branching ratio (%)
152Eu _- 152Sm
28.41(13)
5
2
1 Eu
152 GSm
7.55(4)
152 Eu
152SSm
152 Eu
152 Gd
367.7887(16)
152Eu
152 Gd
411.1163(11)
152 Eu
152Gd
2.237(10)
443.96(4)
152 Eu
152 Sm
3.125(14)
152Eu
152 Sm
0.407(?)
688.670(5)
152Eu
152 Sm
0.834(?)
778.9040(18)
152Eu
152Gd
152EEu
152Sm
12.96(6)
4.241(23)
152Sm
14.62(6)
152Sm
0.647(?)
152Sm
13.40(6)
152Sm
1.415(9)
152Gd
1.632(9)
152Sm
20.85(9)
488.6792(20)
867.378(4)
964.079(18)
1005.272(17)
1112.074(4)
1212.948(11)
1299.140(10)
1408.006(3)
152Eu
152Eu
152Eu
152EU
15 2
Eu
-
0.440(?)
26.58(12)
0.845(?)
Table 4:
226 Ra
and calibration source lines
Energy (keV)
Parent
186.211(13)
241.997(3)
295.224(2)
351.932(2)
609.312(7)
665.453(22)
226Ra
768.356(10)
786.1(4)
806.174(18)
934.061(12)
964.08(3)
1120.287(10)
214Bi
1155.19(2)
1238.110(12)
1280.96(2)
1377.669(12)
1385.31(3)
1401.50(4)
1407.98(4)
1509.228(15)
1583.22(4)
1661.28(6)
1729.595(15)
1764.494(14)
1847.420(25)
2118.55(3)
214Bi
2204.21(4)
2293.40(12)
2447.86(10)
2694.7(2)
2769.9(2)
214Bi
214pb
214pb
214pb
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
214Bi
Branching ratio (%)
3.56(6)
7.43(11)
19.3(2)
37.6(4)
46.1(5)
1.46(3)
4.94(6)
0.31(9)
1.22(2)
3.03(4)
0.362(17)
15.1(2)
1.63(2)
5.79(8)
1.43(2)
4.00(6)
0.757(18)
1.27(2)
2.15(5)
2.11(4)
0.690(15)
1.15(3)
2.92(4)
15.4(2)
2.11(3)
1.14(3)
5.08(4)
0.305(9)
1.57(2)
0.031(2)
0.025(2)
Treating the array as a single spectrometer, an efficiency calibration curve was fit
to either set of data points. The fit was performed in log-energy, log-efficiency space
using a sixth-order polynomial and uncertainty in each data point as uncertainty for
the fit. As suggested by [14] and [3], a high-order polynomial is the standard method
for calibrating solid-state Ge detectors, using a high-enough order to fully specify
the shape of the efficiency curve. For the 152Eu calibration source, these fits had ten
degrees of freedom with a typical reduced x 2 value of 60/29. For the 22 6Ra calibration
source, these fits had twenty-four degrees of freedom with a typical reduced x 2 value
of 82/20.
In this case, the 47r factor on equation 6 was not included, since, by assumption,
GEANIE had close to total angular coverage. The uncertainties in the efficiency curve
polynomial coefficients were given by the least-squares fit parameters.
0o
U
U
500
1000
1500
2000
Energy (keV)
Figure 7: Radium-226 Calibration Source Spectrum
2500
U
4UU
ZO
IUUU
bUU
bUU
LUU
i4UU
ItUU
Energy (keV)
Figure 8: Europium-152 Calibration Source Spectrum
efficiency calibration curve
I{I
·
·
1000
1500
-3.0
-_Q.•
1 0
500
2000
2500
gamma energy (kev)
Figure 9: GEANIE Array Absolute Energy Efficiency Fit
4.5
Gamma-ray Attenuation
A correction had to be made for the attenuation of excited gamma rays travelling
through the target material. Since the target was millimeters wide with the area of
a few centimeters, the effect was more pronounced in detectors facing the "edges" of
the target. An estimation of the gamma-ray attenuation was obtained by calculating
the attenuation resulting from a gamma-ray being created at any depth within the
target, and then integrating along this path.
We call the median distance seen by created gamma-rays the "effective thickness"
seen by that detector. The intensity I (as a ratio with the original intensity lo) of
gamma radiation of energy E that remains after travelling a distance t through a
material with mass attenuation coefficient p/p and density p is given by the National
Institute of Standards and Technology [24]:
I
A
-= exp(-- p-t)
(7)
o0
P
To approximate the effect of the attenuation if the gamma ray is created anywhere
along the path, we integrate equation 7 above from t = 0 to t = 2x, where x is the
effective thickness. The result is
I
10
1 - exp(-2 • -p -x)
0P
2. p P x
(8)
In general, p/p varies with energy. NIST also keeps a list of p/p coefficients for
natural elements at certain energies E [23], measured in cm 2/g A linear extrapolation
was used to approximate the coefficient for intermediate energies. For the copper
target used in this experiment, p = 8.96 g/cm3 . The distance x seen by an individual
detector can be calculated from its (0, ¢) coordinates.
Table 5: Coaxial detector attenuation coefficients
Detector #
Distance
thru target
Detector 6
Detector 7
Detector 12
Detector 14
Detector 15
Detector 16
Detector 17
Detector 19
Detector 22
Detector 24
Detector 25
4.1mm
4.0mm
0.9mm
0.8mm
1.4mm
1.4mm
3.3mm
4.1mm
3.8mm
4.2mm
1.4mm
Ey = 500-keV
E, = 1-MeV
E = 2-MeV
p/p = .08362
.746
.754
.938
.940
.904
.905
p/p = .05901
.810
.817
.956
.957
.931
.931
.844
.810
.825
-.806
.928
p/p = .04205
.860
.865
.968
.969
.950
.950
.885
.860
.871
.856
.948
.788
.746
.764
.741
.899
This table gives the effective distance for each active coaxial detector and, using equation 8, the attenuation coefficient calculated for that detector at the given gamma-ray
energy. p/p is in units of cm 2 /g, and the attenuation coefficients are unitless.
I--
0
U
C
a)
1-i
0
4-J
r(
energy (keV)
Figure 10: Detector Attenuation Correction
Two attenuation coefficient curves. The y-axis unitless. The higher curve is from a
detector which sees a relatively low effective thickness, and the lower curve is from a
detector which sees a relatively high effective thickness.
For high-energy gamma lines (regardless of detector orientation) or for detectors
facing the flat side of the target (regardless of energy), the attenuation I/Io was on
the order of > 80%. In other cases, it could be dramatically smaller.
These individual attenuation calculations had to be synthesized into a single correction for the entire array F. Under the assumption that the absolute efficiencies
of each detector are not significantly different, we take the mean of the attenuation
coefficients for each detector to arrive at one for the array.
Table 5 gives values of p/p for a number of prominent energy values, the effective thickness of each detector (half the maximum path length), and the attenuation
coefficient at that detector at that gamma ray energy. Figure 10 shows attenuation coefficients for detector 6 (positioned almost perpendicular to the sample) and
detector 12 (positioned almost in front of the target).
