Neutron Inelastic Scattering Processes as Background for Double-Beta Decay
Experiments
D.-M. Mei,1, 2, ∗ S.R. Elliott,1 A. Hime,1 V. Gehman,1, 3 and K. Kazkaz3, †
Los Alamos National Laboratory, Los Alamos, NM 87545
The Department of Earth Science and Physics, University of South Dakota, Vermillion, South Dakota 57069
Center for Experimental Nuclear Physics and Astrophysics, and
Department of Physics, University of Washington, Seattle, WA 98195
(Dated: October 29, 2018)
We investigate several Pb(n, n′γ) and Ge(n, n′γ) reactions. We measure γ-ray production from
Pb(n, n′γ) reactions that can be a significant background for double-beta decay experiments which
use lead as a massive inner shield. Particularly worrisome for Ge-based double-beta decay experi-
ments are the 2041-keV and 3062-keV γ rays produced via Pb(n, n′γ). The former is very close to
the 76Ge double-beta decay endpoint energy and the latter has a double escape peak energy near
the endpoint. We discuss the implications of these γ rays on past and future double-beta decay
experiments and estimate the cross section to excite the level that produces the 3062-keV γ ray.
Excitation γ-ray lines from Ge(n, n′γ) reactions are also observed. We consider the contribution of
such backgrounds and their impact on the sensitivity of next-generation searches for neutrinoless
double-beta decay using enriched germanium detectors.
PACS numbers: 23.40.-s, 25.40.Fq, 29.40.Wk
I. INTRODUCTION
Neutrinoless double-beta decay plays a key role in
understanding the neutrino’s absolute mass scale and
particle-antiparticle nature [1, 2, 3, 4]. If this nuclear de-
cay process exists, one would observe a mono-energetic
line originating from a material containing an isotope
subject to this decay mode. One such isotope that may
undergo this decay is 76Ge. Germanium-diode detectors
fabricated from material enriched in 76Ge have estab-
lished the best half-life limits and the most restrictive
constraints on the effective Majorana mass for the neu-
trino [5, 6]. One analysis [7] of the data in Ref. [6] claims
evidence for the decay with a half-life of 1.2 × 1025 y.
Planned Ge-based double beta decay experiments [8, 9]
will test this claim. Eventually, these future experiments
target a sensitivity of > 1027 y or ∼ 1 event/ton-year
to explore mass values near that indicated by the atmo-
spheric neutrino oscillation results.
The key to these experiments lies in the ability to re-
duce intrinsic radioactive background to unprecedented
levels and to adequately shield the detectors from ex-
ternal sources of radioactivity. Previous experiments’
limiting backgrounds have been trace levels of natural
decay chain isotopes within the detector and shielding
components. The γ-ray emissions from these isotopes
can deposit energy in the Ge detectors producing a con-
tinuum, which may overwhelm the potential neutrino-
∗Permanent Address: The Department of Earth Science and
Physics, University of South Dakota, Vermillion, South Dakota
57069
†Permanent Address: Lawrence Livermore National Laboratory,
Livermore CA 94550
less double-beta-decay signal peak at 2039 keV. Great
progress has been made identifying the location and ori-
gin of this contamination, and future efforts will substan-
tially reduce this contribution to the background. The
background level goal of 1 event/ton-year, however, is an
ambitious factor of ≈ 400 improvement over the currently
best achieved background level [6]. If the efforts to re-
duce the natural decay chain isotopes are successful, pre-
viously unimportant components of the background must
be understood and eliminated. The potential for neutron
reactions to be one of these background components is
the focus of this paper. The work of Mei and Hime[10]
recognized that (n, n′γ) reactions will become important
for ton-scale double-beta decay experiments. Specifically,
we have studied neutron reactions in Pb and Ge, materi-
als that play important roles in the Majorana [8] design.
But since lead is used by numerous low-background ex-
periments, the results will have wider utility.
This paper presents measurements and simulations of
Pb(n, n′γ) and Ge(n, n′γ) reactions and estimates the re-
sulting background for Ge-detector based, double-beta
decay experiments for a given neutron flux. With these
results, we then use the neutron flux, energy spectrum,
angular distribution, multiplicity and lateral distribu-
tions determined in [10] to estimate the background in
Ge detectors situated in underground laboratories. In
Section II we describe the experiments, the data, and the
simulations. In Sections III and IV we describe the analy-
sis of these data. Section IV also discusses the important
Pb(n, n′γ) production of γ rays at 2041 and 3062 keV.
The former is dangerously near the 2039-keV Q-value for
zero-neutrino double-beta decay in 76Ge and the latter
can produce a double-escape peak line at 2040 keV. These
dangerous processes for Ge-based double-beta decay ex-
periments are discussed for the first time in this work.
Section V determines an overall background model for
http://arxiv.org/abs/0704.0306v4
our detector and the implications of this model for fu-
ture experimental designs. It also considers the relevant
merits of Cu versus Pb as shielding materials, and the
use of depth to mitigate these backgrounds is discussed.
We also consider the possibility that the double-escape
peak of the 3062-keV γ ray could contribute to the signal
claimed in Ref. [7]. Finally, we summarize our conclu-
sions in Section VI.
II. THE MEASUREMENTS
We collected five data sets to explore the implications
of (n, n′γ) for double-beta decay experiments. All mea-
surements were done in our basement laboratory at Los
Alamos National Laboratory. The laboratory building is
at an atmospheric depth of 792 g/cm2 and provides about
1 mwe concrete (77 g/cm2) overburden against cosmic
ray muons.
Three data sets were taken with a CLOVER detec-
tor [11]. This detector is a set of 4 n-type, segmented
germanium detectors. The four crystals have a total nat-
ural germanium mass of 3 kg and each crystal is seg-
mented in half. The CLOVER detector and its opera-
tion in our laboratory were described in Ref. [12]. The
remaining two measurements were done with a PopTop
detector [13] set up in coincidence with a NaI detector.
The PopTop is a 71.8-mm long by 64-mm diameter p-
type Ge detector. Taking into account the central bore,
the detector is 215 cm3 or 1.14 kg. The NaI crystal is
15.25-cm long by 15.25-cm diameter and is directly con-
nected to a photo-tube. All data were read out using
a pair of X Ray Instrumentation Associates (XIA) [14]
Digital Gamma Finder Four Channel (DGF4C) CAMAC
modules. The CAMAC crate is connected to the PCI bus
of a Dell Optiplex computer running Windows 2000. The
system was controlled using the standard software sup-
plied by XIA. This data acquisition software runs in the
IGOR Pro environment [15] and produces binary data
files that were read in and analyzed using the ROOT
framework[16].
The data sets include:
1. A background run with the CLOVER
2. A Th-wire source run with the CLOVER
3. An AmBe source run with the CLOVER using two
different geometries of moderator
4. An AmBe source run with the PopTop surrounded
by lead
5. An AmBe source run with the PopTop surrounded
by copper
In this section we describe the experiments and the data
collected.
A. The Experimental Configurations
The CLOVER was surrounded by 10 cm of lead shield-
ing to reduce the signal from ambient radioactivity. Un-
derneath and above the lead was 5 cm of 30%-loaded
borated polyethylene to reduce thermal neutrons. The
background run done in this configuration lasted 27.13
live-days. The configuration for the Th-source run was
similar, but with some lead removed to expose the detec-
tor to the source. The Th source run had a live time of
1337 seconds.
The setup was modified somewhat from this
background-run configuration for the measurements with
the AmBe source. Fig. 1 shows the configuration for
one of the AmBe measurements. For these data, the
CLOVER was shielded on four sides with 10 cm of lead.
The AmBe source, 30 mCi of 241Am with a calibrated
neutron yield of ≈ 63,000 Hz (±0.7%), was on one side
of the CLOVER with 5 cm of lead and a layer of pure
polyethylene moderator (either 10 or 15 cm thick) be-
tween the source and detector. The data acquisition sys-
tem is inactive during data transfer. Only the AmBe
runs had a large enough event rate for the dead time to
be appreciable. A 6.13-h live-time data run (57% live)
was taken with 15 cm of moderator, and another 3.57-h
live-time data (38% live) run was taken with 10 cm mod-
erator (pictured). For the analysis presented below, the
data from these two configurations were combined, and
thus the AmBe-CLOVER data set contains 9.7 h of live
time. The observed energy spectrum extended from ≈
10-3100 keV for these data sets.
During the analysis of the AmBe data, we observed
a weak line at 3062 keV. This energy corresponds to a
γ-ray transition in 207Pb, and we therefore hypothesized
that it was generated via Pb(n, n′γ). The double-escape-
peak (DEP) energy (2040 keV) associated with this γ ray
is very dangerous for 76Ge neutrinoless double-beta de-
cay experiments because it falls so close to the transition
energy (2039 keV). Furthermore because the DEP is a
single-site energy deposition, it cannot be distinguished
from double-beta decay through event topology. This is
in contrast to a full-energy γ-ray peak, which tends to
consist of several interactions and therefore is a multiple-
site deposition. (See [12] for a discussion of the use of
event topology to reduce background in Ge detectors.)
The final two measurements were intended to study
this 3062-keV line in the spectrum and demonstrate its
origin. In both cases a PopTop Ge detector faced a 15.25
cm by 15.25 cm NaI detector for coincidence data. By se-
quentially placing a Pb and then a Cu absorber between
an AmBe source and a PopTop Ge detector, we tested
the hypothesis that the line was due to neutron interac-
tions in Pb. By looking for an coincident energy deposit
in the NaI detector, we could be assured the Ge detector
signal originated from a neutron interaction in the sam-
ple. An energy deposit threshold in the NaI of greater
than 200 keV was required for a coincidence. The Pop-
Top was placed 27.3 cm from the NaI detector with the
source placed 20.3 cm (7 cm) from the Ge (NaI) detector.
For the lead study, 5 cm of lead was placed directly be-
tween the Ge detector and the source. Additional lead, in
the form of 5-cm-thick bricks was positioned around the
4 sides of the Ge detector to reduce room background.
For the copper study, a 0.5-cm thick Cu tube was placed
around the PopTop and a 5-cm Cu block was placed be-
tween the PopTop and the source. For this final run, all
the lead was removed. For both of these sets of data, the
observed spectra extended from ≈ 125 keV to ≈ 9 MeV.
For the PopTop data, the Pb and Cu runs were of 19.12
h and 17.76 h live-time, respectively.
FIG. 1: The CLOVER detector as configured for the AmBe
source run. The setup at the time of this photograph used
4′′ of polyethylene. One wall of the lead shield was removed
only to clarify the relationship between the AmBe source,
moderator, and the CLOVER.
B. The Data sets
The crystals were individually calibrated, and the re-
sulting spectra summed together to form a single his-
togram. The peaks within each of the 3 CLOVER data
sets were identified and their intensities determined. If an
event had 2 crystals that responded in coincidence, the
histogram would have two entries. Therefore the spectra
we analyzed and simulated included all single-crystal en-
ergy deposits. By not eliminating events that registered
signals in more than 1 of the CLOVER Ge detectors,
we maximized the event rate. The peak strengths were
estimated by fitting a Gaussian shape to peaks and a
flat background to the spectrum in the region near the
peak. For the nuclear recoil lines, the peak shape was
assumed to be a triangle and not Gaussian. In Table I
the uncertainties derive from this fit. A summary of the
peak strengths is given in Table I and the spectra them-
selves are shown in Fig. 2. The data sets were chosen
to help decouple line blendings. Because the rates in
all peaks and continua are much higher for the source-
induced data than for the background, features in those
spectra are due to the sources and other contributions
can be safely ignored. For example, the 2614.5-keV line
can arise from either the decay of 208Tl or 208Pb(n, n′γ).
When exposed to a Th source, Tl decay dominates the
spectrum, whereas when exposed to an AmBe source,
(n, n′γ) dominates. Hence by normalizing the rate in
this line to the rate in a pure neutron-induced transition
(e.g. the 596-keV 74Ge(n,n’γ)), we can determine the
relative contribution of the two processes to the back-
ground spectrum. In fact, in the background data, both
processes contribute to this line.
Some comments on our choices for line identification
are in order. For an isotope such as 72Ge where a neutron
capture leads to a stable nucleus, almost all (n,γ) lines
could also be interpreted as (n, n′γ) lines in the result-
ing nucleus; in this case 73Ge. For isotopes within the
detector however, such as the 53.5-keV 72Ge(n,γ) tran-
sition, the competing 73Ge(n, n′γ) line would be a sum
of this γ-ray energy and the recoil nucleus energy. At
these low energies where the recoil is a fair fraction of
the γ-ray energy, the (n, n′γ) would simply contribute to
the continuum and not be observed as a line. For the
high energy cases, the blend of a mono-energetic γ-ray
line and a (n, n′γ) process might be present.
For the calibration runs, our threshold was approxi-
mately 70 keV. Also note that we used a thorium wire as
a calibration source. Since the wire is pure natural Th,
we observe the Th X rays in that data. In contrast, the
background run shows lines from the thorium chain as a
contaminant, therefore those lines are absent.
In all spectra, there are a few lines we have not iden-
tified.
TABLE I: A summary of the observed lines in the various spectra taken
with the CLOVER detector. Blank entries indicate that no significant
peak feature above the continuum was found. Single and double escape
peaks are labeled by SEP and DEP respectively. Line assignments for
which we are unsure are indicated by a question mark. Line energies are
taken from the Table of Isotopes [17].
Energy Process Count Rates
(keV) backgrnd Thorium CLOVER
(per hr) (Hz) AmBe (Hz)
23.4 70Ge(n,γ) 1.017(5)
46.5 210Pb 112.75(42)
72Ge(n,γ)
61.01(31) 2.079(8)
63.2 234Th 93.02(38)
67.7 230Th 24.05(19) 0.591(4)
68.8 72Ge(n,γ) 0.440(4)
72.80 Pb x-ray 10.5(1) 0.506(4)
74.97 Pb x-ray 663.5(1.0) 34.1(2) 1.703(7)
76.7 Unidentified 29.0(2)
228Th
Pb x-ray
Pb x-ray
115.28(42) 10.9(1) 0.930(5)
Pb x-ray 55.65(29) 16.8(1) 0.262(3)
Continued
TABLE I – continued
Energy Process Count Rates
(keV) backgrnd Thorium CLOVER
(per hr) (Hz) AmBe (Hz)
89.9 Th x-ray 32.4(2)
92.7 234Th 171.38(51) 0.060(1)
93.4 Th x-ray 47.5(2)
96.0 115In(n,γ) ? 0.166(2)
99.5 228Ac 13.71(15) 3.0(1)
105.3 Unidentified 8.99(12)
104.8
105.6
Th x-ray 20.6(1)
108.7 Th x-ray 7.6(1)
109.9 19F(n, n′γ) 43.00(26) 0.506(4)
129.1 228Ac 12.91(14) 3.2(1)
139.7 74Ge(n,γ) 47.20(27) 2.339(8)
143.9 230Th 20.03(18)
154.0 228Ac 7.69(11) 1.5(1)
159.7 77mGe 0.114(2)
162.4 115In(n,γ) 10.71(13) 1.073(6)
174.9 70Ge(n,γ) 7.45(11) 0.763(5)
186.1
186.2
226Ra
115In(n,γ)
114.60(42) 0.323(3)
197.1
198.4
19F(n, n′γ)
71Ge sum
81.04(35) 2.328(8)
199.2 228Ac 0.66(2)
202.6 115In(n,γ) 0.061(1)
209.5 228Ac 19.38(17) 10.9(1)
215.5 228Th 2.43(6) 0.92(3)
238.6 212Pb 295.77(67) 139.9(1) 0.105(2)
242.0 214Pb 57.49(30) 9.2(1)
247.1 70Ge(n,γ) 0.070(1)
253.7 74Ge(n,γ) 2.76(7) 0.410(3)
270.2 228Ac 21.39(18) 9.1(1)
273.0 115In(n,γ) 0.055(1)
277.4
208Tl
208Pb(n, n′γ)
12.98(14) 5.4(1) 0.086(2)
284.6 Unidentified 2.79(7)
288.1 212Bi ? 1.03(3)
295.2 214Pb 58.02(30)
297.2
298.7
72Ge(n,γ)
115In(n,γ)
0.068(1)
300.1 212Pb 18.59(17) 9.7(1)
306.2 70Ge(n,γ) 1.12(4) 0.046(1)
321.4 228Ac 0.67(2)
326.0 70,72Ge(n, n′γ) 0.487(4)
328.3 228Ac 10.02(12) 8.2(1)
332.9 228Ac 1.14(3)
335.5 115In(n,γ) 0.028(1)
338.7 228Ac 45.13(26) 31.5(2)
351.9 214Pb 95.11(38)
354.1 Unidentified 0.043(1)
385.1 115In(n,γ) 0.048(1)
391.3 70Ge(n,γ) 0.053(1)
409.8 228Ac 4.05(8) 4.3(1)
416.9 116mIn 2.21(6) 0.359(3)
438.9 Unidentified 2.54(6)
445.2 74Ge(n,γ) 0.037(1)
452.3 212Bi? 0.82(2)
463.3 228Ac 10.96(13) 9.2(1)
474.0 72Ge(n,γ) ? 2.54(6)
Continued
TABLE I – continued
Energy Process Count Rates
(keV) backgrnd Thorium CLOVER
(per hr) (Hz) AmBe (Hz)
478.6 228Ac 0.39(2)
470-485
10B(n,α)
7Li∗(γ)7Li
Doppler
Broadened
signf.