4.6
Neutron-induced Copper Spectrum
Figure 11 shows a semi-log plot of the induced copper spectrum seen by the detector
array for a wide range of neutron energies. The spectrum is feature-rich, and many
prominent transitions that are neutron-induced 63 '65 Cu lines are listed in Tables 6,
7 and 8. We have listed the rough peak intensity over this neutron energy range,
uncorrected for efficiency to give a qualitative result for their strength.
Lf
.4-.
C
0
U
0
500
1000
1500
2000
2500
3000
3500
Energy (keV)
Figure 11: Neutron-Induced Natural Copper Spectrum, 3 < E, < 30 MeV
The energy resolution of the apparatus, obtained by taking the full-width at halfmaximum of gamma peaks in the energy region, is two keV for every MeV, which is
a fractional resolution of 0.2%. This applies over the entire detectable energy range.
For individual detectors, however, this resolution can be higher or lower. For solidstate, enriched germanium detector of this type, 0.2% is a good result. We use this
expected full-width at half-maximum when investigating apparatus sensitivities to
peaks hidden by background in Section 4.7.
Table 6: Neutron-induced
Energy (keV)
255.0(13)
312.4(6)
365.2(4)
414.3(4)
Counts
4
10
104
439.7(7)
449.93(5)
105
105
105
105
469.2(4) / 471.0(3)
10 4
499.7(21)
me = 510.998
104
106
533.8(6)
584.82(15)
609.5(1)
612.7(8)
10 4
624.3(3) / 625.6(3)
645.4(3)
669.62(5)
685.6(6) / 686.3(2)
694.3(2)
742.25(10)
754.8(8)
765.7(5)
770.6(2)
836.3(2)
852.7(2)
881.0(1)
899.0(4)
924.3(5)
962.06(4)
978.8(3)
991 / 991.9(3)
10 4
104
104
104
105
105
104
105
104
104
104
105
103
105
105
104
106
105
6 x 104
63 '65 Cu
Spectrum Identification, 0-1MeV
Source
Transition (keV)
2533 -+ 2278
65 Cu
2406 -+ 2094
63 Cu
1326 -* 962
63 Cu
2506 -~ 2092
65 Cu
2533 * 2094
63 Cu
1412 -* 962
63 Cu / 65Cu
2677 -- 2207 / 2094 -> 1623
65 Cu
2593 -- 2094
e
annihilation -y
63 Cu
2081 - 1547
63 Cu
1547 - 962
65 Cu
1725 * 1115
65 Cu
2094 -* 1481
63Cu / 65Cu 2716 - 2092 / 2107 - 1481
63 Cu
2506 -* 1861
63 Cu
699 -- 0
63 Cu 63 Cu
2547 - 1861 / 2696 - 1861
63 Cu
4156 -> 3461
63 Cu
1412 - 669
63 Cu
2081 -> 1326
63Cu
2092 -+ 1326
65 Cu
770 -4 0
63 Cu
5413 -,4577
65 Cu
1623 -+ 770
63 Cu
2207 -- 1326
63 Cu
1861 -> 962
63 Cu
2336 - 1412
63 Cu
962 -- 0
65 Cu
2094 - 1115
63 Cu / 65Cu
2404 -* 1412 / 2107 - 1115
65 Cu
Table 7: Neutron-induced
Energy (keV)
1048.8(5)
1077.8(2)
1115.546(4)
1130.7(3) / 1129
1162.6(11) / 1163.7(11)
1178.9(3)
1245.2(2)
1290.0(19)
1327.03(8)
1341.7(6)
1346.4(2)
1350.1(4)
1374.47(13)
1389.66(8) / 1392.55(8)
1412.08(5)
1437.6(5)
1442.7(1) / 1442.2(3)
1547.04(6)
1558.4(3)
1585.4(2)
1624.0(2) / 1623.42(6)
1638(2)
1724.92(6)
1762.4(3)
1827.0(5)
1861.3(3)
1927.2(7)
1964.1(3)
63 '65 Cu
Spectrum Identification, 1-2MeV
Counts
Source
Transition (keV)
103
104
105
104
104
104
104
104
6x 105
7 x 103
63CU
2011 -+ 962
2404 -> 1326
5x
2x
8 x
9x
7 x
2x
5x
2x
63Cu
65 Cu
63Cu
/
65Cu /
63Cu
63Cu
63Cu
63Cu
65 Cu
63 Cu
63 Cu
8 x 103
63Cu
4 x 104
1 x 104
4 x 104
63Cu
2 x 105
63Cu
103
63Cu
5x
3x
2x
1x
1x
4x
1x
7x
7x
9 x
2x
1x
1x
4
10
63 Cu
63Cu
63Cu
/
65Cu
105
63Cu
104
104
104
104
104
65 Cu
63Cu
63Cu
/
65Cu
65Cu
65Cu
103
65Cu
103
105
104
104
63Cu
63 Cu
63Cu
65Cu
.1115 -- 0
2092 -* 962 / 2678 -* 1547
2278 -- 1115 / 2643 -t 1481
2506 - 1326
2207 -+ 962
2406 - 1115
1326 -+ 0
2011 -* 669
2673 -- 1326
2677 -* 1326
2336 -+ 962
2716 -+ 1326 / 2062 - 962
1412 -- 0
3775 - 2336
2404 -- 962 / 2212 -* 770
1547 - 0
2329 - 770
2547 -* 962
4130 -4 2506 / 1623 -- 0
3120 -+ 1481
1725 -+ 0
2533 - 770
2497 - 669
1861 -+ 0
2888 -+ 962
3079 - 1115
63 '6 5 Cu
Table 8: Neutron-induced
Energy (keV)
2011.4(5) /2012
2026.8(3)
2062.1(3)
2081.4(3)
2092.6(5)
2107 / 2107.4(2)
2188.0(7)
2212.8(2)
2309.0(3)
2329.0(2)
2336.5(3)
2356(3)
2468(3)
2497.4(4)
2512.0(5)
2536.0(3)
2562.0(7)
2627.7(1)
2696.6(3)
2716.9(4)
2780.3(4)
2806.6(6)
2862.7(2)
2874.4(2)
2889.4(8)
2902.4(2)
3032
3044.6(8)
Counts
104
103
103
104
104
104
Spectrum Identification, 2-3MeV
Source
63 Cu
/
63Cu
Transition (keV)
2011 -+ 0 / 2682 -- 669
63 Cu
2696 -+ 669
63 Cu
63 Cu
2062
2082 -+ 0
63 Cu
2092 -- 0
63CU
/
65Cu
2776
-*
669 / 2107
103
63 Cu
2857 -- 669
104
65 Cu
2213 --+ 0
103
65 Cu
3079 -+ 770
103
65 Cu
2329 -+ 0
104
63 Cu
2336 -- 0
103
65 Cu
3127 -- 770
104
63 Cu
3428 -* 962
104
63 Cu
2497 --+ 0
103
63Cu
2512 -+ 0
104
63Cu
2536 -- 0
103
104
103
103
63 Cu
3888 -*
1326
63 Cu
3297 -÷ 669
63Cu
2697 -+ 0
63 Cu
2717 -*
103
63 Cu
2780 -+ 0
103
63 Cu
2807 -* 0
103
103
65 Cu
2862 -+ 0
65 Cu
2874
63 Cu
2889 -- 0
103
65 Cu
2902 -- 0
103
63 Cu
3032 -+ 0
103
63 Cu
3043 -~ 0
10
3
-+
0
0
-
0
4.7
Gamma-ray Yields and Sensitivity Limits
All analysis was performed using gf3 [27], which was developed specifically for use
with Germanium detectors like the ones used in this experiment.
When measuring the yield of a given gamma line in a given neutron bin, two
primary methods were used. When the line in question was well resolved and appeared
on a mostly flat background, the 'pk' function was used to automatically determine
and subtract the background, and sum the remaining counts. This could be quickly
automated to fit dozens of lines over many dozens of neutron energy bins. When the
peak in question was weak or unresolved, the more careful 'nf' method was used. This
procedure performed a least-squares fit for any number of peaks on top of a quadratic
background function. Each peak was fit with three components:
* a main Gaussian lineshape, which provided for most of the area of the peak
* a small skewed Gaussian to model an exponential tail on the low-energy side of
the line
* a small, decaying step function on the lower-energy side to simulate Compton
scattering
When examining the regions of interest, we used a different procedure. When
there were no detectable peaks in the region of interest, we estimated the sensitivity
of our apparatus as follows. We used the resolution of the Germanium detector around
the appropriate gamma-ray energy to estimate the width of the ROI. The full width
at half maximum varied as 0.2% of the neutron energy, as discussed in Section 4.6.
Modeling the background as a Poisson process, we took the square root of the counts
in this region to be the standard deviation in the background. Multiplying this by
2, we obtained the 2a sensitivity threshold. With high probability, any peak yields
with area smaller than this amount could not be distinguished from background.
The livetime L for the gamma-ray spectrometer is described above in Section 4.4.
The yield for a given peak was calculates as follows:
Iy (En)
C=
-t
(1 - ay) L B(E,)
(counts/MeV)
(9)
In equation 9 above, Ict, is the number of counts for a given gamma peak 7 in a
particular neutron energy bin, a, is the internal converstion coefficient for that line,
and L is the livetime fraction for the detector array. To normalize the results per
MeV, we divide by the size of the neutron energy bin B(E,).
In general, the sensitivity threshold was on the order of one millibarn or lower,
with a slight dependence on gamma-ray energy. At low gamma ray energies, the
region of interest was smaller due to the more precise resolution of the apparatus,
but there were a higher number of background counts. When a region of interest
contained a feature, we measured its yield as above, and constructed its cross-section
as given below.
4.8
Constructing the Integral Cross Section
The neutron flux information, efficiency calibration and yield measurements are then
all combined into a single differential cross-section. As noted above in Section 2.3, the
integral cross-section is approximated by treating the whole detector array as making
a single measurement. The three quantities above can be combined to give a measure
of "how many instances of the transition occur per incident neutron". We want to
turn this into a nuclear science measurement, and express the results in barns. The
conversion ratio t is given in Section 3.3. Thus, the integral cross section of a line 3y
in a neutron bin E, is given by:
N I(y, E,)/(-y)
F(y)- (E)
= t
(10)
In equation 10 above, I is the corrected yield of a peak in that neutron energy
bin as described in Section 4.7, c is the corrected efficiency at that gamma energy as
described in Section 4.4, 1 is the corrected flux through that neutron energy bin as
described in Section 4.3, F is the attenuation correction as described in Section 4.5
and t is the target thickness in atoms per barn, which for this experiment is given in
equation 2. All other issues and corrections (internal conversion coefficient, livetime
corrections, gamma attenuation, etc.) are folded into one of those three categories.
N is a factor allowing for an absolute normalization to a reference line. For this
experiment, all cross sections were normalized to the prominent and well-measured
1115-keV transition in 63 Cu. The reference value used for normalization is the result
of the TALYS code [15], and is shown later in Section 6.1.2. The normalization factor
was obtained by taking the ratio between TALYS predictions and experimental results
around the threshold of the reaction and performing a least-squares fit.
The normalization condition can be written as an equation for N. At any value
E,, N is related to the reference value O1 115 at that neutron energy.
Ul5u(En) -=N I(1115, E,)/E(1115)
t
(11)
I(1115) - (En)
Because of this normalization, there is an alternate way to write equation 10 that
relates the cross-section of any measured line to the cross-section of the 1115-keV
transition.
I(y, E,) c(1115) F(1115)
I1(1115, En) E(7)
F(7y)
Since all of the factors in equation 10 are multiplied or divided, standard error
propagation [2] states that the relative error on the final result is the sum of the
relative errors of all of the terms added in quadrature. This is discussed in more
detail in the following section.
When constructing cross-sections for prominent transitions in natural copper,
statistics were good enough that the analysis could be performed using 15ns neutron
energy bins (the limit on granularity, due to apparatus time resolution). However,
when examining the 0v43 regions of interest, statistics were low enough that wider,
150ns bins, had to be used.
5
Error Analysis
The experimental uncertainties of these measurements must be discussed. There are
four major questions here. What fundamental or convenient necessary approximations and assumptions were made while constructing the cross-sections we present?
How do these translate to sources of systematic errors? What sources of statistical
error are there and how significant are they? How can we reduce the effects of these
factors in later experiments?
5.1
Approximations and Systematic Error
There are a number of necessary approximations in our model of the experiment
made during the process of data analysis. They are discussed in order of descending
prominence here, along with potential systematic effects.
The angular distribution problem is the most serious. As of this writing, we do
not have a rigorous treatment of the problem, and have been using the detector as a
full-coverage spectrometer. In fact, as Table 2 shows, detectors tend to fall at specific
angles. The worst-case scenario is that the angular distribution happens to have local
maxima (or minima) at just the angles that detectors in the array sample. To calculate
how bad of an effect this could have, we took typical differential cross-sections for the
most common multipolarities [22], and calculated the average integral cross-section
seen by sampling at the detector angles given in Table 2. For E2 multipolarities and
El + M2 multipolarities, a typical cross-section might look like [22]:
E2 : do•(cos 0) = co(1 + 0.5428P2 (cos 0) - 0.3428P4 (cos 0))
da
M1 + E2: dO (cos 0) = ao(1 - 0.4282P2 (cos 0) - 0.0490P4 (cos 0))
(13)
(14)
Taking the average over the ten active coaxial detectors, our array would see
0.9056 0o for the E2 transitions and 1.054co for the E1+M2 transitions. The situation
is slightly more complicated than this, however. Individual detectors have different
efficiencies and attenuation coefficients, and so this average is idealistic. Furthermore,
the typical differential cross-sections were taken from the reactions at threshold, and
it is known that anisotropy falls off with neutron energy [19]. Since the transition used
for normalization has El + M2 multipolarity, we set the systematic uncertainty from
normalization at 5.4%. Since this is the worst-case analysis, this probably overstates
the systematic error. Nevertheless, we include it.