492.9 73Ge(n,γ) 0.123(2)
499.9 70Ge(n,γ) 0.453(4)
503.9 228Ac 0.34(2)
509.3
510.7
510.7
510.9
228Ac
208Tl
208Pb(n, n′γ)
Annih.γ
171.93(51) 16.8(1) 3.409(10)
516.2 35Cl(n,γ) 0.160(2)
537.5 206Pb(n, n′γ) 5.12(9) 0.158(2)
562.9
563.0
228Ac
76Ge(n, n′γ)
12.83(14) 1.52(3) 0.244(3)
569.7 207Pb(n, n′γ) 14.17(15) 0.422(4)
572.3 228Ac 0.53(2)
574.7 74Ge(n, γ) 0.091(2)
583.1
208Tl
208Pb(n, n′γ)
71.64(33) 49.6(2) 0.256(3)
595.9
74Ge(n, n′γ)
73Ge(n,γ)
59.90(30) 1.869(7)
608.3 73Ge(n,γ) 0.333(3)
609.2 214Bi 60.11(30)
629.6 72Ge(n, n′γ) 0.078(2)
648.2 115In(n,γ) 0.025(1)
657.2 206Pb(n, n′γ) 0.047( 1)
662.0 137Cs 9.04(12)
663.8 206Pb(n, n′γ) 0.069(1)
669.0 70Ge(n, n′γ) 0.030(1)
692.4 72Ge(n, n′e−) 87.70(37) 2.406(8)
701.0 74Ge(n, n′γ) 0.082(2)
708.2 70Ge(n,γ) 0.176(2)
727.3 212Bi 15.72(16) 11.7(1)
747.7 70Ge(n,γ) 0.047(1)
755.3 228Ac 2.19(6) 1.52(3)
763.1 208Tl 0.85(3)
763.1 208Pb(n, n′γ)? 0.032(1)
766.6
768.4
224mPa
214Bi
4.85(9)
771.8 228Ac 2.02(6) 2.11(4)
782.0 228Ac 0.67(2)
785.5 212Bi 4.19(8) 1.57(3)
786.3
786.8
35Cl(n,γ)
208Pb(n, n′γ)
0.041(1)
788.4
788.7
35Cl(n,γ)
70Ge(n,γ)
0.064(1)
795.0 228Ac 7.92(11) 6.1(1)
798.0 208Pb(n, n′γ) 0.023(1)
803.1 206Pb(n, n′γ) 20.90(18) 0.850(5)
806.2 214Bi 3.03(7)
808.2 70Ge(n,γ) 0.048(1)
818.6 116mIn 0.064(1)
824.9 1.03(4)
830.4 228Ac 0.70(2)
834.1 72Ge(n, n′γ) 45.15(26) 0.290(3)
Continued
TABLE I – continued
Energy Process Count Rates
(keV) backgrnd Thorium CLOVER
(per hr) (Hz) AmBe (Hz)
835.6 228Ac 2.30(4)
840.4 228Ac 1.19(3)
843.8 27Al(n, n′γ) 4.48(8) 0.112(2)
846.9 76Ge(n, n′γ) 0.062(1)
860.4
860.4
208Tl
208Pb(n, n′γ)
8.64(12) 6.0(1) 0.090(2)
865.0 Unidentified 0.094(2)
867.9 73Ge(n,γ) 4.25(8) 0.466(4)
881.0 206Pb(n, n′γ) 2.50(6) 0.151(2)
892.9 212Bi 0.42(2)
894.3 72Ge(n, n′γ) 0.029(1)
897.8 207Pb(n, n′γ) 6.28(10) 0.199(2)
904.1 228Ac 0.94(3)
911.2 228Ac 48.86(27) 37.1(2)
934.1 214Bi 1.99(6)
958.4 228Ac 0.37(2)
960.9 74Ge(n, n′γ) 0.095(2)
964.4 228Ac 11.22(13) 6.2(1)
968.8 228Ac 26.83(20) 21.6(1)
981.0 206,8Pb(n, n′γ) 0.035(1)
988.4 228Ac 1.95(5) 0.20(1)
993.7
995.1
74Ge(n, n′γ)
206Pb(n, n′γ)
0.026(1)
999.5 74Ge(n, n′γ) 0.034(1)
1001.5 224mPa 8.03(11)
1004.5 228Ac 0.17(1)
1014.5 27Al(n, n′γ) 7.46(11) 0.173(2)
1033.1 228Ac 0.20(1)
1040.1
1040.8
70Ge(n, n′γ) 16.89(16) 0.210(2)
1063.7 207Pb(n, n′γ) 8.47(11) 0.145(2)
1065.0 228Ac 0.47(2)
1078.8 212Bi 1.11(4) 0.62(2)
1093.9 208Tl sum 511+583 0.90(3)
1095.8
1096.9
207Pb(n, n′γ)
70Ge(n,γ)
116mIn
7.81(11) 0.464(4)
1101.3 74Ge(n, n′γ) 0.123(2)
1105.6 74Ge(n, n′γ) 0.019(1)
1110.4 228Ac sum 0.52(2)
1120.6 214Bi 11.70(13)
1122.5 228Ac sum 0.26(1)
208Pb(n, n′γ)
72Ge(n, n′γ)
0.022(1)
1131.6 73Ge(n,γ)? 1.34(5) 0.034(1)
1139.4 70Ge(n,γ) 1.34(5) 0.077(2)
1153.5 228Ac 0.15(1)
1155.2 214Bi 1.08(4)
1164.9
1166.0
35Cl(n, n′γ)
72Ge(n, n′γ)
0.49(3) 0.072(1)
1173.5 60Co 13.67(14)
1201.2 p(n,γ)d DEP 0.415(3)
1204.2
73Ge(n,γ)
74Ge(n, n′γ)
9.39(12) 0.163(2)
1226.7 74Ge(n, n′γ) 0.017(1)
1238.4 214Bi 5.22(9)
1246.9 228Ac 0.58(2)
Continued
TABLE I – continued
Energy Process Count Rates
(keV) backgrnd Thorium CLOVER
(per hr) (Hz) AmBe (Hz)
1261.0 74Ge(n, n′γ) 0.019(1)
1281.0 214Bi 0.74(3)
1286-7 228Ac Blend 0.14(1)
1293.5 116mIn 4.09(8) 0.462(4)
1298.8 70Ge(n,γ) 0.087(2)
1332.5 74Ge(n, n′γ) 0.018(1)
1332.5 60Co 12.27(14)
1344.5
1345.9
1347.7
74Ge(n,γ)
206Pb(n, n′γ)
70Ge(n,γ)
0.52(3) 0.017(1)
1374.2
228Ac sum
964 + 409
911 + 463
0.28(1)
1378.0 214Bi 3.24(7)
1378.8 70Ge(n,γ) 0.065(1)
1393.8 206Pb(n, n′γ) 0.016(1)
1401.5 214Bi 0.58(3)
1408.6 214Bi 1.84(5)
1413.6 73Ge(n, n′γ) 0.018(1)
1431.1 228Ac 0.15(1)
1433.5 206Pb(n, n′γ) 0.020(1)
1436.9 208Pb(n, n′γ) 0.017(1)
1459.2 228Ac 0.80(2)
1461.0 40K 30.18(22) 0.066(1)
1463.9 72Ge(n, n′γ) 0.114(2)
1466.8 206Pb(n, n′γ) 0.032(1)
1471.6 73Ge(n,γ) 0.047(1)
1489.2 74Ge(n, n′γ) 0.025(1)
1496.2 228Ac 0.73(3) 0.85(3)
1501.7 228Ac 0.42(2)
1508.9 116mIn 0.069(1)
1508.9 214Bi 1.95(3)
1512.7 212Bi 0.38(2)
1538 214Bi 0.54(3)
1557.1 228Ac 0.14(1)
1580.8 228Ac 0.68(3) 0.55(2)
1588.3 228Ac 6.06(10) 2.94(5)
1592.5
1592.5
1593.0
208Tl DEP
208Pb DEP
207Pb(n, n′γ)
7.24(11) 2.10(4) 0.107(2)
1599.3 214Bi 0.38(2)
1601.1
1602.0
35Cl(n,γ)
74Ge(n, n′γ)
0.018(1)
1614.9 208Pb(n, n′γ)? 0.020(1)
1620.5 212Bi 1.81(5) 1.32(3)
1625.0 228Ac 0.34(2)
1630.7 228Ac 1.82(5) 1.46(3)
1631.5
1632.0
74Ge(n, n′γ)
70Ge(n,γ)
0.021(1)
1634.0 76Ge(n,γ) 0.016(1)
1638.3 228Ac 0.43(3) 0.41(2)
1640.4
208Pb(n, n′γ)
74,76Ge(n, n′γ)
0.026(1)
1661.3 214Bi 0.36(2)
1666.3 228Ac 0.17(1)
1699.5 206Pb(n, n′γ)? 0.021(1)
1704.5 206Pb(n, n′γ) 0.72(3) 0.041(1)
Continued
TABLE I – continued
Energy Process Count Rates
(keV) backgrnd Thorium CLOVER
(per hr) (Hz) AmBe (Hz)
1710.9 72Ge(n, n′γ) 0.327(3)
1712.2 p(n,γ)d SEP 0.156(2)
1725.7 207Pb(n, n′γ) 0.029(1)
1729.6 214Bi 3.59(7)
1764.7 214Bi 11.68(13)
1779.0
27Al(n,γ)
28Al ⇒28 Si
2.13(6) 0.127(2)
1806.0 212Bi 0.11(1)
1844.5 206Pb(n, n′γ) 0.044(1)
1846.9 214Bi 2.26(6)
1940.4 74Ge(n, n′γ) 0.027(1)
1951.1 35Cl(n,γ) 0.032(1)
1959.3 35Cl(n,γ) 0.023(1)
2092.1
2092.7
206Pb(n, n′γ)
207Pb(n, n′γ)
0.039(1)
2103.8
208Tl SEP
208Pb SEP
5.21(9) 2.25(4) 0.090(2)
2112.1 116mIn 0.061(1)
2118.5 214Bi 0.64(3)
2204.0 214Bi 3.73(8)
2223.3 p(n,γ)d 5.813(13)
2390.5 116mIn 0.015(1)
2448.5 214Bi 0.51(3)
2614.5
208Tl
208Pb(n, n′γ)
39.39(25) 16.3(1) 0.729(5)
2650.3 206Pb(n, n′γ)? 0.011(1)
2686 sum 208Tl? 0.12(1)
2892 sum 208Tl 0.08(1)
3061.9 207Pb(n, n′γ) 0.010(1)
C. Neutron Spectra Simulation
Fast neutrons (from 100 MeV to 1 GeV or more) tend
to produce additional neutrons through nuclear reactions
as they traverse high-Z material. In particular the flux
of neutrons will increase several-fold while the average
neutron energy decreases through these processes. As a
result, fast neutrons will penetrate deep into a shield pro-
ducing additional neutrons at lower energies. These low
energy neutrons (∼< 20 MeV) give rise to a substantial
γ-ray flux because (n,n
γ) cross sections are large near
10 MeV, but become small at higher energies. Hence
it is these secondary lower-energy neutrons that inter-
act with the shield and detector materials to produce γ
rays, which can give rise to background in double-beta
decay experiments. To understand the process by which
high energy neutrons influence the low-energy neutron
flux and, in turn, the observed γ-ray flux, we simulated
neutrons impinging on an outer shield and tracked how
their spectrum changed as the particles traversed the
shield. We also simulated the production of neutron-
induced γ rays and how the Ge detector responded to
Energy (keV)
0 50 100 150 200 250 300 350
AmBe Spectrum
Background Spectrum
Energy (keV)
400 500 600 700 800 900
AmBe Spectrum
Background Spectrum
Energy (keV)
1000 1200 1400 1600 1800 2000
AmBe Spectrum
Background Spectrum
Energy (keV)
2000 2200 2400 2600 2800 3000 3200
AmBe Spectrum
Background Spectrum
FIG. 2: The AmBe and background spectra taken with the
CLOVER.
them. Specifically, we performed simulations of several
geometries including:
1. A simulation of the cosmic-ray produced neutrons
with energy up to 1 GeV at our lab in Los Alamos
and their propagation through a 10-cm Pb shield.
The response of the CLOVER detector to γ rays
produced by neutron interactions in the shield was
simulated. This simulation, compared to our back-
ground data, tests the precision to which we can
model neutron production, scattering with sec-
ondary neutron production and (n,n’γ) interac-
tions.
2. A simulation of the neutron flux induced on the
CLOVER from the AmBe source (neutron energy
≤11.2 MeV) passing through 15 cm of polyethylene
before impinging on the 10-cm Pb shield. Since the
neutron flux is of low energy, this simulation tests
the precision to which we model (n,n’γ) interac-
tions.
3. A simulation of the neutron flux with neutron en-
ergies up to a few GeV expected at 3200 mwe deep
due to cosmic-ray µ interactions in the surround-
ing rock and 30-cm lead shield and the resulting
response of the CLOVER to the flux of γ rays aris-
ing from this flux. This simulation permits us to
estimate rates in detectors situated in underground
laboratories.
The first two of these simulations are to verify the code’s
predictive power. The third is to aid in understanding the
utility of depth to avoid neutron-induced backgrounds.
The simulation package GEANT3-GCALOR [18, 19]
is described in detail in Ref. [10]. In general, (n, n′)
reactions leave the target nucleus in a highly excited
state which subsequently decays via a γ-ray cascade to
the ground state. In the simulation, inelastic scattering
cross sections for excitation to a given level depends on
the properties of the ground and excited states. These
cross sections were calculated using in-house-written
code based on Hauser-Feshbach [20] theory modified by
Moldauer [21]. The validation of the Hauser-Feshbach
theory has been the subject of several studies [22, 23, 24].
The simulated γ-ray flux arises from the relaxation of the
initial excited-state distribution, which includes a large
number of levels (60 states for 208Pb(n, n′γ) reactions,
for example). The nuclear levels and their decay chan-
nels were provided by the ENSDF[25] database through
the GEANT package. Note however, that the simula-
tion did not predict every possible transition. In particu-
lar the important 2041-keV and 3062-keV emissions from
Pb were not part of this simulation. This situation arises
because the simulation packages only have (n, n′) cross
sections for the lowest lying excited states for most nu-
clei. It is set to zero for most other levels. The details of
this simulation are described in detail in Ref. [10]. Here
we study the effectiveness of the simulation to predict
spectra resulting from (n,n’γ).
The simulation was done by generating neutrons with
the appropriate energy spectrum outside the lead shield
and propagating them through the shield including sec-
ondary interactions that may add to the neutron flux and
alter the energy spectrum. Fig. 3 shows a comparison
between the data and the simulations for the CLOVER
background run and AmBe run. Note only neutrons
as primary particles were simulated for this comparison
and the dominant difference between the two spectra is
due to the room’s natural radioactivity and non-neutron
µ-induced processes. Here we excluded those processes
from the simulation to emphasize the spectral shape, in-
cluding lines, that are a direct result of neutron inter-
actions. The similarity of the spectra in Fig. 3 indicates
that the measured background spectrum is dominated by
neutron-induced reactions.
The uncertainty in the simulation is calculated by com-
paring the well known peaks in Table II which shows
a comparison of the simulation to the line production
for both background and AmBe runs. The measured
neutron produced lines are within about 5% of the pre-
dicted values from simulation, as is the continuum rate
in the AmBe data. Therefore the (n,n’γ) rates are well-
simulated for nuclear states with well-defined cross sec-
tions. (The continuum for the background data includes
processes that were not simulated and hence is not a
good measure of the uncertainty.) Because the neutron
flux estimates come from these line strengths (See Sec-
tion III), the uncertainty in the flux cancels in these es-
timates. The uncertainty in the measured neutron flux
and spectrum underground(≈35%) constrains the preci-
sion to which such simulations can be verified and is well
described in Ref. [10]. This 35% uncertainty due to the
flux is much larger than the uncertainty for the γ-ray
line production described above. Therefore, a total un-
certainty of 35% is used for all predictions of line rates
underground throughout this paper.
III. THE NEUTRON FLUX
In this section, we use the data to determine the neu-
tron fluxes we observed during our various experimental
configurations. We then compare our measured cosmic-
ray induced flux with that predicted from past measure-
ments and our simulation.
A. Ge(n, n′γ) Analysis
Spectral lines that indicate neutron interactions in nat-
ural Ge detectors have been studied previously. See Ref-
erences [26, 27, 28, 29], for example. In particular, the
sawtooth-shaped peaks due to 72,74Ge(n, n′) at 693 keV
and 596 keV respectively are clear indications of neu-
trons and have been used to deduce neutron fluxes [30].
Operating Ge detectors in a low-background configura-
tion, these lines can be used to help interpret the back-
ground components. Recent double-beta decay experi-
ments [5, 6] have constructed their detectors from Ge en-
riched in isotope 76. Although an appreciable amount of
74Ge remained (14%), 70,72,73Ge are depleted. For such
Energy (keV)
500 1000 1500 2000 2500 3000
Am-Be, MC
Am-Be, Data
Background, Data
Background, MC
Am-Be, MC
Am-Be, Data
Background, Data
Background, MC
Energy (keV)
500 550 600 650 700 750 800
Am-Be, MC
Am-Be, Data
Background, Data
Background, MC
Am-Be, MC
Am-Be, Data
Background, Data
Background, MC
FIG. 3: Comparison of the measured and simulated AmBe
spectra for the CLOVER detector surrounded by 10 cm lead
and 15 cm of moderator. The upper plot shows the energy
range between 10 - 3100 keV. The lower plot shows the range
470 - 830 KeV where the most significant (n, n′γ) lines can
be seen. The simulated AmBe neutron spectrum was nor-
malized to the AmBe source strength for 6.13-h live-time.
The measured total neutron flux in the background spectrum
(see Section IIIC) was used to normalize the simulated back-
ground spectrum. Note, only neutrons as primary particles
were simulated for this comparison and the difference between
the spectra is due to the room’s natural radioactivity and non-
neutron, µ-induced processes.
detectors, only lines originating in isotopes 74 and 76
are useful for neutron interaction analysis. As these ex-
periments reach for lower background, neutron-induced
backgrounds become a greater concern and the diagnos-
tic tools more important.
Neutrons from (α,n) and fission reactions have an en-
ergy spectrum with an average energy similar to the
AmBe spectrum used in this study. Furthermore, the
average energy of the AmBe neutrons is similar to that
of the neutrons within the hadronic cosmic-ray flux im-
pinging on our surface laboratory although the latter ex-
tend to much higher energies. Therefore the Ge-detector
signatures indicating the presence of neutrons described
above will be similar to those arising from neutrons origi-
nating from the rock walls of an underground laboratory.
However, low-background experiments that use Ge de-
tectors are typically deep underground and are shielded
TABLE II: A comparison of the simulated to measured rates
(Background: per hour and AmBe: Hz) for several lines pro-
duced by neutron interactions. The 2041-keV and 3062-keV
lines are not included in the simulation.
Process γ-ray Background-CLOVER
Energy Simulation Measurement
74Ge(n, n′γ) 596 keV 56.21 59.90(30)
74Ge(n, n′γ) 254 keV 2.63 2.76(7)
76Ge(n, n′γ) 2023 keV 3.2×10−7 below sensitivity
206Pb(n, n′γ) 537 keV 4.82 5.12(9)
207Pb(n, n′γ) 898 keV 6.21 6.28(10)
206Pb(n, n′γ) 1706 keV 0.69 0.72(3)
206Pb(n, n′γ) 2041 keV none not seen
Continuum region 2000-2100 keV 110.2 187.35(19)
207Pb(n, n′γ) 3062 keV none not seen
Process γ-ray AmBe-CLOVER
Energy Simulation Measurement
74Ge(n, n′γ) 596 keV 1.8 1.87
74Ge(n, n′γ) 254 keV 0.36 0.41
76Ge(n, n′γ) 2023 keV 8.5×10−4 below sensitivity
206Pb(n, n′γ) 537 keV 0.15 0.16
207Pb(n, n′γ) 898 keV 0.14 0.20
206Pb(n, n′γ) 1706 keV 0.04 0.04
206Pb(n, n′γ) 2041 keV none not seen
Continuum region 2000-2100 keV 7.01 7.33
207Pb(n, n′γ) 3062 keV none 0.01
from environmental radioactivity by a thick shield. This
shield, typically made of Pb, is then usually surrounded
by a neutron moderator. This configuration is effective at
greatly reducing the neutron flux originating from (α,n)
and fission reactions in the cavity walls of the under-
ground laboratory. In contrast, although neutrons origi-
nating from µ interactions underground are much rarer,
they have much higher energy. Therefore these µ-induced
neutrons can penetrate the shield more readily and be-
come a major fraction of the neutrons impinging on the
detector.
B. The AmBe Neutron Flux
The estimate of the flux of neutrons with energies
greater than 692 keV is given by [30, 31, 32]
Φn = k
, (1)
where I is the counts s−1 under the asymmetric 692-keV
peak, V is the volume of the detector in cm3 (566 cm3)
and k is a parameter found by Ref. [30] to be 900 ± 150
cm. For the 15-cm moderator data, this formula predicts
a neutron flux of 2.3/(cm2 s) whereas our simulation,
using the known flux of the source, predicts 1.8/(cm2
s). This difference (20-30%) is somewhat greater than
the 17% uncertainty claimed by Ref. [30]. The geometry
for our measurement was complicated and perhaps this
added complexity of neutron propagation contributes to
the difference. For the uncertainty associated with the
flux of neutrons produced from cosmic ray µ, we use the
35% value as it is much larger than the value associated
with Eqn. 1.
For the Am-Be neutron source, the rate in the 692-keV
peak is 2.406 ± 0.008 Hz. This results in Φamben = 3.8
± 1.1 /(cm2 s). This rate is an average over the two
moderator configurations. The neutron flux during the
10-cm moderator run is estimated to be about a factor
2.3 larger than for the 15-cm moderator run. For the
PopTop-AmBe run on Pb for the raw data (in coinci-
dence with the NaI detector), the effective flux was 8.6
± 2.6/(cm2 s) (0.26 ± 0.08 /(cm2 s)).
C. Cosmic-ray Induced Neutron Fluxes
In the background spectrum the rate in the 692-keV
peak is 87.7 ± 0.4/hr. Using Eqn. (1) with I = (2.44 ±
0.06)×10−2 Hz for the background spectrum, one obtains
a fast neutron flux of Φbackn = (3.9 ± 1.2)×10
−2 /(cm2
s) at the detector in our surface laboratory.
Ref. [30] provides a similar formula to estimate the
thermal neutron flux, which is accurate to approximately
30%. Using the intensity of the 139.68-keV γ-ray line of
75mGe:
980I139.68
139.68 + 1.6)V
, (2)
139.68 ≃ 1−
1− e−V
V 1/3
where I = 47.2 ± 0.3 /h = 0.013 Hz is the event rate in
the peak of 139.68-keV line and V is the volume of the
detector in cm3. Using V = 566 cm3 we obtain Φbackth =
(9.1 ± 2.7)×10−3 /(cm2 s). We also measure the thermal
neutron flux for the Am-Be neutron source, Φambeth = 1.6
± 0.5 /(cm2 s).
Thus the total neutron flux incident on the Ge detector
measured for the background run is approximately Φbacktot
= Φbackn + Φ
th = (4.8 ± 0.7) × 10
−2 /(cm2 s).
D. Neutron Flux as a Function of Depth
In our basement laboratory, there are 3 primary
sources of environmental neutrons. The largest contri-
bution comes from the hadronic cosmic ray flux. The
next largest arises from µ interactions in the 77 g/cm2
thick overhead concrete layer in the building. Finally
there is the negligible contribution from (α,n) and fission
neutrons from natural radioactivity in the room. The at-
mospheric depth at the altitude of our laboratory is 792
g/cm2. Including the concrete, the depth is 869 g/cm2.
Using the analysis of Ziegler [33, 34], the flux at our lab
due to the hadronic flux can be estimated to be 3.0 times
larger than that at sea level. The flux at sea level has
been measured to be 1.22 × 10−2 /(cm2 s) [35] result-
ing in a flux in our laboratory of 3.7 × 10−2 /(cm2 s).
To estimate the additional neutron flux originating from
µ interactions in the concrete above our laboratory, we
rely on our simulations of neutron generation and prop-
agation. The simulation predicts 1.4 × 10−2 /(cm2 s)
(3.3 × 10−2 /(cm2 s)) for the muon-induced (hadronic)
neutron flux inside the lead shield for a total simulated
neutron flux of 4.7 × 10−2 /(cm2 s) in acceptable agree-
ment with our measurement of (4.8 ± 2.2) × 10−2 /(cm2
s) = (1.51 ± 0.69) × 106 ± /(cm2 y). The success of this
simulation lends credence to the neutron flux estimate in
the following sections.
The neutron flux onto the detector will be increased
due to the neutron interactions with shield materials and
neutron back-scattering from the cavity walls. For exam-
ple, our simulations show that the fast neutron flux will
increase by a factor of ≈ 10 by traversing a 30-cm lead
layer. Also, neutrons will backscatter from the cavity
walls and reflect back toward the experimental appara-
tus, effectively increasing the impinging neutron flux by
a factor of 2-3 depending on the specific geometries of
the detector and experimental hall. Therefore, it is im-
portant to account for these effects when estimating the
neutron flux at the detector.
Muon-induced neutron production in different shield-
ing materials and in the detector itself was also stud-
ied in Ref. [10]. For example, with 30 cm of lead sur-
rounding a CLOVER-style detector at 3200 mwe, the to-
tal muon-induced neutron flux impinging on the detector
was calculated to be (8.6 ± 4.0) × 10−8 /(cm2 s) = 2.7
± 1.2/(cm2 y). Some of the interactions resulting from
these neutrons would be eliminated by a µ veto. Assum-
ing a veto efficiency of 90% for muons traversing this lead
shield, the effective neutron flux is estimated to be (2.0
± 0.9) × 10−8 /(cm2 s) = 0.63 ± 0.29 /(cm2 y). The
energy spectrum of neutrons at the lead/detector bound-
ary at 3200 mwe is shown in Fig. 4 and has an average
value of 45 MeV.
The average energy of the µ-induced neutrons is 100-
200 MeV and much higher than that of (α,n) neutrons
(≈ 5 MeV). The simulated flux of the µ-induced neutrons
((2 ± 0.9) × 10−8 /cm2 s = 0.63 ± 0.29/cm2 y) inside
the detector shield at a depth of 3200 mwe is a factor 2.4
greater than the simulated (α,n) flux surviving the shield
((0.85 ± 0.39)× 10−8 /cm2 s = 0.27 ± 0.12/cm2 y). The
average energy of these (α,n) originating neutrons is 3-5
MeV at the detector surface.
With this estimate of the neutron flux at depth and
with our measurements of the Pb and Ge neutron-
induced detector response, we can proceed to estimate
these processes in underground Ge-detector experiments.
There are effects in addition to the incident flux, however,
that must be taken into account when extrapolating our
surface laboratory results to different geometries and lo-
Energy (MeV)
10 1 10
: Lead/Detector boundary!
,n):  Lead/Detector boundary!(
FIG. 4: The effective neutron flux onto the simulated detector
described in the text at a depth of 3200 mwe. Shown are the
neutron flux from two sources: (1) the effective neutron flux
induced by muons that transverse the surrounding rock and
shielding materials assuming a 90% muon-veto efficiency and
(2) the neutron flux from (α,n) reactions in the rock.
cations.
1. As the thickness of the Pb shield increases, addi-
tional secondary neutrons will be generated. Our
simulation predicts that a factor kshield = 2.16
more neutrons will be produced by a 30-cm thick
shield as compared to a 10-cm thick shield.
2. As the energy of the neutrons increases, the number
of multiply scattered neutrons increases and there-
fore the number of interactions that might produce
a γ ray increases. For the average energy of neu-
trons at our surface laboratory (at 3200 mwe), the
average scattering length is λL=7.1 cm (λUG = 12.5
3. Also as the energy increases, the number of states
that can be excited in the target nucleus increases.
In the shield at our surface laboratory (at 3200
m.w.e), the average neutron energy is 6.5 MeV (45
MeV).
All of these factors can be incorporated into a scaling
formula derived from our simulation. The rate (RUGROI)
of background near the region of interest (ROI) in an
underground laboratory can be related to that measured
in our surface laboratory (RLROI) as
ROI = (1 +
)kshield((
EUGn − Ex
ELn − Ex
)0.8)
ROI ,
where ΦLn (Φ
n ) is the neutron flux in our surface labo-
ratory (at 3200 mwe), En is the neutron energy and Ex
is the excitation energy for a typical level. This formula
reproduces our simulated results well and the uncertainty
of its use is dominated by the precision of simulation. Us-
ing the 2.6-MeV level in 208Pb as an example, RUGROI ∼
1.7 × 10−5RLROI . Fig. 5 shows a comparison between the
Monte Carlo simulation and the scaling formula Eqn. 4
for several lines.
-ray Energy (keV)γ
500 1000 1500 2000 2500
-610×
Monte Carlo simulation
Scaling formula
FIG. 5: The comparison between the Monte Carlo simulation
of a detector as described in the text and the scaling formula
for several excitation lines. The 35% uncertainties shown in
this figure arise from the cross section uncertainty and the
statistical uncertainty of determining the peak counts in the
simulated spectra. The latter dominates.
IV. ANALYSIS
A. Pb(n, n′γ) analysis
If fast neutrons are present, then one will also see γ-ray
lines from Pb(n, n′) interactions. In very low background
configurations, γ rays from neutron-induced excitations
in 208Pb and 207Pb can be masked by or confused for de-
cays of 208Tl and 207Bi respectively. Therefore it is the
stronger transitions in 206Pb (537.5, 1704.5 keV) that are
most useful for determining if these processes are taking
place. In 207Pb the relative strength of the 898-keV tran-
sition, compared to the 570- and 1064-keV transitions, is
much stronger when it originates from 207Pb(n,n’γ) as
opposed to 207Bi β decay to 207Pb. Therefore this line
can also be used as a tell-tale signature of neutron inter-
actions.
Our data show indications of 206,207,208Pb(n, n′γ). As
noted earlier, the 2614-keV γ ray from 208Pb can orig-
inate from 208Tl decay or from 208Pb(n,n’γ). The 692-
keV peak arises only from neutron interactions on 72Ge.
Since the Pb shielding was similar in both the background
and AmBe runs, we can compare the ratio of the rate in
the 2614-keV peak to that in the 72Ge(n, n′γ) 692-keV
peak in the two data sets to deduce the fraction of the
2614-keV in the background run that can be attributed
to neutron interactions. This ratio in the Am-Be spec-
trum is 0.30 and that in the background spectrum is 0.45,
and therefore, we conclude that ≈ 67% of the strength
in the background run is due to neutron reactions and
the remainder is due to 208Tl decay. Clearly, in our sur-
face laboratory, environmental neutrons are a significant
contributor to the observed signal.
B. The Special Cases of the 2023-keV, 2041-keV
and 3062-keV γ rays
The 2023-keV level in 76Ge can be excited by neutrons.
The simulation predicts that this line is too weak to be
seen in the CLOVER AmBe data, but the CLOVER is
built of natural Ge. In the enriched detectors planned
by future double-beta decay experiments, the fraction of
isotope 76 is much larger and this line would be enhanced.
Still our simulation (Table V) predicts it would be a very
small peak.
The 3714-keV level in 206Pb can emit a 2041-keV γ
ray. We only observed a candidate γ-ray peak in the
coincidence data (Ge detector event in coincidence with
a 4.4-MeV γ ray in the NaI detector) with the AmBe
source radiating the Pb shield around the PopTop detec-
tor. The magnitude of this peak if it exists is small and
not convincing. We use this data set to place a limit on
the production rate of this line as it results in the most
conservative limit.
In the AmBe-irradiated CLOVER and the non-
coincidence PopTop spectra, we observed a 3062-keV γ
ray that we assign to a transition from the 3633-keV level
in 207Pb. (See Fig. 6.) This line is only present when
Pb surrounds the detector: It is absent when Cu forms
the shield. The statistical sensitivity was too weak in
the PopTop coincidence spectrum to observe this weak
line. In the CLOVER AmBe spectrum, the rate of this
line is 5.3 × 10−3 that of 596-keV 74Ge peak rate and
in the raw AmBe PopTop with Pb spectrum the ratio is
4.5 × 10−3. From these data we can estimate an approx-
imate rate that these dangerous backgrounds would be
produced for a given neutron flux. In our surface labora-
tory, the CLOVER background rate for the 74Ge 596-keV
peak was 59.9 events/hr. This leads to a predicted rate of
0.3 events/hr in the 3062-keV peak. Note that our data
indicate that any peak at 3062 keV is statistically weak
(≤ 0.2 events/hr) but reasonably consistent with this pre-
diction. Note, in the AmBe-CLOVER runs, polyethylene
blocks were used to increase the flux of thermal neutrons.
It appears that these blocks contain some Cl and there-
fore we see indications of Cl(n,γ) lines. Even though 35Cl
has a neutron capture line at 3062-keV, we do not assign
the observed line in our data to that process. Because the
35Cl(n,γ) line at 2863 keV is not observed and because
the line at 1959 keV is weak, we conclude that assigning
this line to Cl would be inconsistent with the predicted
line ratios for neutron capture. However, a concern re-
garding our assignment of the 3062-keV line to 207Pb is
that one also expects a 2737-keV emission from the same
3633-keV level. This companion γ ray is not observed
in our data and we plan future measurements dedicated
to measuring the neutron-induced relative intensities of
these two lines. If we assume that the entire rate (0.01
Hz) of the 3062-keV line is due to (n, n′γ), we can make a
crude estimate of the cross section by scaling to the rate
in the 2614-keV line. The cross section for the 2614-keV
(n,n’γ) is 2.1 b ± 10% [23]. Using this cross section, the
relative rates in the two peaks, the different isotopic ra-
tios of 208Pb and 207Pb, and the different γ-ray detection
efficiencies, the average cross section for 207Pb(4.5-MeV
n, n′ 3062-keV γ ray) is estimated to be 75 mb. The
uncertainty is estimated to be about 20% or ∼ 15 mb.
Energy (keV)
3000 3020 3040 3060 3080 3100
AmBe activation, 6.1 h with 6" poly, 3.6 h with 4" poly
FIG. 6: The energy spectrum near 3000 keV showing the
207Pb(n, n′γ) 3062-keV γ-ray line in the AmBe spectrum with
the CLOVER.
From measurements with the CLOVER and a 56Co
source, which has γ-ray energies near 3100 keV, we expect
0.13 DEP events per full-energy γ-ray event. Therefore,
in our surface lab, we expect 0.03 events/hr in the DEP
at 2039 keV due to 207Pb(n, n′γ). This is well below
our continuum rate of 2.5 events/keV-hr or 10/hr in an
energy window corresponding to a 4-keV wide peak.
Since our simulation does not predict all these lines, we
summarize the measured rates normalized to the neutron
flux in Table III to provide simple scaling to different ex-
perimental configurations. The uncertainties in Table III
are estimates based on a minor contribution of the sta-
tistical uncertainty in the peak strengths and a major
contribution resulting from the ≈ 35% uncertainty in the
neutron flux determination as described in Section III B.
Because the uncertainty is mostly systematic, there is a
good possibility that the total uncertainties for each in-
dividual measurement are correlated. Therefore, to esti-
mate the average values in this Table, we took a straight
average of the individual values and then assigned an un-
certainty equal to the largest fractional value. This pro-
cedure, although not rigorous, is more conservative than
a weighted average. In addition, some peaks were not
observed in all spectra. The upper limits on the strength
of these peaks were estimated from the rates of weak-
est peaks observed near the associated energy region in
the spectrum. Such peaks are considered to represent
the level of sensitivity of our peak detection procedures.