The gamma ray attenuation problem is the next most prominent. We approximated the attenuation coefficient for the array by averaging the individual coefficients seen by each detector. However, individual detectors have a slightly different
efficiency, so this is not absolutely correct. In fact, the standard deviation in the
mean absolute efficiency of all the detectors is 16 - 17% over the majority of the
energy range. In this manuscript, we are unable to provide a systematic uncertainty
associated with the attenuation problem. It is one of the few key issues we are still
investigating. However, there are two reasons why this effect falls off at high energies
and is thus likely to be less relevant to our region of interest results. First, the attenuation of a given gamma ray through any amount of material decreases asymptotically
with increasing neutron energy. Second, the spread of detector efficiency is greater at
lower energies because the detectors have different low-energy suppression behavior.
Another potential problem is the even distribution of deadtime. In the worst-case
scenario, the data acquisition system is less able to write events to disk when many of
them happen at once. Thus, at neutron energies that cause a large amount of gamma
ray events, the deadtime might be higher. After the deadtime correction was made,
the net effect of this would be to supress high cross sections and abnormally raise low
cross sections. However, we are not concerned with this for two reasons. First, this
is somewhat cancelled out by a similar effect in the fission chamber. Second, when
the cross-section is written using the normalization to the 1115-keV line in equation
12, any livetime correction to the corrected flux, yields and efficiency measurements
cancels.
The promptness of the excitation and decay of the target is an issue. If the excited
states of the nuclei have a long half-life, and there is a significant delay between
excitation and decay, then transitions measured later would be interpreted by the
experimenter as being caused by a later-arriving (i.e. slower) neutron. The overall
effect would be to distort the cross-section as a function of neutron energy towards
the lower energies. In practice, all of the transitions presented here are produced
by levels with half-lives on the order of picoseconds [17]. There is a possibility that
some very high-lying levels have a half-life on the order of nanoseconds, and in the
cascade of gamma rays down to the ground state. To measure this effect directly, we
examined the spectrum at neutron energy levels below threshold for the first excited
states in 63,65 Cu. There was no significant signal.
Similarly, the time it takes for a created gamma ray to leave the target and enter
a detector (-
15cm in just
-
0.5ns) is not a significant fraction of the apparatus
senstivity. Another issue is the neutron-overlap problem. Specifically, as the highenergy neutrons of the next micropulse are arriving, the slow neutrons from the
previous pulse are still hitting the target. However, with a micropulse width of 1.8 ps
and a distance of 20.34m between the spallation source and the target, only neutrons
with E, = 650keV have not yet hit the target. This is not high enough in energy to
activate either first excited state (e.g. the 670-keV level).
Another possibility for a small adjustment is the difference between the collision
rest frame and the lab frame in which transitions are measured. The conservation
of linear momentum in the incident neutron + atom at rest system means that the
direction of motion of created gamma rays have some non-zero component along the
direction of the beam, on average. A recent publication [25] covers this effect in more
detail, giving a correction to the angular distribution caused by this effect. While
this effect is prominent in reactions on light nuclei (e.g. In +1 H), it is not significant in relatively large atoms such as 63 '65 Cu, which are many orders of magnitude
more massive than the incident neutrons. The velocity of the rest frame (v = .003c
even with incident energy E, = 200 MeV) is not fast enough to skew the angular
distribution.
Because of the neutron arrival resolution time in the experimental apparatus, our
measure of the cross-section from inelastic neutron scattering has to be reported in
neutron bins that are, at the minimum, 15 ns wide. When the cross-section as a
function of energy is slowly-changing, this is a fine approximation. However, this
smudging out of the cross section makes it impossible to measure phenomena at
specific neutron energies, such as the threshold for a transition. In general, neutron
binning distorts the shape of the cross-section. Since this experiment is primarily
interested in measuring lines in the regions of interest with very small cross-sections,
very large neutron bins are used anyway, and we are not concerned with this effect.
The last minor issue is that the experimental target was natural, not isotopic, copper. This had a few implications. First, it was impossible to seperate any overlapping
lines in 63Cu and 65 Cu, such as the important 63 Cu 365.2-keV and 65 Cu 366.3-keV
lines, and report their cross-sections separately. Secondly, for 63 Cu transitions, it is
impossible in theory to seperate the contribution to the cross-section from 63 Cu (n,n)
reactions from the contribution from 65 Cu (n,3n) reactions. In practice however, the
latter reactions had a much higher-energy threshold, by which point the former crosssection had largely fallen off. Finally, while it was possible to take measured (n,xn)
reactions in isotopic copper, take a weighted sum and measure them against our
data, the reverse process does not work. This point is mitigated by the fact that the
aim of this experiment is to see how natural copper behaves in future experiments:
information about individual isotopes is not required.
5.2
Statistical Error
Every counting experiment has statistical error. For an experiment measuring nuclear
events, the error associated with any number has a Poisson uncertainty. This applies
to two key of the total cross-section.
Individual peak yields have a roughly square root error. When statistics for a
given peak are low (for example, because of a small choice of neutron energy bin or
for a rare transition), the relative error can be significant. This kind of error applies
both to peak yields used in constructing cross sections as described in Section 4.7 and
also to measurements used to provide an efficiency calibration as described in Section
4.4.
When incident neutrons cause fission in 235,238 U atoms, the fission chamber registeres a number of counts due to this process. The number of decays measured by
the fission chamber is a nuclear measurement, but due to several other issues such as
experimental uncertainty in the (n, f) cross-sections, degradation of the fission chamber over time, and apparatus time resolution, the experimentally determined relative
error is on the order of 5%. This amount decreases slightly with neutron energy.
The error in the efficiency calibration comes from the uncertainty in the fitted
efficiency function coefficient, which tends to be very small since the efficiency spectra
have good statistics. However, it increases with gamma-ray energy, especially past
2.5-MeV, since there are no efficiency calibration peaks there. Since the efficiency
calibration has no neutron-energy dependence, we consider it a source of systematic,
instead of statistical, error.
Although the livetime correction for the efficiency calibration, yield and fission
chamber measurements are significant and important, since they concern such a large
number of counts, the statistical error introduced by these corrections is not significant.
These two key sources of statistical uncertainty are added in quadrature to come
up with the final statistical error in the experimentally measured cross-section.
5.3
Error Propagation
The major sources of statistical error come from the counts used to construct the
gamma-peak yield and the flux through a given neutron bin. The major sources of
systematic error are the uncertainty in the overall normalization due to angular effects
and the systematic uncertainty involving the efficiency.
Following [2] and equation 10, the final uncertainty at a neutron bin E, for a peak
y is given by equation 15 below.