The 2041-keV line is a special case. We quote an up-
per limit based on the only spectrum that indicated a
possible peak.
These measurements were done for a CLOVER de-
tector inside a 10-cm Pb shield. The relative energy-
dependent efficiency (ǫrel) for a full-energy peak in the
CLOVER can be approximated by,
TABLE III: The raw count rates for select processes normalized to neutron flux of 1/(cm2y). When extrapolating to neutron
energies distant from that near the measurements, the uncertainty (35%) associated with the extrapolation must be included.
See text for a discussion of the uncertainty estimates in this table especially with respect to the average.
Process Rate Rate Rate Rate
AmBe-CLOVER AmBe-PopTop Background Average
( events
206Pb(n, n′537− keV γ) 13.9±4.9 20.5±7.2 12.2±4.3 15.5±5.4
74Ge(n, n′596− keV γ) 164±57 unresolveda 142±50 153±54
207Pb(n, n′898− keV γ) 17.5±6.1 21.2±7.4 14.9±5.2 17.9±6.3
206Pb(n, n′1705− keV γ) 3.6±1.3 3.2±1.1 1.7±0.6 2.8±1.0
206Pb(n, n′2041− keV γ) <6.3 < 0.5 <1.7 < 5.0b
207Pb(n, n′3062− keV γ) 0.88±0.31 0.6±0.21 <1.0 0.7±0.2
( events
(keV ty)
Continuum Rate from Pb,Ge(n, n′γ) 2.6±0.9 2.0±0.7 2.5±0.9 2.4±0.8
aIn the PopTop data, the 596-keV line was not resolved from
nearby lines.
bThe 2041 line was not observed in any of our spectra, however,
a weak peak-like feature was present in the AmBe-PopTop coinci-
dence data. We used the upper limit for the rate in that peak as
the ”average” as we considered this to be most conservative.
ǫrel = 0.15 + 0.93e
−(Eγ−148)
766 , (5)
where Eγ is the γ-ray energy in keV. This expression is
normalized to 1.0 at 209 keV and is estimated to have an
accuracy of about 20% near 200 keV improving to about
10% at 2600 keV. The quoted relative efficiency for each
of the 4 individual CLOVER detectors is 26% at 1.33
MeV as quoted by the manufacturer. Table III does not
incorporate this efficiency correction, therefore the table
presents the measured count rates with a minimum of
assumptions. The thickness of Pb is large compared to
the mean free path of the γ rays of interest, therefore, the
scaling should hold for other thick-shield configurations.
Even so, the rates will be geometry-dependent so these
results can only be considered guides when applied to
other experimental designs. The rate of these excitations
also depends on neutron energy. For the background run
(AmBe run) the average neutron energy is ≈ 6.5 MeV (≈
5.5 MeV). Our simulations predict that the rate of these
excitations scales as energy to the 0.81 power.
V. DISCUSSION
A. A Model of the CLOVER Background
We can use these experimental results to create a back-
ground model for our surface lab and deduce the contri-
bution to the continuum near 2039 keV due to (n,n’γ) re-
actions. We then use simulation of high-energy neutron
production and propagation to extrapolate this model
to better understand experiments done at depth. The
measured rate for the continuum near 2039 keV was 14.8
events/(keV kg d). For the Th-wire data, this continuum
rate was 0.10 events/(keV s) (2900 events/(keV kg d))
and for the AmBe data it was 0.09 events/(keV s) (2600
events/(keV kg d)). To determine the neutron-induced
continuum rates in the AmBe data, however, we have
to correct for the contribution from the tail of two high-
energy γ rays that are not part of the neutron-induced
spectrum in the background. These are the γ rays from
the 2223-keV p(n, γ)d and the 4.4-MeV γ rays originat-
ing from the (α,n) reaction of the AmBe source itself.
Although only ≈ 10% of these AmBe γ rays penetrate
the 5-cm Pb shield, there is still a significant flux.
A simple simulation of the detector response to 2223-
keV γ rays can easily determine ratio of the rate in the
2039-keV region to that in the full-energy peak. Simula-
tion indicates that this ratio is 5.2 × 10−2 /keV. Since
the full-energy peak count rate is 5.813 Hz, we find this
contribution to the continuum is 0.03 events/(keV s). For
the 4.4-MeV γ ray from the source itself, simulation must
determine an absolute rate in the continuum because the
high-energy threshold prevented the observation of the
full-energy peak or its escape peaks. The simulation pre-
dicts 0.03 events/(keV s). Subtracting these two contri-
butions from the continuum rate for the AmBe source
near 2039 keV results in a final value of 0.03 events/(keV
s) or 860 events/(keV kg d).
Our background measurements were done without a
cosmic ray anti-coincidence system. From auxiliary mea-
surements with a scintillator in coincidence with the
CLOVER and a similar shielding geometry, we measured
the rate of µ passing through the detector. In the contin-
uum near the 2039-keV region, the rate is 5.4 events/(keV
kg d).
From the Th-wire source data, we measure the ratio
TABLE IV: A summary of the count rate in the CLOVER
background data in the energy region near 2039 keV based
on the model deduced for the surface lab described in the
text. The precision of the neutron-induced and muon-induced
spectra simulations (Section IIC and Ref [10]) is estimated to
be about 35%. We take this to be a conservative estimate for
the uncertainties associated with this Table.
Process CLOVER Event Rate
Surface Lab
events/(keV kg d)
neutron-induced 8.3±2.9
208Tl Compton scattering 0.7±0.3
high energy µ continuum 5.4±1.9
Total from model 14.4±5.0
Measured Rate 14.8±0.2
of the rate in the continuum near 2039 keV to that in
the 2614 keV (16.3 Hz) peak to be 6 × 10−3/keV. Of
the 2614-keV peak rate in the background data, ≈ 33%
is due to 208Tl decay. Scaling from the 2614-keV peak in
the background data, the count rate near the 2039-keV
region due to the Compton tail of the 208Tl 2614-keV
peak is 0.7 events/(keV kg d).
The remainder of the 2614-keV peak is due to neutron-
induced processes. The contribution due to neutrons can
be estimated from the AmBe data. For the AmBe data,
the ratio of the rate in the continuum near the 2039-
keV region (0.03 events(keV s)) to that for the 596-keV
74Ge(n, n′γ) peak (1.87 Hz) is 1.6 × 10−2/keV. Scaling
from the 74Ge peak rate in the background data (59.9/h)
indicates a rate of 7.8 events/(keV kg d) in the contin-
uum near 2039 keV. That is, 53% of the events in that
region are due to neutrons. One can do a similar scal-
ing from the 692-keV 72Ge rates. Here the ratio is 1.3 ×
10−2/keV and the continuum rate is 8.8 events/(keV kg
d). We use the average of the Ge values as our estimate
(8.3 events/(keV kg d) = 3030 events/(keV kg y)) for
the neutron induced contribution to the continuum rate.
Table IV summarizes the deduced contributions to the
spectrum in the 2039-keV region in the CLOVER back-
ground spectrum and the following section discusses how
these data are used along with simulation to estimate
rates in experimental apparatus underground.
B. Solving the Problem with Overburden
The primary purpose of this study is to better under-
stand the impact of neutrons on the background for fu-
ture double-beta decay experiments. In this subsection,
we use neutron fluxes from our simulations of the surface
laboratory, measurements with the AmBe source, and
simulations of the neutron flux in an underground lab-
oratory to estimate the contribution of neutron-induced
backgrounds underground. In the following subsection,
we examine data from previous underground experi-
ments.
The simulation of neutron processes in the 10-cm
Pb shield and Ge comprising the CLOVER detector at
the altitude of our laboratory predicts about 1594±558
events/(keV kg y) between 2000 and 2100 keV due to lead
excitation and about 1337±468 events/(keV kg y) in this
energy region due to germanium excitation. Our mea-
sured value for the neutron-induced events is 3030±1061
events/(keV kg y) to be compared with this predicted
value of 2931±1026 events/(keV kg y).
The simulation of the CLOVER within a 30-cm
lead shield at a depth of 3200 mwe, predicts about
0.019±0.007 events/(keV kg y) contributed from lead
excitation and about 0.016±0.006 events/(keV kg y)
contributed from germanium excitation for a total of
0.035±0.012 events/(keV kg y). One can also just
scale our surface-laboratory measurement of the neutron-
induced rate near 2039 keV by the factor derived from
Eqn. 4 above. This results in 0.05±0.02 events/(keV
kg y). For a detector like the CLOVER, analysis based
on pulse shape discrimination (PSD), and the response
of individual segments or crystals can help reduce back-
ground based on its multiple-site energy deposit nature.
These backgrounds can then be distinguished from the
single-site energy deposit character of double-beta decay.
We have measured the background reduction factor via
these techniques to be ≈ 5.9 for the CLOVER [12].
Reference [10] provides a quick reference formula to
estimate the neutron flux as a function of depth. The
µ flux and its associated activity is reduced by ≈ 10 for
each 1500 m.w.e of added depth. Future double-beta
decay experiments hope to reach backgrounds near 0.25
events/(keV t y). Our estimate of the rate at 3200 mwe
is 35-50 events/(keV t y), which is a factor of 150 above
the goal. Hence, greater depths would be desirable.
C. Discussion of Previous Underground
Experiments
Previous Ge-based double-beta decay experiments con-
ducted deep underground [5, 6] set the standard for low
levels of background. The future proposals however [8, 9]
hope to build experiments with much lower backgrounds.
In this subsection, we estimate how large the neutron
contribution was to the previous efforts and future de-
signs. Using the scaling summarized in Eqn. 4, we can
compare the expectations of our simulated underground
apparatus with previously published results. Table V
shows this comparison. This table also presents a sum-
mary of how the rates would be affected by a change in
depth only. The IGEX collaboration [5] has not pub-
lished its data in sufficient detail to do a similar com-
parison. Other underground Ge detector experiments do
not have the required sensitivity.
The Heidelberg-Moscow experiment [6] is a critical
case study for such backgrounds and it was operated at
TABLE V: A summary of the key count rates arising from neutron interactions in the CLOVER background data in the energy
region near 2039 keV as predicted by our analysis for three representative depths. The shield thickness is taken to be 30 cm
and a veto system with an assumed efficiency of 90% is included. Except for the 2023-keV line, we used the scaling of Eqn. 4 to
scale our CLOVER background measurements to the 3200 mwe depth and then used the muon fluxes at WIPP, Gran Sasso, and
SNOLAB[10] to scale to the other depths. The Ge rates are also scaled for an enriched detector (86% isotope 76, 14% isotope
74). The scalings require the results from the simulations. The uncertainty is dominated by the simulated flux uncertainty
and is estimated to be 35%. Since we did not observe the 2023-keV line, we used simulation to predict the rate. We used the
measured upper limit for the 2041-keV line. For comparison, the results of Ref. [37] is shown. Reference [37] claims a result for
zero-neutrino double-beta decay in an experiment performed at 3200 mwe. We entered the claimed event rate for that process
in the same row as the 2041-keV line for comparison. The rate limits for the other lines assigned to Ref.[37] result from our
estimates based on the figures in their papers and does not come directly from their papers.
Process 1600 mwe 3200 mwe 6000 mwe Ref. [37]
74Ge 596 keV 19400±6800/(t y) 1130±400/(t y) 15±5/(t y) <800/(t y)
76Ge 2023 keV 30±10/(t y) 2±1/(t y) 0.02±0.01/(t y) 300/(t y)
206Pb 537 keV 4400±1500/(t y) 250±88/(t y) 3.4±1.2/(t y)
207Pb 898 keV 5300±1900/(t y) 310±110/(t y) 4.2±1.5/(t y)
206Pb 1705 keV 610±210/(t y) 36±13/(t y) 0.5±0.2/(t y)
206Pb 2041 keV <1300±450/(t y) <74±26/(t y) <1.0±0.3/(t y) 400/(t y)
207Pb 3062 keV 145±51/(t y) 8.4±2.9/(t y) 0.1±0.03/(t y) <71/(t y)
continuum 880±310/(keV t y) 50±17/(keV t y) 0.7±0.24/(keV t y) 110/(keV t y)
a depth of 3200 mwe. One is clearly led to consider if
the 3062-keV γ ray can explain the signal reported in
Ref. [36, 37]. Figure 36 in Ref. [37], shows that no more
than a few counts can be assigned to a 3062-keV γ ray. If
the 23 counts assigned to double-beta decay were actually
a DEP from this γ ray, the one would expect 175 counts
or so in the 3062-keV peak. Therefore, it is difficult to
explain the claimed peak by this mechanism. It is also
clear that the predicted rate of the 2041-keV γ ray is too
low to explain their data. The data from Ref. [37] show
lines at 570 and 1064 keV and the authors assigned these
lines to 207Bi present in the Cu. However, the spectra dis-
played in Fig. 13 of that paper shows that only detectors
surrounded by Pb indicate the 570-keV line. Since there
is no evidence for the 898-keV line in the data, we agree
with the 207Bi assignment, however, we hypothesize that
it must reside in the Pb and not the Cu. Perhaps this
contamination is cosmogenically produced in Pb when it
resides on the surface and not as a result of bomb testing
as hypothesized by the authors[37].
Reference [37] also observed lines at 2011, 2017, 2022,
and 2053 keV. These lines had rates of approximately
500/(t y), 500/(t y), 300/(t y) and 380/(t y) respectively.
The line at 2022 keV is near a line we predict at 2023 keV.
Reference [37] attributes these lines to weak transitions
in 214Bi. From our analysis it is indicated that a negligi-
ble fraction of the peak at 2023 keV is neutron-induced.
However, since the predicted strength of the tell-tale lines
that would indicate a presence of neutron interactions is
just below the sensitivity of that experiment, this conclu-
sion is not without uncertainty. It has been pointed out
that the strength in the 2022-keV line is too strong with
respect to the 214Bi branching ratios even when sum-
ming uncertainties are taken into account [38, 39]. The
analysis in Ref. [38], however, was based on a incorrectly
normalized Fig. 1 in Ref [6]. A recent analysis [39] tak-
ing this into account still points to an inconsistency in
the line strengths. This discrepancy could be resolved if
one attributes a significant fraction of that peak to neu-
tron interactions on 76Ge. Such an attribution is not
supported by our simulations.
Reference [36] simulates the background in the
Heidelberg-Moscow experiment resulting in a predicted
signal of 646 ± 93 counts in the region between 2000 and
2100 keV during an exposure of 49.6 kg-y. This is a count
rate of 130/(keV t y) to be compared with the quoted
measured value for the data period simulated of 160/(keV
t y). Their estimate indicates that only 0.2/(keV t y) are
due to neutrons and they argue that µ-generated neu-
trons are a negligible contribution. Our estimates indi-
cate that neutrons are a more significant contribution and
that the µ contribution is significant. We are aware of no
direct neutron flux measurements for neutrons above 25
MeV. The flux of neutrons with energy greater than 25
MeV is estimated in Ref. [36] to be 10−11/(cm2 s) and
they considered these neutrons to produce a negligible
contribution to the background. In contrast, the simula-
tion in Ref. [10] gives 56 × 10−11/(cm2 s) at 3200 m.w.e
for the neutrons with energy greater than 25 MeV. We
use this higher flux value and as a result, our estimate
of the background rate near 2 MeV of 50/(keV t y) is
comparable to the excess (30/(keV t y)) of the measured
rate in comparison to the simulated rate in Ref. [36].
D. Is Copper an Alternative to Lead?
One has to consider the existence of a DEP line at the
double-beta decay endpoint a serious design considera-
tion for Ge-detector experiments. From the above anal-
ysis, the dangerous lines at 2041 and 3062 keV due to
Pb(n, n′γ) are not significant contributors to the spec-
trum of Ref. [37]. However, as future efforts reduce
the natural activity irradiating the detectors, these Pb-
neutron interactions will become important. One solu-
tion could be the use of Cu as a shield instead of Pb.
Copper is rather expensive and building the entire shield
of this material is probably not necessary. A thick inner
liner of Cu might suffice, but if a peak is observed and
Pb is present near the detector, arguments based on the
spectrum near 3062 keV will be critical.
Although the problematic lines we observed in the Pb
data were absent in our Cu data, the shields were too
dissimilar to make a quantitative comparison regarding
the effectiveness of reducing the continuum background.
Furthermore, our experience with the lead and the sim-
ulation of (n, n′γ) spectra reduces confidence in the con-
clusion regarding the Cu in the absence of such data. We
are preparing better experimental studies to address this
question.
VI. CONCLUSION
As double-beta decay experiments become more sen-
sitive, the potential background must be constrained to
ever-lower levels. Much progress has been made in reduc-
ing naturally-occurring radioactive isotopes from mate-
rials from which the detector is constructed. As these
isotopes that have traditionally limited the experimen-
tal sensitivity are eliminated, rarer processes will become
the dominant contributors. Here we have considered
neutron-induced processes and have quantified them. Re-
actions involving neutrons can result in a wide variety of
contributions to the background. That is, no single com-
ponent is likely to dominate. Therefore, tell-tale signa-
tures for neutrons are needed and were identified in this
work.
In addition to the general continuum background
that neutrons might produce, two specific dangerous
Pb(n, n′γ) lines were identified. These two backgrounds
can be significantly reduced using depth and/or an inner
layer of Cu within the shield. In particular, the 3062-
keV transition in 207Pb has a double escape peak at the
endpoint energy for double-beta decay in 76Ge. A com-
parison of past double-beta decay data indicates the rate
of this transition is too small to explain a claim of double-
beta decay.
VII. ACKNOWLEDGMENT
We thank R.L. Brodzinski for discussions regarding the
historical production of 207Bi and its possible presence in
the environment. We thank John Wilkerson and Jason
Detwiler for useful suggestions and discussion. Finally,
we also thank Alan Poon and Werner Tornow for use-
ful discussions and a careful reading of the manuscript.
This work was supported in part by Laboratory Directed
Research and Development at Los Alamos National Lab-
oratory.
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  We investigate several Pb$(n,n'\gamma$) and Ge$(n,n'\gamma$) reactions. We
measure $\gamma$-ray production from Pb$(n,n'\gamma$) reactions that can be a
significant background for double-beta decay experiments which use lead as a
massive inner shield. Particularly worrisome for Ge-based double-beta decay
experiments are the 2041-keV and 3062-keV $\gamma$ rays produced via
Pb$(n,n'\gamma$). The former is very close to the ^{76}Ge double-beta decay
endpoint energy and the latter has a double escape peak energy near the
endpoint. Excitation $\gamma$-ray lines from Ge$(n,n'\gamma$) reactions are
also observed. We consider the contribution of such backgrounds and their
impact on the sensitivity of next-generation searches for neutrinoless
double-beta decay using enriched germanium detectors.

Neutron Inelastic Scattering Processes as Background for Double-Beta Decay
Experiments
D.-M. Mei,1, 2, ∗ S.R. Elliott,1 A. Hime,1 V. Gehman,1, 3 and K. Kazkaz3, †
Los Alamos National Laboratory, Los Alamos, NM 87545
The Department of Earth Science and Physics, University of South Dakota, Vermillion, South Dakota 57069
Center for Experimental Nuclear Physics and Astrophysics, and
Department of Physics, University of Washington, Seattle, WA 98195
(Dated: October 29, 2018)
We investigate several Pb(n, n′γ) and Ge(n, n′γ) reactions. We measure γ-ray production from
Pb(n, n′γ) reactions that can be a significant background for double-beta decay experiments which
use lead as a massive inner shield. Particularly worrisome for Ge-based double-beta decay experi-
ments are the 2041-keV and 3062-keV γ rays produced via Pb(n, n′γ). The former is very close to
the 76Ge double-beta decay endpoint energy and the latter has a double escape peak energy near
the endpoint. We discuss the implications of these γ rays on past and future double-beta decay
experiments and estimate the cross section to excite the level that produces the 3062-keV γ ray.
Excitation γ-ray lines from Ge(n, n′γ) reactions are also observed. We consider the contribution of
such backgrounds and their impact on the sensitivity of next-generation searches for neutrinoless
double-beta decay using enriched germanium detectors.
PACS numbers: 23.40.-s, 25.40.Fq, 29.40.Wk
I. INTRODUCTION
Neutrinoless double-beta decay plays a key role in
understanding the neutrino’s absolute mass scale and
particle-antiparticle nature [1, 2, 3, 4]. If this nuclear de-
cay process exists, one would observe a mono-energetic
line originating from a material containing an isotope
subject to this decay mode. One such isotope that may
undergo this decay is 76Ge. Germanium-diode detectors
fabricated from material enriched in 76Ge have estab-
lished the best half-life limits and the most restrictive
constraints on the effective Majorana mass for the neu-
trino [5, 6]. One analysis [7] of the data in Ref. [6] claims
evidence for the decay with a half-life of 1.2 × 1025 y.
Planned Ge-based double beta decay experiments [8, 9]
will test this claim. Eventually, these future experiments
target a sensitivity of > 1027 y or ∼ 1 event/ton-year
to explore mass values near that indicated by the atmo-
spheric neutrino oscillation results.
The key to these experiments lies in the ability to re-
duce intrinsic radioactive background to unprecedented
levels and to adequately shield the detectors from ex-
ternal sources of radioactivity. Previous experiments’
limiting backgrounds have been trace levels of natural
decay chain isotopes within the detector and shielding
components. The γ-ray emissions from these isotopes
can deposit energy in the Ge detectors producing a con-
tinuum, which may overwhelm the potential neutrino-
∗Permanent Address: The Department of Earth Science and
Physics, University of South Dakota, Vermillion, South Dakota
57069
†Permanent Address: Lawrence Livermore National Laboratory,
Livermore CA 94550
less double-beta-decay signal peak at 2039 keV. Great
progress has been made identifying the location and ori-
gin of this contamination, and future efforts will substan-
tially reduce this contribution to the background. The
background level goal of 1 event/ton-year, however, is an
ambitious factor of ≈ 400 improvement over the currently
best achieved background level [6]. If the efforts to re-
duce the natural decay chain isotopes are successful, pre-
viously unimportant components of the background must
be understood and eliminated. The potential for neutron
reactions to be one of these background components is
the focus of this paper. The work of Mei and Hime[10]
recognized that (n, n′γ) reactions will become important
for ton-scale double-beta decay experiments. Specifically,
we have studied neutron reactions in Pb and Ge, materi-
als that play important roles in the Majorana [8] design.
But since lead is used by numerous low-background ex-
periments, the results will have wider utility.
This paper presents measurements and simulations of
Pb(n, n′γ) and Ge(n, n′γ) reactions and estimates the re-
sulting background for Ge-detector based, double-beta
decay experiments for a given neutron flux. With these
results, we then use the neutron flux, energy spectrum,
angular distribution, multiplicity and lateral distribu-
tions determined in [10] to estimate the background in
Ge detectors situated in underground laboratories. In
Section II we describe the experiments, the data, and the
simulations. In Sections III and IV we describe the analy-
sis of these data. Section IV also discusses the important
Pb(n, n′γ) production of γ rays at 2041 and 3062 keV.
The former is dangerously near the 2039-keV Q-value for
zero-neutrino double-beta decay in 76Ge and the latter
can produce a double-escape peak line at 2040 keV. These
dangerous processes for Ge-based double-beta decay ex-
periments are discussed for the first time in this work.
Section V determines an overall background model for
http://arxiv.org/abs/0704.0306v4
our detector and the implications of this model for fu-
ture experimental designs. It also considers the relevant
merits of Cu versus Pb as shielding materials, and the
use of depth to mitigate these backgrounds is discussed.
We also consider the possibility that the double-escape
peak of the 3062-keV γ ray could contribute to the signal
claimed in Ref. [7]. Finally, we summarize our conclu-
sions in Section VI.
II. THE MEASUREMENTS
We collected five data sets to explore the implications
of (n, n′γ) for double-beta decay experiments. All mea-
surements were done in our basement laboratory at Los
Alamos National Laboratory. The laboratory building is
at an atmospheric depth of 792 g/cm2 and provides about
1 mwe concrete (77 g/cm2) overburden against cosmic
ray muons.
Three data sets were taken with a CLOVER detec-
tor [11]. This detector is a set of 4 n-type, segmented
germanium detectors. The four crystals have a total nat-
ural germanium mass of 3 kg and each crystal is seg-
mented in half. The CLOVER detector and its opera-
tion in our laboratory were described in Ref. [12]. The
remaining two measurements were done with a PopTop
detector [13] set up in coincidence with a NaI detector.
The PopTop is a 71.8-mm long by 64-mm diameter p-
type Ge detector. Taking into account the central bore,
the detector is 215 cm3 or 1.14 kg. The NaI crystal is
15.25-cm long by 15.25-cm diameter and is directly con-
nected to a photo-tube. All data were read out using
a pair of X Ray Instrumentation Associates (XIA) [14]
Digital Gamma Finder Four Channel (DGF4C) CAMAC
modules. The CAMAC crate is connected to the PCI bus
of a Dell Optiplex computer running Windows 2000. The
system was controlled using the standard software sup-
plied by XIA. This data acquisition software runs in the
IGOR Pro environment [15] and produces binary data
files that were read in and analyzed using the ROOT
framework[16].
The data sets include:
1. A background run with the CLOVER
2. A Th-wire source run with the CLOVER
3. An AmBe source run with the CLOVER using two
different geometries of moderator
4. An AmBe source run with the PopTop surrounded
by lead
5. An AmBe source run with the PopTop surrounded
by copper
In this section we describe the experiments and the data
collected.
A. The Experimental Configurations
The CLOVER was surrounded by 10 cm of lead shield-
ing to reduce the signal from ambient radioactivity. Un-
derneath and above the lead was 5 cm of 30%-loaded
borated polyethylene to reduce thermal neutrons. The
background run done in this configuration lasted 27.13
live-days. The configuration for the Th-source run was
similar, but with some lead removed to expose the detec-
tor to the source. The Th source run had a live time of
1337 seconds.
The setup was modified somewhat from this
background-run configuration for the measurements with
the AmBe source. Fig. 1 shows the configuration for
one of the AmBe measurements. For these data, the
CLOVER was shielded on four sides with 10 cm of lead.
The AmBe source, 30 mCi of 241Am with a calibrated
neutron yield of ≈ 63,000 Hz (±0.7%), was on one side
of the CLOVER with 5 cm of lead and a layer of pure
polyethylene moderator (either 10 or 15 cm thick) be-
tween the source and detector. The data acquisition sys-
tem is inactive during data transfer. Only the AmBe
runs had a large enough event rate for the dead time to
be appreciable. A 6.13-h live-time data run (57% live)
was taken with 15 cm of moderator, and another 3.57-h
live-time data (38% live) run was taken with 10 cm mod-
erator (pictured). For the analysis presented below, the
data from these two configurations were combined, and
thus the AmBe-CLOVER data set contains 9.7 h of live
time. The observed energy spectrum extended from ≈
10-3100 keV for these data sets.
During the analysis of the AmBe data, we observed
a weak line at 3062 keV. This energy corresponds to a
γ-ray transition in 207Pb, and we therefore hypothesized
that it was generated via Pb(n, n′γ). The double-escape-
peak (DEP) energy (2040 keV) associated with this γ ray
is very dangerous for 76Ge neutrinoless double-beta de-
cay experiments because it falls so close to the transition
energy (2039 keV). Furthermore because the DEP is a
single-site energy deposition, it cannot be distinguished
from double-beta decay through event topology. This is
in contrast to a full-energy γ-ray peak, which tends to
consist of several interactions and therefore is a multiple-
site deposition. (See [12] for a discussion of the use of
event topology to reduce background in Ge detectors.)
The final two measurements were intended to study
this 3062-keV line in the spectrum and demonstrate its
origin. In both cases a PopTop Ge detector faced a 15.25
cm by 15.25 cm NaI detector for coincidence data. By se-
quentially placing a Pb and then a Cu absorber between
an AmBe source and a PopTop Ge detector, we tested
the hypothesis that the line was due to neutron interac-
tions in Pb. By looking for an coincident energy deposit
in the NaI detector, we could be assured the Ge detector
signal originated from a neutron interaction in the sam-
ple. An energy deposit threshold in the NaI of greater
than 200 keV was required for a coincidence. The Pop-
Top was placed 27.3 cm from the NaI detector with the
source placed 20.3 cm (7 cm) from the Ge (NaI) detector.
For the lead study, 5 cm of lead was placed directly be-
tween the Ge detector and the source. Additional lead, in
the form of 5-cm-thick bricks was positioned around the
4 sides of the Ge detector to reduce room background.
For the copper study, a 0.5-cm thick Cu tube was placed
around the PopTop and a 5-cm Cu block was placed be-
tween the PopTop and the source. For this final run, all
the lead was removed. For both of these sets of data, the
observed spectra extended from ≈ 125 keV to ≈ 9 MeV.
For the PopTop data, the Pb and Cu runs were of 19.12
h and 17.76 h live-time, respectively.
FIG. 1: The CLOVER detector as configured for the AmBe
source run. The setup at the time of this photograph used
4′′ of polyethylene. One wall of the lead shield was removed
only to clarify the relationship between the AmBe source,
moderator, and the CLOVER.
B. The Data sets
The crystals were individually calibrated, and the re-
sulting spectra summed together to form a single his-
togram. The peaks within each of the 3 CLOVER data
sets were identified and their intensities determined. If an
event had 2 crystals that responded in coincidence, the
histogram would have two entries. Therefore the spectra
we analyzed and simulated included all single-crystal en-
ergy deposits. By not eliminating events that registered
signals in more than 1 of the CLOVER Ge detectors,
we maximized the event rate. The peak strengths were
estimated by fitting a Gaussian shape to peaks and a
flat background to the spectrum in the region near the
peak. For the nuclear recoil lines, the peak shape was
assumed to be a triangle and not Gaussian. In Table I
the uncertainties derive from this fit. A summary of the
peak strengths is given in Table I and the spectra them-
selves are shown in Fig. 2. The data sets were chosen
to help decouple line blendings. Because the rates in
all peaks and continua are much higher for the source-
induced data than for the background, features in those
spectra are due to the sources and other contributions
can be safely ignored. For example, the 2614.5-keV line
can arise from either the decay of 208Tl or 208Pb(n, n′γ).
When exposed to a Th source, Tl decay dominates the
spectrum, whereas when exposed to an AmBe source,
(n, n′γ) dominates. Hence by normalizing the rate in
this line to the rate in a pure neutron-induced transition
(e.g. the 596-keV 74Ge(n,n’γ)), we can determine the
relative contribution of the two processes to the back-
ground spectrum. In fact, in the background data, both
processes contribute to this line.
Some comments on our choices for line identification
are in order. For an isotope such as 72Ge where a neutron
capture leads to a stable nucleus, almost all (n,γ) lines
could also be interpreted as (n, n′γ) lines in the result-
ing nucleus; in this case 73Ge. For isotopes within the
detector however, such as the 53.5-keV 72Ge(n,γ) tran-
sition, the competing 73Ge(n, n′γ) line would be a sum
of this γ-ray energy and the recoil nucleus energy. At
these low energies where the recoil is a fair fraction of
the γ-ray energy, the (n, n′γ) would simply contribute to
the continuum and not be observed as a line. For the
high energy cases, the blend of a mono-energetic γ-ray
line and a (n, n′γ) process might be present.
For the calibration runs, our threshold was approxi-
mately 70 keV. Also note that we used a thorium wire as
a calibration source. Since the wire is pure natural Th,
we observe the Th X rays in that data. In contrast, the
background run shows lines from the thorium chain as a
contaminant, therefore those lines are absent.
In all spectra, there are a few lines we have not iden-
tified.
TABLE I: A summary of the observed lines in the various spectra taken
with the CLOVER detector. Blank entries indicate that no significant
peak feature above the continuum was found. Single and double escape
peaks are labeled by SEP and DEP respectively. Line assignments for
which we are unsure are indicated by a question mark. Line energies are
taken from the Table of Isotopes [17].
Energy Process Count Rates
(keV) backgrnd Thorium CLOVER
(per hr) (Hz) AmBe (Hz)
23.4 70Ge(n,γ) 1.017(5)
46.5 210Pb 112.75(42)
72Ge(n,γ)
61.01(31) 2.079(8)
63.2 234Th 93.02(38)
67.7 230Th 24.05(19) 0.591(4)
68.8 72Ge(n,γ) 0.440(4)
72.80 Pb x-ray 10.5(1) 0.506(4)
74.97 Pb x-ray 663.5(1.0) 34.1(2) 1.703(7)
76.7 Unidentified 29.0(2)
228Th
Pb x-ray
Pb x-ray
115.28(42) 10.9(1) 0.930(5)
Pb x-ray 55.65(29) 16.8(1) 0.262(3)
Continued
TABLE I – continued
Energy Process Count Rates
(keV) backgrnd Thorium CLOVER
(per hr) (Hz) AmBe (Hz)
89.9 Th x-ray 32.4(2)
92.7 234Th 171.38(51) 0.060(1)
93.4 Th x-ray 47.5(2)
96.0 115In(n,γ) ? 0.166(2)
99.5 228Ac 13.71(15) 3.0(1)
105.3 Unidentified 8.99(12)
104.8
105.6
Th x-ray 20.6(1)
108.7 Th x-ray 7.6(1)
109.9 19F(n, n′γ) 43.00(26) 0.506(4)
129.1 228Ac 12.91(14) 3.2(1)
139.7 74Ge(n,γ) 47.20(27) 2.339(8)
143.9 230Th 20.03(18)
154.0 228Ac 7.69(11) 1.5(1)
159.7 77mGe 0.114(2)
162.4 115In(n,γ) 10.71(13) 1.073(6)
174.9 70Ge(n,γ) 7.45(11) 0.763(5)
186.1
186.2
226Ra
115In(n,γ)
114.60(42) 0.323(3)
197.1
198.4
19F(n, n′γ)
71Ge sum
81.04(35) 2.328(8)
199.2 228Ac 0.66(2)
202.6 115In(n,γ) 0.061(1)
209.5 228Ac 19.38(17) 10.9(1)
215.5 228Th 2.43(6) 0.92(3)
238.6 212Pb 295.77(67) 139.9(1) 0.105(2)
242.0 214Pb 57.49(30) 9.2(1)
247.1 70Ge(n,γ) 0.070(1)
253.7 74Ge(n,γ) 2.76(7) 0.410(3)
270.2 228Ac 21.39(18) 9.1(1)
273.0 115In(n,γ) 0.055(1)
277.4
208Tl
208Pb(n, n′γ)
12.98(14) 5.4(1) 0.086(2)
284.6 Unidentified 2.79(7)
288.1 212Bi ? 1.03(3)
295.2 214Pb 58.02(30)
297.2
298.7
72Ge(n,γ)
115In(n,γ)
0.068(1)
300.1 212Pb 18.59(17) 9.7(1)
306.2 70Ge(n,γ) 1.12(4) 0.046(1)
321.4 228Ac 0.67(2)
326.0 70,72Ge(n, n′γ) 0.487(4)
328.3 228Ac 10.02(12) 8.2(1)
332.9 228Ac 1.14(3)
335.5 115In(n,γ) 0.028(1)
338.7 228Ac 45.13(26) 31.5(2)
351.9 214Pb 95.11(38)
354.1 Unidentified 0.043(1)
385.1 115In(n,γ) 0.048(1)
391.3 70Ge(n,γ) 0.053(1)
409.8 228Ac 4.05(8) 4.3(1)
416.9 116mIn 2.21(6) 0.359(3)
438.9 Unidentified 2.54(6)
445.2 74Ge(n,γ) 0.037(1)
452.3 212Bi? 0.82(2)
463.3 228Ac 10.96(13) 9.2(1)
474.0 72Ge(n,γ) ? 2.54(6)
Continued
TABLE I – continued
Energy Process Count Rates
(keV) backgrnd Thorium CLOVER
(per hr) (Hz) AmBe (Hz)
478.6 228Ac 0.39(2)
470-485
10B(n,α)
7Li∗(γ)7Li
Doppler
Broadened
signf.