+ I
4b (E,) )2E
) ( (Ia(E")
(En)
+
N(E,))
+
_(E
)
(15)
To give an illustration of how each relative error term contributes to the final
result, and which uncertainties are prominent at which regions of neutron energy,
the terms in equation 15 are plotted in Figure 12 for the measured cross-section of
the 962-keV transition. At low neutron energies, the uncertainty in the flux tends
to dominate. At higher neutron energies, the uncertainty in the peak yields tends to
dominate.
I ..
o
0J
w
41-J
Cu
neutron energy (MeV)
Figure 12: Contributions to Error in the 962-keV Cross-Section
The highest curve is the sum of all of the error terms.
In general, the error from peak yields dominates these measurements. When
statistics are low, such as with region of interest-contaminating line cross sections,
statistical error from background dominates all other factors. In fact, for the ROIs,
statistics are so low that we report results in 150ns-wide bins. When statistics are
high, such as with the (n, n') cross sections of prominent copper lines, systematic
errors below are responsible for the discreprancy betwen simulation and experiment.
5.4
Future Error Reduction
There are two components to fully investigating the angular problem. The first is
a theoretical understanding of the cos 0 dependence of the cross-section for given
transitions, and how these vary as a function of neutron energy. The second is to
understand the systematics and efficiency issues of each individual detector so that
differential cross-sections can be constructed. When we attempted to do this in
the past, we found that although GEANIE's results for integral cross-sections were
mostly faithful given appropriate calibration and normalization, systematic errors and
eccentricities between individual detectors were larger than the measured differences
in the differential cross-section between them. Both of these are potential tasks to
work on in future experiments of this type at this facility. In particular, as individual
detector systematics are understood, a measurement of angular dependence becomes
more of a possibility.
To fully investigate the gamma attenuation issue, a full Monte Carlo N-Particle
(MCNP) code simulation of the gamma ray attenuation through the target should be
done. This simulation will take into account the geometric details of the target and
detector array. One of the advantages of this treatment is that the attenuation and
efficiency calibration would take place within a single measurement.
To ensure that all transitions under investigation are prompt, a coincidence analysis between transitions between higher energy levels and lower energy levels and
between lower energy levels and the ground state should be performed. This way, the
connection between which excited energy levels cause which observed transitions can
be made explicit. For example, if the second excited ground state has a high halflife,
but the first excited state has a very prompt one, then a coincidence measurement
between 2 -* 1 and 1 -- gs events can establish what proportion of the 1 --+ gs
cross-section is caused by the second ecxited energy level.
Unfortunately, the only way to defeat statistical error is with more statistics. Since
the statistics in this experiment come from Poisson-process nuclear decay events, the
error varies as the square root of the number of counts. For both fission chamber and
detector array events, the total number of events varies linearly with the runtime.
Since each data point contains contributions from these errors in quadrature, doubling
the run time is likely to supress uncertainty by a factor of V2. The unfortunate upside
is that to obtain an extra digit of precision in any measurement, the experiment would
need to run for ten times as many days. Since this data was obtained with two weeks
at the facility, which is only operational for part of the year, this is not feasible.
In summary, there are numerous systematics. Some of them can be shown to
be insignificant or not applicable, we can put a numerical cap on the effect of some
others, and others are still under investigation. Future experimenters can probably
make significant improvements to these systematics. As we said above, the statistical
errors are unlikely to improve unless run time increases significantly. To that extent,
the statistical uncertainty on the data presented in this experiment is likely to be the
best that this facility can produce.
6
6.1
Experimental Results
natCu
(n,xn'y) Cross Sections
Below are results for the integral cross section of prominent neutron-induced transitions in natural copper. We present four prominent lines in 63Cu and two in the
less-abundant 65 Cu isotope.
6.1.1
63 '65 Cu
(n,xn'y)
6 5Cu
We present integral gamma-ray production cross-section measurements for (n, n'y)
on 63 Cu and (n, n'-) reactions on 65 Cu that result in 63 Cu lines. Understanding the
disreprancies between theory and experiment both drives nuclear data simulations
and validates region of interest results, presented in the next subsection.
Below, the cross-section for the 670-keV first-excited state to ground state transition is shown in Figure 13, the cross-section for the 962-keV second-excited state
to ground state transition is shown in Figure 14, the cross-section for the 1327-keV
third-excited state to ground state transition is shown in Figure 15 and the crosssection for the 1412-keV fourth-excited state to ground state transition is shown in
Figure 16.
All of the plots have similar qualitative features. There is a threshold energy
equal to the energy of the transition (below this energy, the neutron can't actually
excite the nucleus high enough). There is a peak at which the (n, n') reaction is most
probable, and then a fall-off. In the case of 63 Cu lines, there are two peaks. The
first is from (n, in') reactions with energy 3 - 10MeV neutrons. The second, smaller
peak is from (n, 3n') reactions on 65 Cu with energy 12+ MeV. Since more energy
is required to knock neutrons out of the nucleus, the threshold for this reaction is
higher. The total (n, xn) cross-section is the super-position of these two effects.
The plots on left side show the experimentally determined cross-section in blue
and the result of a TALYS code simulation in red. The plots on the right side show
the relative experimental error in blue and the relative difference between theory and
experiment in red.
-
(Exp - Th) / Th
Stat. Error
Ii
02
0.
..
,,
63 Cu
Figure 13: Calculated and Simulated
nat-Cu (n,n') 63-Cu 962-keV transition integral cross section
ncident
neutron
energy (MeV)
incident neutron
energy (MeV)
670-keV cross-section
0.61
-
(Exp - Th)/ Th I
- Stat. Error
I
A\
i;
0.0
10i
Incident neutron energy (MeV)
Figure 14: Calculated and Simulated
Incident neutron energy (MeV)
63
Cu 962-keV cross-section
nat-Cu (nn') 63-Cu 1327-keV transition integral cross section
Incident neutron energy (MeV)
Incident neutron energy (MeV)
Figure 15: Calculated and Simulated
63 Cu
1327-keV cross-section
nat-Cu (n,n') 63-Cu 1412-keV transition integral cross section
Incident neutron energy (MeV)
Figure 16: Calculated and Simulated
6.1.2
65 Cu
(n,n'7)
Incident neutron energy (MeV)
63 Cu
1412-keV cross-section
6 5 Cu
Similarly, we present integral gamma-ray production cross-section measurements for
(n, n't) on 65 Cu that result in 65 Cu lines.
The cross-section for the 1115-keV second-excited state to ground state transition is shown in Figure 17 and the cross-section for the 1481-keV third-excited state
to ground state transition is shown in Figure 18. In this case, there is no (n, xn)
contribution from isotopes with a higher N number, so the total cross-section is just
the result of (n, n) reactions. The 1115-keV line was used to perform an absolute
normalization. This is the reason for the agreement between theory and experiment
in the threshold region for the reaction.