492.9 73Ge(n,γ) 0.123(2)
499.9 70Ge(n,γ) 0.453(4)
503.9 228Ac 0.34(2)
509.3
510.7
510.7
510.9
228Ac
208Tl
208Pb(n, n′γ)
Annih.γ
171.93(51) 16.8(1) 3.409(10)
516.2 35Cl(n,γ) 0.160(2)
537.5 206Pb(n, n′γ) 5.12(9) 0.158(2)
562.9
563.0
228Ac
76Ge(n, n′γ)
12.83(14) 1.52(3) 0.244(3)
569.7 207Pb(n, n′γ) 14.17(15) 0.422(4)
572.3 228Ac 0.53(2)
574.7 74Ge(n, γ) 0.091(2)
583.1
208Tl
208Pb(n, n′γ)
71.64(33) 49.6(2) 0.256(3)
595.9
74Ge(n, n′γ)
73Ge(n,γ)
59.90(30) 1.869(7)
608.3 73Ge(n,γ) 0.333(3)
609.2 214Bi 60.11(30)
629.6 72Ge(n, n′γ) 0.078(2)
648.2 115In(n,γ) 0.025(1)
657.2 206Pb(n, n′γ) 0.047( 1)
662.0 137Cs 9.04(12)
663.8 206Pb(n, n′γ) 0.069(1)
669.0 70Ge(n, n′γ) 0.030(1)
692.4 72Ge(n, n′e−) 87.70(37) 2.406(8)
701.0 74Ge(n, n′γ) 0.082(2)
708.2 70Ge(n,γ) 0.176(2)
727.3 212Bi 15.72(16) 11.7(1)
747.7 70Ge(n,γ) 0.047(1)
755.3 228Ac 2.19(6) 1.52(3)
763.1 208Tl 0.85(3)
763.1 208Pb(n, n′γ)? 0.032(1)
766.6
768.4
224mPa
214Bi
4.85(9)
771.8 228Ac 2.02(6) 2.11(4)
782.0 228Ac 0.67(2)
785.5 212Bi 4.19(8) 1.57(3)
786.3
786.8
35Cl(n,γ)
208Pb(n, n′γ)
0.041(1)
788.4
788.7
35Cl(n,γ)
70Ge(n,γ)
0.064(1)
795.0 228Ac 7.92(11) 6.1(1)
798.0 208Pb(n, n′γ) 0.023(1)
803.1 206Pb(n, n′γ) 20.90(18) 0.850(5)
806.2 214Bi 3.03(7)
808.2 70Ge(n,γ) 0.048(1)
818.6 116mIn 0.064(1)
824.9 1.03(4)
830.4 228Ac 0.70(2)
834.1 72Ge(n, n′γ) 45.15(26) 0.290(3)
Continued
TABLE I – continued
Energy Process Count Rates
(keV) backgrnd Thorium CLOVER
(per hr) (Hz) AmBe (Hz)
835.6 228Ac 2.30(4)
840.4 228Ac 1.19(3)
843.8 27Al(n, n′γ) 4.48(8) 0.112(2)
846.9 76Ge(n, n′γ) 0.062(1)
860.4
860.4
208Tl
208Pb(n, n′γ)
8.64(12) 6.0(1) 0.090(2)
865.0 Unidentified 0.094(2)
867.9 73Ge(n,γ) 4.25(8) 0.466(4)
881.0 206Pb(n, n′γ) 2.50(6) 0.151(2)
892.9 212Bi 0.42(2)
894.3 72Ge(n, n′γ) 0.029(1)
897.8 207Pb(n, n′γ) 6.28(10) 0.199(2)
904.1 228Ac 0.94(3)
911.2 228Ac 48.86(27) 37.1(2)
934.1 214Bi 1.99(6)
958.4 228Ac 0.37(2)
960.9 74Ge(n, n′γ) 0.095(2)
964.4 228Ac 11.22(13) 6.2(1)
968.8 228Ac 26.83(20) 21.6(1)
981.0 206,8Pb(n, n′γ) 0.035(1)
988.4 228Ac 1.95(5) 0.20(1)
993.7
995.1
74Ge(n, n′γ)
206Pb(n, n′γ)
0.026(1)
999.5 74Ge(n, n′γ) 0.034(1)
1001.5 224mPa 8.03(11)
1004.5 228Ac 0.17(1)
1014.5 27Al(n, n′γ) 7.46(11) 0.173(2)
1033.1 228Ac 0.20(1)
1040.1
1040.8
70Ge(n, n′γ) 16.89(16) 0.210(2)
1063.7 207Pb(n, n′γ) 8.47(11) 0.145(2)
1065.0 228Ac 0.47(2)
1078.8 212Bi 1.11(4) 0.62(2)
1093.9 208Tl sum 511+583 0.90(3)
1095.8
1096.9
207Pb(n, n′γ)
70Ge(n,γ)
116mIn
7.81(11) 0.464(4)
1101.3 74Ge(n, n′γ) 0.123(2)
1105.6 74Ge(n, n′γ) 0.019(1)
1110.4 228Ac sum 0.52(2)
1120.6 214Bi 11.70(13)
1122.5 228Ac sum 0.26(1)
208Pb(n, n′γ)
72Ge(n, n′γ)
0.022(1)
1131.6 73Ge(n,γ)? 1.34(5) 0.034(1)
1139.4 70Ge(n,γ) 1.34(5) 0.077(2)
1153.5 228Ac 0.15(1)
1155.2 214Bi 1.08(4)
1164.9
1166.0
35Cl(n, n′γ)
72Ge(n, n′γ)
0.49(3) 0.072(1)
1173.5 60Co 13.67(14)
1201.2 p(n,γ)d DEP 0.415(3)
1204.2
73Ge(n,γ)
74Ge(n, n′γ)
9.39(12) 0.163(2)
1226.7 74Ge(n, n′γ) 0.017(1)
1238.4 214Bi 5.22(9)
1246.9 228Ac 0.58(2)
Continued
TABLE I – continued
Energy Process Count Rates
(keV) backgrnd Thorium CLOVER
(per hr) (Hz) AmBe (Hz)
1261.0 74Ge(n, n′γ) 0.019(1)
1281.0 214Bi 0.74(3)
1286-7 228Ac Blend 0.14(1)
1293.5 116mIn 4.09(8) 0.462(4)
1298.8 70Ge(n,γ) 0.087(2)
1332.5 74Ge(n, n′γ) 0.018(1)
1332.5 60Co 12.27(14)
1344.5
1345.9
1347.7
74Ge(n,γ)
206Pb(n, n′γ)
70Ge(n,γ)
0.52(3) 0.017(1)
1374.2
228Ac sum
964 + 409
911 + 463
0.28(1)
1378.0 214Bi 3.24(7)
1378.8 70Ge(n,γ) 0.065(1)
1393.8 206Pb(n, n′γ) 0.016(1)
1401.5 214Bi 0.58(3)
1408.6 214Bi 1.84(5)
1413.6 73Ge(n, n′γ) 0.018(1)
1431.1 228Ac 0.15(1)
1433.5 206Pb(n, n′γ) 0.020(1)
1436.9 208Pb(n, n′γ) 0.017(1)
1459.2 228Ac 0.80(2)
1461.0 40K 30.18(22) 0.066(1)
1463.9 72Ge(n, n′γ) 0.114(2)
1466.8 206Pb(n, n′γ) 0.032(1)
1471.6 73Ge(n,γ) 0.047(1)
1489.2 74Ge(n, n′γ) 0.025(1)
1496.2 228Ac 0.73(3) 0.85(3)
1501.7 228Ac 0.42(2)
1508.9 116mIn 0.069(1)
1508.9 214Bi 1.95(3)
1512.7 212Bi 0.38(2)
1538 214Bi 0.54(3)
1557.1 228Ac 0.14(1)
1580.8 228Ac 0.68(3) 0.55(2)
1588.3 228Ac 6.06(10) 2.94(5)
1592.5
1592.5
1593.0
208Tl DEP
208Pb DEP
207Pb(n, n′γ)
7.24(11) 2.10(4) 0.107(2)
1599.3 214Bi 0.38(2)
1601.1
1602.0
35Cl(n,γ)
74Ge(n, n′γ)
0.018(1)
1614.9 208Pb(n, n′γ)? 0.020(1)
1620.5 212Bi 1.81(5) 1.32(3)
1625.0 228Ac 0.34(2)
1630.7 228Ac 1.82(5) 1.46(3)
1631.5
1632.0
74Ge(n, n′γ)
70Ge(n,γ)
0.021(1)
1634.0 76Ge(n,γ) 0.016(1)
1638.3 228Ac 0.43(3) 0.41(2)
1640.4
208Pb(n, n′γ)
74,76Ge(n, n′γ)
0.026(1)
1661.3 214Bi 0.36(2)
1666.3 228Ac 0.17(1)
1699.5 206Pb(n, n′γ)? 0.021(1)
1704.5 206Pb(n, n′γ) 0.72(3) 0.041(1)
Continued
TABLE I – continued
Energy Process Count Rates
(keV) backgrnd Thorium CLOVER
(per hr) (Hz) AmBe (Hz)
1710.9 72Ge(n, n′γ) 0.327(3)
1712.2 p(n,γ)d SEP 0.156(2)
1725.7 207Pb(n, n′γ) 0.029(1)
1729.6 214Bi 3.59(7)
1764.7 214Bi 11.68(13)
1779.0
27Al(n,γ)
28Al ⇒28 Si
2.13(6) 0.127(2)
1806.0 212Bi 0.11(1)
1844.5 206Pb(n, n′γ) 0.044(1)
1846.9 214Bi 2.26(6)
1940.4 74Ge(n, n′γ) 0.027(1)
1951.1 35Cl(n,γ) 0.032(1)
1959.3 35Cl(n,γ) 0.023(1)
2092.1
2092.7
206Pb(n, n′γ)
207Pb(n, n′γ)
0.039(1)
2103.8
208Tl SEP
208Pb SEP
5.21(9) 2.25(4) 0.090(2)
2112.1 116mIn 0.061(1)
2118.5 214Bi 0.64(3)
2204.0 214Bi 3.73(8)
2223.3 p(n,γ)d 5.813(13)
2390.5 116mIn 0.015(1)
2448.5 214Bi 0.51(3)
2614.5
208Tl
208Pb(n, n′γ)
39.39(25) 16.3(1) 0.729(5)
2650.3 206Pb(n, n′γ)? 0.011(1)
2686 sum 208Tl? 0.12(1)
2892 sum 208Tl 0.08(1)
3061.9 207Pb(n, n′γ) 0.010(1)
C. Neutron Spectra Simulation
Fast neutrons (from 100 MeV to 1 GeV or more) tend
to produce additional neutrons through nuclear reactions
as they traverse high-Z material. In particular the flux
of neutrons will increase several-fold while the average
neutron energy decreases through these processes. As a
result, fast neutrons will penetrate deep into a shield pro-
ducing additional neutrons at lower energies. These low
energy neutrons (∼< 20 MeV) give rise to a substantial
γ-ray flux because (n,n
γ) cross sections are large near
10 MeV, but become small at higher energies. Hence
it is these secondary lower-energy neutrons that inter-
act with the shield and detector materials to produce γ
rays, which can give rise to background in double-beta
decay experiments. To understand the process by which
high energy neutrons influence the low-energy neutron
flux and, in turn, the observed γ-ray flux, we simulated
neutrons impinging on an outer shield and tracked how
their spectrum changed as the particles traversed the
shield. We also simulated the production of neutron-
induced γ rays and how the Ge detector responded to
Energy (keV)
0 50 100 150 200 250 300 350
AmBe Spectrum
Background Spectrum
Energy (keV)
400 500 600 700 800 900
AmBe Spectrum
Background Spectrum
Energy (keV)
1000 1200 1400 1600 1800 2000
AmBe Spectrum
Background Spectrum
Energy (keV)
2000 2200 2400 2600 2800 3000 3200
AmBe Spectrum
Background Spectrum
FIG. 2: The AmBe and background spectra taken with the
CLOVER.
them. Specifically, we performed simulations of several
geometries including:
1. A simulation of the cosmic-ray produced neutrons
with energy up to 1 GeV at our lab in Los Alamos
and their propagation through a 10-cm Pb shield.
The response of the CLOVER detector to γ rays
produced by neutron interactions in the shield was
simulated. This simulation, compared to our back-
ground data, tests the precision to which we can
model neutron production, scattering with sec-
ondary neutron production and (n,n’γ) interac-
tions.
2. A simulation of the neutron flux induced on the
CLOVER from the AmBe source (neutron energy
≤11.2 MeV) passing through 15 cm of polyethylene
before impinging on the 10-cm Pb shield. Since the
neutron flux is of low energy, this simulation tests
the precision to which we model (n,n’γ) interac-
tions.
3. A simulation of the neutron flux with neutron en-
ergies up to a few GeV expected at 3200 mwe deep
due to cosmic-ray µ interactions in the surround-
ing rock and 30-cm lead shield and the resulting
response of the CLOVER to the flux of γ rays aris-
ing from this flux. This simulation permits us to
estimate rates in detectors situated in underground
laboratories.
The first two of these simulations are to verify the code’s
predictive power. The third is to aid in understanding the
utility of depth to avoid neutron-induced backgrounds.
The simulation package GEANT3-GCALOR [18, 19]
is described in detail in Ref. [10]. In general, (n, n′)
reactions leave the target nucleus in a highly excited
state which subsequently decays via a γ-ray cascade to
the ground state. In the simulation, inelastic scattering
cross sections for excitation to a given level depends on
the properties of the ground and excited states. These
cross sections were calculated using in-house-written
code based on Hauser-Feshbach [20] theory modified by
Moldauer [21]. The validation of the Hauser-Feshbach
theory has been the subject of several studies [22, 23, 24].
The simulated γ-ray flux arises from the relaxation of the
initial excited-state distribution, which includes a large
number of levels (60 states for 208Pb(n, n′γ) reactions,
for example). The nuclear levels and their decay chan-
nels were provided by the ENSDF[25] database through
the GEANT package. Note however, that the simula-
tion did not predict every possible transition. In particu-
lar the important 2041-keV and 3062-keV emissions from
Pb were not part of this simulation. This situation arises
because the simulation packages only have (n, n′) cross
sections for the lowest lying excited states for most nu-
clei. It is set to zero for most other levels. The details of
this simulation are described in detail in Ref. [10]. Here
we study the effectiveness of the simulation to predict
spectra resulting from (n,n’γ).
The simulation was done by generating neutrons with
the appropriate energy spectrum outside the lead shield
and propagating them through the shield including sec-
ondary interactions that may add to the neutron flux and
alter the energy spectrum. Fig. 3 shows a comparison
between the data and the simulations for the CLOVER
background run and AmBe run. Note only neutrons
as primary particles were simulated for this comparison
and the dominant difference between the two spectra is
due to the room’s natural radioactivity and non-neutron
µ-induced processes. Here we excluded those processes
from the simulation to emphasize the spectral shape, in-
cluding lines, that are a direct result of neutron inter-
actions. The similarity of the spectra in Fig. 3 indicates
that the measured background spectrum is dominated by
neutron-induced reactions.
The uncertainty in the simulation is calculated by com-
paring the well known peaks in Table II which shows
a comparison of the simulation to the line production
for both background and AmBe runs. The measured
neutron produced lines are within about 5% of the pre-
dicted values from simulation, as is the continuum rate
in the AmBe data. Therefore the (n,n’γ) rates are well-
simulated for nuclear states with well-defined cross sec-
tions. (The continuum for the background data includes
processes that were not simulated and hence is not a
good measure of the uncertainty.) Because the neutron
flux estimates come from these line strengths (See Sec-
tion III), the uncertainty in the flux cancels in these es-
timates. The uncertainty in the measured neutron flux
and spectrum underground(≈35%) constrains the preci-
sion to which such simulations can be verified and is well
described in Ref. [10]. This 35% uncertainty due to the
flux is much larger than the uncertainty for the γ-ray
line production described above. Therefore, a total un-
certainty of 35% is used for all predictions of line rates
underground throughout this paper.
III. THE NEUTRON FLUX
In this section, we use the data to determine the neu-
tron fluxes we observed during our various experimental
configurations. We then compare our measured cosmic-
ray induced flux with that predicted from past measure-
ments and our simulation.
A. Ge(n, n′γ) Analysis
Spectral lines that indicate neutron interactions in nat-
ural Ge detectors have been studied previously. See Ref-
erences [26, 27, 28, 29], for example. In particular, the
sawtooth-shaped peaks due to 72,74Ge(n, n′) at 693 keV
and 596 keV respectively are clear indications of neu-
trons and have been used to deduce neutron fluxes [30].
Operating Ge detectors in a low-background configura-
tion, these lines can be used to help interpret the back-
ground components. Recent double-beta decay experi-
ments [5, 6] have constructed their detectors from Ge en-
riched in isotope 76. Although an appreciable amount of
74Ge remained (14%), 70,72,73Ge are depleted. For such
Energy (keV)
500 1000 1500 2000 2500 3000
Am-Be, MC
Am-Be, Data
Background, Data
Background, MC
Am-Be, MC
Am-Be, Data
Background, Data
Background, MC
Energy (keV)
500 550 600 650 700 750 800
Am-Be, MC
Am-Be, Data
Background, Data
Background, MC
Am-Be, MC
Am-Be, Data
Background, Data
Background, MC
FIG. 3: Comparison of the measured and simulated AmBe
spectra for the CLOVER detector surrounded by 10 cm lead
and 15 cm of moderator. The upper plot shows the energy
range between 10 - 3100 keV. The lower plot shows the range
470 - 830 KeV where the most significant (n, n′γ) lines can
be seen. The simulated AmBe neutron spectrum was nor-
malized to the AmBe source strength for 6.13-h live-time.
The measured total neutron flux in the background spectrum
(see Section IIIC) was used to normalize the simulated back-
ground spectrum. Note, only neutrons as primary particles
were simulated for this comparison and the difference between
the spectra is due to the room’s natural radioactivity and non-
neutron, µ-induced processes.
detectors, only lines originating in isotopes 74 and 76
are useful for neutron interaction analysis. As these ex-
periments reach for lower background, neutron-induced
backgrounds become a greater concern and the diagnos-
tic tools more important.
Neutrons from (α,n) and fission reactions have an en-
ergy spectrum with an average energy similar to the
AmBe spectrum used in this study. Furthermore, the
average energy of the AmBe neutrons is similar to that
of the neutrons within the hadronic cosmic-ray flux im-
pinging on our surface laboratory although the latter ex-
tend to much higher energies. Therefore the Ge-detector
signatures indicating the presence of neutrons described
above will be similar to those arising from neutrons origi-
nating from the rock walls of an underground laboratory.
However, low-background experiments that use Ge de-
tectors are typically deep underground and are shielded
TABLE II: A comparison of the simulated to measured rates
(Background: per hour and AmBe: Hz) for several lines pro-
duced by neutron interactions. The 2041-keV and 3062-keV
lines are not included in the simulation.
Process γ-ray Background-CLOVER
Energy Simulation Measurement
74Ge(n, n′γ) 596 keV 56.21 59.90(30)
74Ge(n, n′γ) 254 keV 2.63 2.76(7)
76Ge(n, n′γ) 2023 keV 3.2×10−7 below sensitivity
206Pb(n, n′γ) 537 keV 4.82 5.12(9)
207Pb(n, n′γ) 898 keV 6.21 6.28(10)
206Pb(n, n′γ) 1706 keV 0.69 0.72(3)
206Pb(n, n′γ) 2041 keV none not seen
Continuum region 2000-2100 keV 110.2 187.35(19)
207Pb(n, n′γ) 3062 keV none not seen
Process γ-ray AmBe-CLOVER
Energy Simulation Measurement
74Ge(n, n′γ) 596 keV 1.8 1.87
74Ge(n, n′γ) 254 keV 0.36 0.41
76Ge(n, n′γ) 2023 keV 8.5×10−4 below sensitivity
206Pb(n, n′γ) 537 keV 0.15 0.16
207Pb(n, n′γ) 898 keV 0.14 0.20
206Pb(n, n′γ) 1706 keV 0.04 0.04
206Pb(n, n′γ) 2041 keV none not seen
Continuum region 2000-2100 keV 7.01 7.33
207Pb(n, n′γ) 3062 keV none 0.01
from environmental radioactivity by a thick shield. This
shield, typically made of Pb, is then usually surrounded
by a neutron moderator. This configuration is effective at
greatly reducing the neutron flux originating from (α,n)
and fission reactions in the cavity walls of the under-
ground laboratory. In contrast, although neutrons origi-
nating from µ interactions underground are much rarer,
they have much higher energy. Therefore these µ-induced
neutrons can penetrate the shield more readily and be-
come a major fraction of the neutrons impinging on the
detector.
B. The AmBe Neutron Flux
The estimate of the flux of neutrons with energies
greater than 692 keV is given by [30, 31, 32]
Φn = k
, (1)
where I is the counts s−1 under the asymmetric 692-keV
peak, V is the volume of the detector in cm3 (566 cm3)
and k is a parameter found by Ref. [30] to be 900 ± 150
cm. For the 15-cm moderator data, this formula predicts
a neutron flux of 2.3/(cm2 s) whereas our simulation,
using the known flux of the source, predicts 1.8/(cm2
s). This difference (20-30%) is somewhat greater than
the 17% uncertainty claimed by Ref. [30]. The geometry
for our measurement was complicated and perhaps this
added complexity of neutron propagation contributes to
the difference. For the uncertainty associated with the
flux of neutrons produced from cosmic ray µ, we use the
35% value as it is much larger than the value associated
with Eqn. 1.
For the Am-Be neutron source, the rate in the 692-keV
peak is 2.406 ± 0.008 Hz. This results in Φamben = 3.8
± 1.1 /(cm2 s). This rate is an average over the two
moderator configurations. The neutron flux during the
10-cm moderator run is estimated to be about a factor
2.3 larger than for the 15-cm moderator run. For the
PopTop-AmBe run on Pb for the raw data (in coinci-
dence with the NaI detector), the effective flux was 8.6
± 2.6/(cm2 s) (0.26 ± 0.08 /(cm2 s)).
C. Cosmic-ray Induced Neutron Fluxes
In the background spectrum the rate in the 692-keV
peak is 87.7 ± 0.4/hr. Using Eqn. (1) with I = (2.44 ±
0.06)×10−2 Hz for the background spectrum, one obtains
a fast neutron flux of Φbackn = (3.9 ± 1.2)×10
−2 /(cm2
s) at the detector in our surface laboratory.
Ref. [30] provides a similar formula to estimate the
thermal neutron flux, which is accurate to approximately
30%. Using the intensity of the 139.68-keV γ-ray line of
75mGe:
980I139.68
139.68 + 1.6)V
, (2)
139.68 ≃ 1−
1− e−V
V 1/3
where I = 47.2 ± 0.3 /h = 0.013 Hz is the event rate in
the peak of 139.68-keV line and V is the volume of the
detector in cm3. Using V = 566 cm3 we obtain Φbackth =
(9.1 ± 2.7)×10−3 /(cm2 s). We also measure the thermal
neutron flux for the Am-Be neutron source, Φambeth = 1.6
± 0.5 /(cm2 s).
Thus the total neutron flux incident on the Ge detector
measured for the background run is approximately Φbacktot
= Φbackn + Φ
th = (4.8 ± 0.7) × 10
−2 /(cm2 s).
D. Neutron Flux as a Function of Depth
In our basement laboratory, there are 3 primary
sources of environmental neutrons. The largest contri-
bution comes from the hadronic cosmic ray flux. The
next largest arises from µ interactions in the 77 g/cm2
thick overhead concrete layer in the building. Finally
there is the negligible contribution from (α,n) and fission
neutrons from natural radioactivity in the room. The at-
mospheric depth at the altitude of our laboratory is 792
g/cm2. Including the concrete, the depth is 869 g/cm2.
Using the analysis of Ziegler [33, 34], the flux at our lab
due to the hadronic flux can be estimated to be 3.0 times
larger than that at sea level. The flux at sea level has
been measured to be 1.22 × 10−2 /(cm2 s) [35] result-
ing in a flux in our laboratory of 3.7 × 10−2 /(cm2 s).
To estimate the additional neutron flux originating from
µ interactions in the concrete above our laboratory, we
rely on our simulations of neutron generation and prop-
agation. The simulation predicts 1.4 × 10−2 /(cm2 s)
(3.3 × 10−2 /(cm2 s)) for the muon-induced (hadronic)
neutron flux inside the lead shield for a total simulated
neutron flux of 4.7 × 10−2 /(cm2 s) in acceptable agree-
ment with our measurement of (4.8 ± 2.2) × 10−2 /(cm2
s) = (1.51 ± 0.69) × 106 ± /(cm2 y). The success of this
simulation lends credence to the neutron flux estimate in
the following sections.
The neutron flux onto the detector will be increased
due to the neutron interactions with shield materials and
neutron back-scattering from the cavity walls. For exam-
ple, our simulations show that the fast neutron flux will
increase by a factor of ≈ 10 by traversing a 30-cm lead
layer. Also, neutrons will backscatter from the cavity
walls and reflect back toward the experimental appara-
tus, effectively increasing the impinging neutron flux by
a factor of 2-3 depending on the specific geometries of
the detector and experimental hall. Therefore, it is im-
portant to account for these effects when estimating the
neutron flux at the detector.
Muon-induced neutron production in different shield-
ing materials and in the detector itself was also stud-
ied in Ref. [10]. For example, with 30 cm of lead sur-
rounding a CLOVER-style detector at 3200 mwe, the to-
tal muon-induced neutron flux impinging on the detector
was calculated to be (8.6 ± 4.0) × 10−8 /(cm2 s) = 2.7
± 1.2/(cm2 y). Some of the interactions resulting from
these neutrons would be eliminated by a µ veto. Assum-
ing a veto efficiency of 90% for muons traversing this lead
shield, the effective neutron flux is estimated to be (2.0
± 0.9) × 10−8 /(cm2 s) = 0.63 ± 0.29 /(cm2 y). The
energy spectrum of neutrons at the lead/detector bound-
ary at 3200 mwe is shown in Fig. 4 and has an average
value of 45 MeV.
The average energy of the µ-induced neutrons is 100-
200 MeV and much higher than that of (α,n) neutrons
(≈ 5 MeV). The simulated flux of the µ-induced neutrons
((2 ± 0.9) × 10−8 /cm2 s = 0.63 ± 0.29/cm2 y) inside
the detector shield at a depth of 3200 mwe is a factor 2.4
greater than the simulated (α,n) flux surviving the shield
((0.85 ± 0.39)× 10−8 /cm2 s = 0.27 ± 0.12/cm2 y). The
average energy of these (α,n) originating neutrons is 3-5
MeV at the detector surface.
With this estimate of the neutron flux at depth and
with our measurements of the Pb and Ge neutron-
induced detector response, we can proceed to estimate
these processes in underground Ge-detector experiments.
There are effects in addition to the incident flux, however,
that must be taken into account when extrapolating our
surface laboratory results to different geometries and lo-
Energy (MeV)
10 1 10
: Lead/Detector boundary!
,n):  Lead/Detector boundary!(
FIG. 4: The effective neutron flux onto the simulated detector
described in the text at a depth of 3200 mwe. Shown are the
neutron flux from two sources: (1) the effective neutron flux
induced by muons that transverse the surrounding rock and
shielding materials assuming a 90% muon-veto efficiency and
(2) the neutron flux from (α,n) reactions in the rock.
cations.
1. As the thickness of the Pb shield increases, addi-
tional secondary neutrons will be generated. Our
simulation predicts that a factor kshield = 2.16
more neutrons will be produced by a 30-cm thick
shield as compared to a 10-cm thick shield.
2. As the energy of the neutrons increases, the number
of multiply scattered neutrons increases and there-
fore the number of interactions that might produce
a γ ray increases. For the average energy of neu-
trons at our surface laboratory (at 3200 mwe), the
average scattering length is λL=7.1 cm (λUG = 12.5
3. Also as the energy increases, the number of states
that can be excited in the target nucleus increases.
In the shield at our surface laboratory (at 3200
m.w.e), the average neutron energy is 6.5 MeV (45
MeV).
All of these factors can be incorporated into a scaling
formula derived from our simulation. The rate (RUGROI)
of background near the region of interest (ROI) in an
underground laboratory can be related to that measured
in our surface laboratory (RLROI) as
ROI = (1 +
)kshield((
EUGn − Ex
ELn − Ex
)0.8)
ROI ,
where ΦLn (Φ
n ) is the neutron flux in our surface labo-
ratory (at 3200 mwe), En is the neutron energy and Ex
is the excitation energy for a typical level. This formula
reproduces our simulated results well and the uncertainty
of its use is dominated by the precision of simulation. Us-
ing the 2.6-MeV level in 208Pb as an example, RUGROI ∼
1.7 × 10−5RLROI . Fig. 5 shows a comparison between the
Monte Carlo simulation and the scaling formula Eqn. 4
for several lines.
-ray Energy (keV)γ
500 1000 1500 2000 2500
-610×
Monte Carlo simulation
Scaling formula
FIG. 5: The comparison between the Monte Carlo simulation
of a detector as described in the text and the scaling formula
for several excitation lines. The 35% uncertainties shown in
this figure arise from the cross section uncertainty and the
statistical uncertainty of determining the peak counts in the
simulated spectra. The latter dominates.
IV. ANALYSIS
A. Pb(n, n′γ) analysis
If fast neutrons are present, then one will also see γ-ray
lines from Pb(n, n′) interactions. In very low background
configurations, γ rays from neutron-induced excitations
in 208Pb and 207Pb can be masked by or confused for de-
cays of 208Tl and 207Bi respectively. Therefore it is the
stronger transitions in 206Pb (537.5, 1704.5 keV) that are
most useful for determining if these processes are taking
place. In 207Pb the relative strength of the 898-keV tran-
sition, compared to the 570- and 1064-keV transitions, is
much stronger when it originates from 207Pb(n,n’γ) as
opposed to 207Bi β decay to 207Pb. Therefore this line
can also be used as a tell-tale signature of neutron inter-
actions.
Our data show indications of 206,207,208Pb(n, n′γ). As
noted earlier, the 2614-keV γ ray from 208Pb can orig-
inate from 208Tl decay or from 208Pb(n,n’γ). The 692-
keV peak arises only from neutron interactions on 72Ge.
Since the Pb shielding was similar in both the background
and AmBe runs, we can compare the ratio of the rate in
the 2614-keV peak to that in the 72Ge(n, n′γ) 692-keV
peak in the two data sets to deduce the fraction of the
2614-keV in the background run that can be attributed
to neutron interactions. This ratio in the Am-Be spec-
trum is 0.30 and that in the background spectrum is 0.45,
and therefore, we conclude that ≈ 67% of the strength
in the background run is due to neutron reactions and
the remainder is due to 208Tl decay. Clearly, in our sur-
face laboratory, environmental neutrons are a significant
contributor to the observed signal.
B. The Special Cases of the 2023-keV, 2041-keV
and 3062-keV γ rays
The 2023-keV level in 76Ge can be excited by neutrons.
The simulation predicts that this line is too weak to be
seen in the CLOVER AmBe data, but the CLOVER is
built of natural Ge. In the enriched detectors planned
by future double-beta decay experiments, the fraction of
isotope 76 is much larger and this line would be enhanced.
Still our simulation (Table V) predicts it would be a very
small peak.
The 3714-keV level in 206Pb can emit a 2041-keV γ
ray. We only observed a candidate γ-ray peak in the
coincidence data (Ge detector event in coincidence with
a 4.4-MeV γ ray in the NaI detector) with the AmBe
source radiating the Pb shield around the PopTop detec-
tor. The magnitude of this peak if it exists is small and
not convincing. We use this data set to place a limit on
the production rate of this line as it results in the most
conservative limit.
In the AmBe-irradiated CLOVER and the non-
coincidence PopTop spectra, we observed a 3062-keV γ
ray that we assign to a transition from the 3633-keV level
in 207Pb. (See Fig. 6.) This line is only present when
Pb surrounds the detector: It is absent when Cu forms
the shield. The statistical sensitivity was too weak in
the PopTop coincidence spectrum to observe this weak
line. In the CLOVER AmBe spectrum, the rate of this
line is 5.3 × 10−3 that of 596-keV 74Ge peak rate and
in the raw AmBe PopTop with Pb spectrum the ratio is
4.5 × 10−3. From these data we can estimate an approx-
imate rate that these dangerous backgrounds would be
produced for a given neutron flux. In our surface labora-
tory, the CLOVER background rate for the 74Ge 596-keV
peak was 59.9 events/hr. This leads to a predicted rate of
0.3 events/hr in the 3062-keV peak. Note that our data
indicate that any peak at 3062 keV is statistically weak
(≤ 0.2 events/hr) but reasonably consistent with this pre-
diction. Note, in the AmBe-CLOVER runs, polyethylene
blocks were used to increase the flux of thermal neutrons.
It appears that these blocks contain some Cl and there-
fore we see indications of Cl(n,γ) lines. Even though 35Cl
has a neutron capture line at 3062-keV, we do not assign
the observed line in our data to that process. Because the
35Cl(n,γ) line at 2863 keV is not observed and because
the line at 1959 keV is weak, we conclude that assigning
this line to Cl would be inconsistent with the predicted
line ratios for neutron capture. However, a concern re-
garding our assignment of the 3062-keV line to 207Pb is
that one also expects a 2737-keV emission from the same
3633-keV level. This companion γ ray is not observed
in our data and we plan future measurements dedicated
to measuring the neutron-induced relative intensities of
these two lines. If we assume that the entire rate (0.01
Hz) of the 3062-keV line is due to (n, n′γ), we can make a
crude estimate of the cross section by scaling to the rate
in the 2614-keV line. The cross section for the 2614-keV
(n,n’γ) is 2.1 b ± 10% [23]. Using this cross section, the
relative rates in the two peaks, the different isotopic ra-
tios of 208Pb and 207Pb, and the different γ-ray detection
efficiencies, the average cross section for 207Pb(4.5-MeV
n, n′ 3062-keV γ ray) is estimated to be 75 mb. The
uncertainty is estimated to be about 20% or ∼ 15 mb.
Energy (keV)
3000 3020 3040 3060 3080 3100
AmBe activation, 6.1 h with 6" poly, 3.6 h with 4" poly
FIG. 6: The energy spectrum near 3000 keV showing the
207Pb(n, n′γ) 3062-keV γ-ray line in the AmBe spectrum with
the CLOVER.