Again, the plots on left side show the experimentally determined cross-section in
blue and the result of a TALYS code simulation in red. The plots on the right side
show the relative experimental error in blue and the relative difference between theory
and experiment in red.
Figure 17: Calculated and Simulated
65 Cu
1115-keV cross-section
on
Incident neutron energy (MeV)
Incident neutron energy (MeV)
Figure 18: Calculated and Simulated
6.2
65 Cu
1481-keV cross-section
OvP,3 Regions of Interest
Below are results on the regions of interest for seven neutrinoless double-beta decay
isotope candidates. Again, we examined the region around the energy at the reaction
endpoint and the region 1022-keV higher because of the possibility of an electron
signal from a double-escape peak. In cases of an overlapping line, we present the
integral cross-section. All of the lines we observes were known transitions in 63 ,65 Cu.
Otherwise, we give the sensitivity limit of the apparatus. A summary of our results
is given in Table 9.
We do not have results for regions of interest above the upper energy limit of our
0
detector (- 4MeV), for the double-escape peak ROI in ooMo
and 15 0Nd and in both
48 Ca regions. For each isotope, we discuss a few current, future and
past experiments
that use this candidate to search for v0/3. The list is not comprehensive, but rather
a sampling of current research.
Table 9: Experimental Ovoy
Isotope
Region of Interest Results
ROI Energy
2039-keV
3061-keV
2995-keV
4017-keV
ROI Spectrum
Result at E, = 8 MeV
n/a
n/a
< 0.39 mbarn
looMo
3035-keV
3034-keV line
116Cd
2809-keV
3831-keV
2808-keV line
n/a
2530.3-keV
3552-keV
2536-keV line
n/a
76
Ge
82Se
130Te
3003-keV line
n/a
< 0.42 mbarn
4.2 mbarn
< 0.29 mbarn
4.6 mbarn
4.4 mbarn
< 0.30 mbarn
8.5 mbarn
< 0.35 mbarn
2457-keV
n/a
< 0.39 mbarn
3479-keV
3476-keV line
2.4 mbarn
15 0
Nd 150Nd
3368-keV
< 0.38 mbarn
n/a
1 J
,
i
A summary of our results. For every isotope which had regions of interest within
our visible energy range, we report on any lines that fell within that ROI, and give
the measured cross-section at E, = 8 MeV.
13aXe
6.2.1
76 Ge
76Ge
is a popular double-beta decay candidate and is used in several current, past
and future experiments. One of its advantages is that it can be used as both detector
and source in these experiments, two of which we list here. In the present work, we
present sensitivity limits on the otherwise-clean 76 Ge regions of interest in Figures 19
and 20.
The MAJORANA experiment aims to perform a low-background measurement
of neutrinoless double-beta decay in 86% enriched 76 Ge, and refute or confirm the
Klapdor-Kleingrothaus claim of OvPP3 in 76 Ge. The experimental site will be held underground, and recent R&D efforts are focused on keeping the germanium crystals in
an electropurified copper cryostat. One of the original motivations for this experiment
was to make (n, n') background measurements for the MAJORANA collaboration.
The GERmanium Detector Array (GERDA) is a 76 Ge experiment currently under
construction, which plans to use enriched germanium crystals in a sealed copperplated cryostat filled with a liquid noble gas. Like other experiments outlined in this
section, the experimental site would be installed deep underground in the Laboratori
Nazionali del Gran Sasso (LNGS), in Italy.
1i0n
00
-.10o
Figure 19:
76 Ge
Energy (kev)
Figure 20:
76 Ge
nat-Cu (nn') 2040-keV ROIsensitivity limit
10o
Incident neutron energy (MeV)
OvPP Q-value ROI and sensitivity limit.
Incident neutron energy (MeV)
Ov/3 Q-value DEP ROI and sensitivity limit.
6.2.2
82 Se
The wide 3004(3)-keV line from the 63 Cu 4416 -4 1412 transition contaminates the
region around the 82 Se Q-value, and we give an integrated cross-section for it in Figure
21. The higher ROI is clean, and we give a sensitivity limit in Figure 22.
This isotope is one of the ones used by the Neutrino Ettore Majorana Observatory
(NEMO) in the current NEMO-3 incarnation of the experiment, which has a movable
center into which different sources can be placed. The apparatus is installed below
the earth's surface at the Frejus Underground Laboratory in France, at a depth of
4800 meters of water equivalent, and the source is surrounded by a purified copper
shield. Recently, the NEMO collaboration has published results using Ikg of 97%
enriched s2 Se.
nat-Cu (n,n') 63-Cu 3003 keV
''
10c
Incident neutron energy (MeV)
Energy (kev)
Figure 21:
82 Se
Ovo0 Q-value ROI and cross-section.
nat-Cu (n,n') 4017-keV ROI sensitivity limit
Ln
C:
0
U
_i~
3970
3980
3990
4000
4010
Energy (kev)
Figure 22:
82 Se
4020
4030
4040
101
Incident neutron energy (MeV)
0v3/3 Q-value DEP ROI and sensitivity limits.
1 00Mo
6.2.3
The 3032.1(10)-keV line from the 63 Cu 3032 --+ 0 transition contaminates the region
around the 10oMo Q-value, and we give an integrated cross-section for it in Figure 23.
The higher ROI, at 4055-keV, was beyond the limits of the experimental facility.
The MOlybdenum Observation of Neutrinos (MOON) proposes to study double
beta decay using one ton of 85% pure 10 0Mo as the source. In addition to being a
O/30 candidate, 100Mo has several attractive properties in neutrino physics such as
being a good solar neutrino detector through inverse beta decay.
The NEMO-3 experiment above also uses a 98% pure 100Mo foil as a source.
nat-Cu (n,n') 63-Cu 3032 keV
4200
4000
4-
3800
3
W 3600
0
3400
0
u
3200
3000
0100
Energy (kev)
Figure 23:
6.2.4
100Mo
01
102
Incident neutron energy (MeV)
Ov/3 Q-value ROI and cross-section.
116 Cd
The 2806.6(6)-keV line from the 63 Cu 2806 --, 0 contaminates the region around the
116 Cd Q-value, and we give an integrated
cross-section for it in Figure 24. The higher
ROI is clean, and we give a sensitivity limit in Figure 25.
The Cadmium-Telluride O-neutrino double-Beta Research Apparatus (COBRA)
experiment aims to detect neutrinoless double beta decay using CdZnTe ("CZT")
crystals, which contain 11 Cd as well as 30oTe, both beta-decay candidates. The
COBRA prototype array of CZT crystals sits inside a a thick natural copper core,
making the present work particularlt relevant. The experiment takes place deep
underground, in the Laboratori Nazionali del Gran Sasso (LNGS).
nat-Cu (n,n') 63-Cu 2808 keV
++
U
neutron
0Incident
energy (MeV)
Incident neutron energy (MeV)
Figure 24: 116 Cd Ovil
Q-value ROI and cross-section.
nat-Cu (n,n') 3831-keV ROIsensitivity limit
Incident
neutron
energy (MeV
Incident neutron energy (MeV)
Figure 25: "116CdOv/3 Q-value DEP ROI and sensitivity limit.
6.2.5
130Te
The 2536.0(3)-keV line from the 63 Cu 2536 - 0 transition contaminates the region
around the 130Te Q-value, and we give an integrated cross-section for it in Figure 26.
The higher ROI is clean, and we give a sensitivity limit in Figure 27.
This isotope is used in the Cryogenic Underground Observatory for Rare Events
(CUORE) experiment, which proposes to use a large array of TeO 2 crystals (with
33.8% abundant 130Te) to measure neutrinoless double-beta decay. CUORE will use
741 kg of TeO 2 deep underground in the Laboratori Nazionali del Gran Sasso (LNGS)
installation in Italy, at 3400 meters of water equivalent.
As mentioned above, the COBRA experiment is searching for OvP/ in 130 Te.
nat-Cu (n,n') 63-Cu 2536-key + 65-Cu 2533-keV
4%
4-t
2
-t
0
101
Incident neutron energy (MeV)
13 0Te
Figure 26:
S--
2500
OvoP
Q-value ROI and cross-section.
u target3-30 MeV
1.0
nat-Cu (n,n') 3552-keV ROI sensitivity limit
1
2400
2300
U
%lia1~ "¼
S200
-
------ ..
1900
1800
3520
3540
3560
Energy (kev)
Figure 27:
6.2.6
13 0Te
3580
3600
.,i
10i
Incident neutron energy (MeV)
I
O3/03 Q-value DEP ROI and sensitivity limit.
136 Xe
The lower ROI is clean, and we give a sensitivity limit in Figure 27. The 3476-keV
line from the 63 Cu 3476
0 transition contaminates the region around the higher
136Xe Q-value, and we give
an integrated cross-section for it in Figure 29.
-
This isotope is used in the Enriched Xenon Observatory (EXO) experiment, which
proposes to use over 200kg of 80% enriched 136 Xe cylinders to search for neutrinoless
double-beta decay. EXO-200 will be installed underground at the Waste Isolation
Pilot Plant (WIPP) in Carlsbad, New Mexico.
The Gotthard underground laboratory is also conducting a 136 Xe experiment,
using 2 x 105 cm3 of xenon gas at 5 bar, with 62.5% pure 13 6Xe. A copper shield
protects the xenon, which serves both as source and detector, so this measurement
is particularly relevant. The experiment takes place underground at a laboratory in
the Swiss alps, at 3700 meters of water equivalent.
rn
I
nat-Cu (n,n') 2457-keV ROI sensitivity limit
0.8
0.4
o
-E
z=
0.2
[) o0
i
Figure 28:
136 Xe
v0/3
l
10
Incident neutron energy (MeV)
Q-value ROI and sensitivity limit.
nat-Cu (n,n') 63-Cu 3476 keV
101
Energy (kev)
Figure 29: 136Xe Ov0/
6.2.7
Incident neutron energy (MeV)
Q-value DEP ROI and sensitivity limit.
15 0Nd
There were no identificable features in the region of interest for 5's Nd. The sensitivity
limits on the otherwise-clean ROI are shown in Figure 30. The higher ROI, at 4389keV, was beyond the limits of the experimental facility.
The SuperNEMO experiment, an improvement of the NEMO-3 experiment listed
earlier, proposes to use an 15 0Nd source, but is still under development.
The Drift Chamber Beta-ray Analyzer (DCBA) proposes to use a large-magnetic
field tracking chamber to search for neutrinoless double-beta decay in 80% enriched
150 Nd. This project is under development in Japan.
~nnn
nat-Cu (n,n') 3367-keV ROIsensitivity limit
1.0
-- Cu target 3-30 MeV I
2900
2800
02700
~2600
~i-L~.;
2500
2400
~n
i
1
i
2300
3320
3340
3360
3380
nn
U.
10o
3400
Energy (kev)
Figure 30:
15 0Nd
dent
neutron
energy
e)
Incident neutron energy (MeV)
Ov,0 Q-value ROI and sensitivity limit.
62
7
Conclusion
We have presented a quantitative investigation of the neutron-induced gamma ray
radiation in natural copper that contaminate regions of interest corresponding to the
Q-value and double-escape peak regions in six double-beta decay candidate isotopes.
When a neutron-excited 63 '65 Cu transition overlapped with a given region of interest,
we calculated the integral cross section over the neutron energy region from 1 to 200
MeV. When the region of interest had no visible features, we reported the limits of
our sensitivity.
To give our results credibility, we discuss the experimental apparatus in some
detail and calculate the (n, xn'y) cross sections for prominent transitions in natCu
and compare them with the results of TALYS nuclear simulations. We discussed the
efficiency calibration and data analysis process. We investigated sources of systematic
error such as the angular problem, overall normalization, deadtime issues, gamma ray
attenuation and statistical error.
These measurements are important for experimenters planning the next generation
of underground double-beta decay experiments. Integral cross section measurements
for region of interest contaminants in natural copper, along with an understanding of
cosmic ray-induced spallation neutron flux, give important benchmarking data points
for Monte Carlo simulations and background studies.
Since the regions of interest for many Ov00 candidate isotopes were investigated,
these results apply to many experiments under development which take place underground, where neutron flux is a source of background, and with significant natural
copper around the experimental site. This analysis can be performed with other detector and shielding materials. Within the last year, data was taken at GEANIE
using a natural lead target, and a similar analysis with enriched germanium is being
performed in parallel. Our team at Los Alamos has recently proposed beam time at
LANSCE for a CZT target.
We hope that the results presented here will contribute to the exciting experimental efforts in neutrino physics.
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8
#
#
#
#
Appendix I: geanie.py Source Code
This is a set of GEANIE (n,n') measurement-related functions. There
are utilities to usefully manage data in the formats used throughout
the GEANIE analysis, and also utilities to intelligently construct
cross-section measurements.
# copyright 2007 Dennis V. Perepelitsa (dvp@mit.edu, dvp@lanl.gov)
# import a non-linear least-squared fitting module written by dvp
import jlabfit
# import numerical analysis and plotting python packages
import scipy, pylab
# import other useful modules
import os
# we model the efficiency as a high-order polynomial in log-energy,
# log-efficiency space
def f6(params, y):
"""This is a helper function which defines the functional form of
the efficiency for a solid-state, high-purity germanium
detector. You shouldn't call it directly."""
# this is the energy to which the logarithm of all else is
# relative
x = scipy.log(y/1000.0)
return params[0] + params[l] *x + params[2]*(x**2)\
+ params[3]*(x**3)
+ params[4]*(x**4)
+ params[5]*(x**5)
def writeout(fil, desc, cols):
,I II II
This is a simple function that writes out data to a file. It's
intended to have an easy interface.
fil : filename to write to
desc : the first line of the file
cols : an array of columns of data
II II II
f = file(fil,'w')
f.write(desc + '\n')
for i in range(len(cols[O])):
for j in range(len(cols)):
f.write('cols[j] [i]'
+
'1
)
f.write('\n')
f.close()
def __sum_scaler(scalerfile):
"""This is a helper function that extracts a scaler from an
appropriate scaler *.spe converted to a textfile. You shouldn't
call it directly."""
f = file(scalerfile, "r")
lines = []
n = []
line = f.readline() # cut the first one
line = f.readline()
while line != "":
for j in line.split():
n += [int(j),]
line = f.readline()
s =0
for i in range(4096):
s += i * n[i]
f.close()
return s
def getlivetime(gmtfile,detarray):
"""Returns an array of livetimes in a given .gmt for each detector
index in the passed array (FC1 and 2 are treated as det# 29 and
30, respectively). Currently ignores livetime uncertainty."""
livetimes = []
for det in detarray:
res = os.popen4("echo -e \"id " + 'det' + "\\nws tmp-" +\
'det' + "\" I rgmt " + gmtfile)
for line in res[l].readlines(): pass
res = os.popen4("echo -e \"id " + '290+det' + "\\nws tmp-"\
+ '290+det' + "\" I rgmt " + gmtfile)
for line in res[l].readlines(): pass
res = os.popen4("sumspe tmp-" + 'det' + ".spe")
# we need the standard output result here
for line in res[ll.readlines():
adc = float(line.split() [-1])
res = os.popen4("echo -e \"1\\nn\\ntmp-" + '290+det' +\
".spe\\n\" I spec_ascii")
for line in res[l].readlines(): pass
scaler = __sum_scaler("tmp-" + '290+det' + ".txt")
print adc, scaler
livetimes += [adc/scaler,]
res = os.popen4("rm tmp-" + 'det' + ".spe tmp-" + 'det'\
+ ".txt tmp-" + 'det+290' + ".spe + tmp-"\
+ 'det+290' + ".txt")
for line in res[ll.readlines(): pass
return livetimes
def getefficiency(effparams, effparamrelerr, E):
"""Returns the calculated efficiency at this value of energy as a
tuple with relative uncertainty."""
eff = scipy.exp(f6(effparams,E))
x = scipy.log(E/1000.0)
abserrsq = 0
# propagate absolute error term by term
for i in range(len(effparams)):
abserrsq += (eff**2)*(effparamrelerr[i]**2)*((x**i)**2)
return (eff, scipy.sqrt(abserrsq))
def calculate_efficiency(efffile,effsource,decays,livetime,\
plot=False,silent=True):
"""Takes a source calibration file, a calibration file for this
detector, total number of decays and detector deadtime, and
returns a set of polynomial coefficients that describe the best
fit. """"
# read in intensities here
fil = file(effsource,'r')
sourcelines = fil.readlines()
fil.close()
fil = file(efffile,'r')
caliblines = fil.readlines()
fil.close()
E = []
intensity = []
intensityrelerr = []
cts = []
ctsrelerr = []
if not len(sourcelines) == len(caliblines):
print "Number of source and eff peaks MISFIT"
for i in range(len(sourcelines)):
x = caliblines[i] .split()
# if we didn't see this peak, skip to the next source peak
if not int(x[1]) == 0:
cts += [float(x[1]),]
ctsrelerr += [float(x[2] )/float(x[l]),]
x = sourcelines[i] .split()
E += [float(x[O]),]
intensity += [float(x[1)/100.,]
intensityrelerr += [float(x[21 )/float(x[1]) ,]
E = scipy.array(E)
intensity = scipy.array(intensity)
intensityrelerr = scipy.array(intensityrelerr)
# canonical use of 4\pi solid angle factor
logeff = scipy.log(4*scipy.pi*scipy.array(cts)\
/(decays*(livetime)*intensity))
# perform correct error propagation
logeffrelerr = scipy.sqrt(scipy.array(ctsrelerr)**2\
+ intensityrelerr**2)/logeff
pO = [1.0,1.0,1.0,1.0,1.0,1.0]
res = jlabfit.fit(f6,E,logeff,logeffrelerr*logeff,p0,\
plot,None,silent)
return (res[O],scipy.array(res[1])/res[0])
def getflux(fluxfile,livetime):
"""Takes a flux per MeV output file created with fluxperMeV.f and
fission chamber deadtime and returns a tuple of flux and flux
relative uncertainty."""
flux = []
fluxrelerr = []
fil = file(fluxfile,'r')
lines = fil.readlines()[1:]
fil.close()
for line in lines:
x = line.split()
flux += [float(x[1]),]
fluxrelerr += [float(x[2] )/float(x[1]),]
flux = scipy.array(flux)/(livetime)
fluxrelerr = scipy.array(fluxrelerr)
return (flux, fluxrelerr)
def getbins(binfile):
"""Takes a .bin file output by exbins and returns a tuple of
neutron bin mid-points and bin sizes."""
binmid = [1
binwidth = []
fil = file(binfile,'r')
lines = fil.readlines()[6:]
fil.close()
for line in lines:
x = line.split()
binmid += [float(x[2]),]
binwidth += [float(x[1])
- float(x[O]),]
binmid = scipy.array(binmid)
binwidth = scipy.array(binwidth)
return (binmid, binwidth)
def get_yields(yieldfile,column,bins,livetime,alpha=O.0):
""" Takes a pointer to a file (and which column within said file),
a bin data construct, deadtime and internal conversion
corrections, and outputs a tuple of yield (per MeV) and relative
error therein."""
y = []
yerr = [1
fil = file(yieldfile,'r')
lines = fil.readlines()[1:]
fil.close()
for line in lines:
x = line.split()
y += [float(x[2*column-1]),]
if not float(x[2*column-1]) == 0:
yerr += [float(x[2*column])/float(x[2*column-1]),]
else:
yerr += [0,]
# convert to MeV, apply other correctional factors
y = (scipy.array(y)/bins[1])/(livetime*(1-alpha))
yerr = scipy.array(yerr)
return (y, yerr)
def dcs_energy(yields,eff,flux,t):
""" Computes a differential cross-section at one angle as a
function of incident neutron energy. Requires calculated yield,
efficiency and flux output, as well as the thickness in
atoms/barn. """
ys = yields[0]
yerr = yields[l]
e = eff [0]
eerr = eff[1]
f = flux[O]
ferr = flux[1]
# vector arithmetic
cs = ((ys/f)/e)/t
# this is still relative error
cserr = scipy.sqrt(yerr**2 + eerr**2 + ferr**2)
return (cs, cserr)
def getattenuation(rho,detector thickness,mu):
""" Computes the attenuation at a given gamma ray energy, averaged
over all detectors in an array. Requires the density rho, an array
of the effective thicknesses seen by each detector, and the value
mu/rho at the desired gamma ray energy."""
# for the copper runs, rho = 8.96
sum = 0.0
for d in detector_thickness:
sum += -(scipy.exp(-2*mu*rho*d)-l)/(2*mu*rho*d)
return sum/len(detector_thickness)