From measurements with the CLOVER and a 56Co
source, which has γ-ray energies near 3100 keV, we expect
0.13 DEP events per full-energy γ-ray event. Therefore,
in our surface lab, we expect 0.03 events/hr in the DEP
at 2039 keV due to 207Pb(n, n′γ). This is well below
our continuum rate of 2.5 events/keV-hr or 10/hr in an
energy window corresponding to a 4-keV wide peak.
Since our simulation does not predict all these lines, we
summarize the measured rates normalized to the neutron
flux in Table III to provide simple scaling to different ex-
perimental configurations. The uncertainties in Table III
are estimates based on a minor contribution of the sta-
tistical uncertainty in the peak strengths and a major
contribution resulting from the ≈ 35% uncertainty in the
neutron flux determination as described in Section III B.
Because the uncertainty is mostly systematic, there is a
good possibility that the total uncertainties for each in-
dividual measurement are correlated. Therefore, to esti-
mate the average values in this Table, we took a straight
average of the individual values and then assigned an un-
certainty equal to the largest fractional value. This pro-
cedure, although not rigorous, is more conservative than
a weighted average. In addition, some peaks were not
observed in all spectra. The upper limits on the strength
of these peaks were estimated from the rates of weak-
est peaks observed near the associated energy region in
the spectrum. Such peaks are considered to represent
the level of sensitivity of our peak detection procedures.
The 2041-keV line is a special case. We quote an up-
per limit based on the only spectrum that indicated a
possible peak.
These measurements were done for a CLOVER de-
tector inside a 10-cm Pb shield. The relative energy-
dependent efficiency (ǫrel) for a full-energy peak in the
CLOVER can be approximated by,
TABLE III: The raw count rates for select processes normalized to neutron flux of 1/(cm2y). When extrapolating to neutron
energies distant from that near the measurements, the uncertainty (35%) associated with the extrapolation must be included.
See text for a discussion of the uncertainty estimates in this table especially with respect to the average.
Process Rate Rate Rate Rate
AmBe-CLOVER AmBe-PopTop Background Average
( events
206Pb(n, n′537− keV γ) 13.9±4.9 20.5±7.2 12.2±4.3 15.5±5.4
74Ge(n, n′596− keV γ) 164±57 unresolveda 142±50 153±54
207Pb(n, n′898− keV γ) 17.5±6.1 21.2±7.4 14.9±5.2 17.9±6.3
206Pb(n, n′1705− keV γ) 3.6±1.3 3.2±1.1 1.7±0.6 2.8±1.0
206Pb(n, n′2041− keV γ) <6.3 < 0.5 <1.7 < 5.0b
207Pb(n, n′3062− keV γ) 0.88±0.31 0.6±0.21 <1.0 0.7±0.2
( events
(keV ty)
Continuum Rate from Pb,Ge(n, n′γ) 2.6±0.9 2.0±0.7 2.5±0.9 2.4±0.8
aIn the PopTop data, the 596-keV line was not resolved from
nearby lines.
bThe 2041 line was not observed in any of our spectra, however,
a weak peak-like feature was present in the AmBe-PopTop coinci-
dence data. We used the upper limit for the rate in that peak as
the ”average” as we considered this to be most conservative.
ǫrel = 0.15 + 0.93e
−(Eγ−148)
766 , (5)
where Eγ is the γ-ray energy in keV. This expression is
normalized to 1.0 at 209 keV and is estimated to have an
accuracy of about 20% near 200 keV improving to about
10% at 2600 keV. The quoted relative efficiency for each
of the 4 individual CLOVER detectors is 26% at 1.33
MeV as quoted by the manufacturer. Table III does not
incorporate this efficiency correction, therefore the table
presents the measured count rates with a minimum of
assumptions. The thickness of Pb is large compared to
the mean free path of the γ rays of interest, therefore, the
scaling should hold for other thick-shield configurations.
Even so, the rates will be geometry-dependent so these
results can only be considered guides when applied to
other experimental designs. The rate of these excitations
also depends on neutron energy. For the background run
(AmBe run) the average neutron energy is ≈ 6.5 MeV (≈
5.5 MeV). Our simulations predict that the rate of these
excitations scales as energy to the 0.81 power.
V. DISCUSSION
A. A Model of the CLOVER Background
We can use these experimental results to create a back-
ground model for our surface lab and deduce the contri-
bution to the continuum near 2039 keV due to (n,n’γ) re-
actions. We then use simulation of high-energy neutron
production and propagation to extrapolate this model
to better understand experiments done at depth. The
measured rate for the continuum near 2039 keV was 14.8
events/(keV kg d). For the Th-wire data, this continuum
rate was 0.10 events/(keV s) (2900 events/(keV kg d))
and for the AmBe data it was 0.09 events/(keV s) (2600
events/(keV kg d)). To determine the neutron-induced
continuum rates in the AmBe data, however, we have
to correct for the contribution from the tail of two high-
energy γ rays that are not part of the neutron-induced
spectrum in the background. These are the γ rays from
the 2223-keV p(n, γ)d and the 4.4-MeV γ rays originat-
ing from the (α,n) reaction of the AmBe source itself.
Although only ≈ 10% of these AmBe γ rays penetrate
the 5-cm Pb shield, there is still a significant flux.
A simple simulation of the detector response to 2223-
keV γ rays can easily determine ratio of the rate in the
2039-keV region to that in the full-energy peak. Simula-
tion indicates that this ratio is 5.2 × 10−2 /keV. Since
the full-energy peak count rate is 5.813 Hz, we find this
contribution to the continuum is 0.03 events/(keV s). For
the 4.4-MeV γ ray from the source itself, simulation must
determine an absolute rate in the continuum because the
high-energy threshold prevented the observation of the
full-energy peak or its escape peaks. The simulation pre-
dicts 0.03 events/(keV s). Subtracting these two contri-
butions from the continuum rate for the AmBe source
near 2039 keV results in a final value of 0.03 events/(keV
s) or 860 events/(keV kg d).
Our background measurements were done without a
cosmic ray anti-coincidence system. From auxiliary mea-
surements with a scintillator in coincidence with the
CLOVER and a similar shielding geometry, we measured
the rate of µ passing through the detector. In the contin-
uum near the 2039-keV region, the rate is 5.4 events/(keV
kg d).
From the Th-wire source data, we measure the ratio
TABLE IV: A summary of the count rate in the CLOVER
background data in the energy region near 2039 keV based
on the model deduced for the surface lab described in the
text. The precision of the neutron-induced and muon-induced
spectra simulations (Section IIC and Ref [10]) is estimated to
be about 35%. We take this to be a conservative estimate for
the uncertainties associated with this Table.
Process CLOVER Event Rate
Surface Lab
events/(keV kg d)
neutron-induced 8.3±2.9
208Tl Compton scattering 0.7±0.3
high energy µ continuum 5.4±1.9
Total from model 14.4±5.0
Measured Rate 14.8±0.2
of the rate in the continuum near 2039 keV to that in
the 2614 keV (16.3 Hz) peak to be 6 × 10−3/keV. Of
the 2614-keV peak rate in the background data, ≈ 33%
is due to 208Tl decay. Scaling from the 2614-keV peak in
the background data, the count rate near the 2039-keV
region due to the Compton tail of the 208Tl 2614-keV
peak is 0.7 events/(keV kg d).
The remainder of the 2614-keV peak is due to neutron-
induced processes. The contribution due to neutrons can
be estimated from the AmBe data. For the AmBe data,
the ratio of the rate in the continuum near the 2039-
keV region (0.03 events(keV s)) to that for the 596-keV
74Ge(n, n′γ) peak (1.87 Hz) is 1.6 × 10−2/keV. Scaling
from the 74Ge peak rate in the background data (59.9/h)
indicates a rate of 7.8 events/(keV kg d) in the contin-
uum near 2039 keV. That is, 53% of the events in that
region are due to neutrons. One can do a similar scal-
ing from the 692-keV 72Ge rates. Here the ratio is 1.3 ×
10−2/keV and the continuum rate is 8.8 events/(keV kg
d). We use the average of the Ge values as our estimate
(8.3 events/(keV kg d) = 3030 events/(keV kg y)) for
the neutron induced contribution to the continuum rate.
Table IV summarizes the deduced contributions to the
spectrum in the 2039-keV region in the CLOVER back-
ground spectrum and the following section discusses how
these data are used along with simulation to estimate
rates in experimental apparatus underground.
B. Solving the Problem with Overburden
The primary purpose of this study is to better under-
stand the impact of neutrons on the background for fu-
ture double-beta decay experiments. In this subsection,
we use neutron fluxes from our simulations of the surface
laboratory, measurements with the AmBe source, and
simulations of the neutron flux in an underground lab-
oratory to estimate the contribution of neutron-induced
backgrounds underground. In the following subsection,
we examine data from previous underground experi-
ments.
The simulation of neutron processes in the 10-cm
Pb shield and Ge comprising the CLOVER detector at
the altitude of our laboratory predicts about 1594±558
events/(keV kg y) between 2000 and 2100 keV due to lead
excitation and about 1337±468 events/(keV kg y) in this
energy region due to germanium excitation. Our mea-
sured value for the neutron-induced events is 3030±1061
events/(keV kg y) to be compared with this predicted
value of 2931±1026 events/(keV kg y).
The simulation of the CLOVER within a 30-cm
lead shield at a depth of 3200 mwe, predicts about
0.019±0.007 events/(keV kg y) contributed from lead
excitation and about 0.016±0.006 events/(keV kg y)
contributed from germanium excitation for a total of
0.035±0.012 events/(keV kg y). One can also just
scale our surface-laboratory measurement of the neutron-
induced rate near 2039 keV by the factor derived from
Eqn. 4 above. This results in 0.05±0.02 events/(keV
kg y). For a detector like the CLOVER, analysis based
on pulse shape discrimination (PSD), and the response
of individual segments or crystals can help reduce back-
ground based on its multiple-site energy deposit nature.
These backgrounds can then be distinguished from the
single-site energy deposit character of double-beta decay.
We have measured the background reduction factor via
these techniques to be ≈ 5.9 for the CLOVER [12].
Reference [10] provides a quick reference formula to
estimate the neutron flux as a function of depth. The
µ flux and its associated activity is reduced by ≈ 10 for
each 1500 m.w.e of added depth. Future double-beta
decay experiments hope to reach backgrounds near 0.25
events/(keV t y). Our estimate of the rate at 3200 mwe
is 35-50 events/(keV t y), which is a factor of 150 above
the goal. Hence, greater depths would be desirable.
C. Discussion of Previous Underground
Experiments
Previous Ge-based double-beta decay experiments con-
ducted deep underground [5, 6] set the standard for low
levels of background. The future proposals however [8, 9]
hope to build experiments with much lower backgrounds.
In this subsection, we estimate how large the neutron
contribution was to the previous efforts and future de-
signs. Using the scaling summarized in Eqn. 4, we can
compare the expectations of our simulated underground
apparatus with previously published results. Table V
shows this comparison. This table also presents a sum-
mary of how the rates would be affected by a change in
depth only. The IGEX collaboration [5] has not pub-
lished its data in sufficient detail to do a similar com-
parison. Other underground Ge detector experiments do
not have the required sensitivity.
The Heidelberg-Moscow experiment [6] is a critical
case study for such backgrounds and it was operated at
TABLE V: A summary of the key count rates arising from neutron interactions in the CLOVER background data in the energy
region near 2039 keV as predicted by our analysis for three representative depths. The shield thickness is taken to be 30 cm
and a veto system with an assumed efficiency of 90% is included. Except for the 2023-keV line, we used the scaling of Eqn. 4 to
scale our CLOVER background measurements to the 3200 mwe depth and then used the muon fluxes at WIPP, Gran Sasso, and
SNOLAB[10] to scale to the other depths. The Ge rates are also scaled for an enriched detector (86% isotope 76, 14% isotope
74). The scalings require the results from the simulations. The uncertainty is dominated by the simulated flux uncertainty
and is estimated to be 35%. Since we did not observe the 2023-keV line, we used simulation to predict the rate. We used the
measured upper limit for the 2041-keV line. For comparison, the results of Ref. [37] is shown. Reference [37] claims a result for
zero-neutrino double-beta decay in an experiment performed at 3200 mwe. We entered the claimed event rate for that process
in the same row as the 2041-keV line for comparison. The rate limits for the other lines assigned to Ref.[37] result from our
estimates based on the figures in their papers and does not come directly from their papers.
Process 1600 mwe 3200 mwe 6000 mwe Ref. [37]
74Ge 596 keV 19400±6800/(t y) 1130±400/(t y) 15±5/(t y) <800/(t y)
76Ge 2023 keV 30±10/(t y) 2±1/(t y) 0.02±0.01/(t y) 300/(t y)
206Pb 537 keV 4400±1500/(t y) 250±88/(t y) 3.4±1.2/(t y)
207Pb 898 keV 5300±1900/(t y) 310±110/(t y) 4.2±1.5/(t y)
206Pb 1705 keV 610±210/(t y) 36±13/(t y) 0.5±0.2/(t y)
206Pb 2041 keV <1300±450/(t y) <74±26/(t y) <1.0±0.3/(t y) 400/(t y)
207Pb 3062 keV 145±51/(t y) 8.4±2.9/(t y) 0.1±0.03/(t y) <71/(t y)
continuum 880±310/(keV t y) 50±17/(keV t y) 0.7±0.24/(keV t y) 110/(keV t y)
a depth of 3200 mwe. One is clearly led to consider if
the 3062-keV γ ray can explain the signal reported in
Ref. [36, 37]. Figure 36 in Ref. [37], shows that no more
than a few counts can be assigned to a 3062-keV γ ray. If
the 23 counts assigned to double-beta decay were actually
a DEP from this γ ray, the one would expect 175 counts
or so in the 3062-keV peak. Therefore, it is difficult to
explain the claimed peak by this mechanism. It is also
clear that the predicted rate of the 2041-keV γ ray is too
low to explain their data. The data from Ref. [37] show
lines at 570 and 1064 keV and the authors assigned these
lines to 207Bi present in the Cu. However, the spectra dis-
played in Fig. 13 of that paper shows that only detectors
surrounded by Pb indicate the 570-keV line. Since there
is no evidence for the 898-keV line in the data, we agree
with the 207Bi assignment, however, we hypothesize that
it must reside in the Pb and not the Cu. Perhaps this
contamination is cosmogenically produced in Pb when it
resides on the surface and not as a result of bomb testing
as hypothesized by the authors[37].
Reference [37] also observed lines at 2011, 2017, 2022,
and 2053 keV. These lines had rates of approximately
500/(t y), 500/(t y), 300/(t y) and 380/(t y) respectively.
The line at 2022 keV is near a line we predict at 2023 keV.
Reference [37] attributes these lines to weak transitions
in 214Bi. From our analysis it is indicated that a negligi-
ble fraction of the peak at 2023 keV is neutron-induced.
However, since the predicted strength of the tell-tale lines
that would indicate a presence of neutron interactions is
just below the sensitivity of that experiment, this conclu-
sion is not without uncertainty. It has been pointed out
that the strength in the 2022-keV line is too strong with
respect to the 214Bi branching ratios even when sum-
ming uncertainties are taken into account [38, 39]. The
analysis in Ref. [38], however, was based on a incorrectly
normalized Fig. 1 in Ref [6]. A recent analysis [39] tak-
ing this into account still points to an inconsistency in
the line strengths. This discrepancy could be resolved if
one attributes a significant fraction of that peak to neu-
tron interactions on 76Ge. Such an attribution is not
supported by our simulations.
Reference [36] simulates the background in the
Heidelberg-Moscow experiment resulting in a predicted
signal of 646 ± 93 counts in the region between 2000 and
2100 keV during an exposure of 49.6 kg-y. This is a count
rate of 130/(keV t y) to be compared with the quoted
measured value for the data period simulated of 160/(keV
t y). Their estimate indicates that only 0.2/(keV t y) are
due to neutrons and they argue that µ-generated neu-
trons are a negligible contribution. Our estimates indi-
cate that neutrons are a more significant contribution and
that the µ contribution is significant. We are aware of no
direct neutron flux measurements for neutrons above 25
MeV. The flux of neutrons with energy greater than 25
MeV is estimated in Ref. [36] to be 10−11/(cm2 s) and
they considered these neutrons to produce a negligible
contribution to the background. In contrast, the simula-
tion in Ref. [10] gives 56 × 10−11/(cm2 s) at 3200 m.w.e
for the neutrons with energy greater than 25 MeV. We
use this higher flux value and as a result, our estimate
of the background rate near 2 MeV of 50/(keV t y) is
comparable to the excess (30/(keV t y)) of the measured
rate in comparison to the simulated rate in Ref. [36].
D. Is Copper an Alternative to Lead?
One has to consider the existence of a DEP line at the
double-beta decay endpoint a serious design considera-
tion for Ge-detector experiments. From the above anal-
ysis, the dangerous lines at 2041 and 3062 keV due to
Pb(n, n′γ) are not significant contributors to the spec-
trum of Ref. [37]. However, as future efforts reduce
the natural activity irradiating the detectors, these Pb-
neutron interactions will become important. One solu-
tion could be the use of Cu as a shield instead of Pb.
Copper is rather expensive and building the entire shield
of this material is probably not necessary. A thick inner
liner of Cu might suffice, but if a peak is observed and
Pb is present near the detector, arguments based on the
spectrum near 3062 keV will be critical.
Although the problematic lines we observed in the Pb
data were absent in our Cu data, the shields were too
dissimilar to make a quantitative comparison regarding
the effectiveness of reducing the continuum background.
Furthermore, our experience with the lead and the sim-
ulation of (n, n′γ) spectra reduces confidence in the con-
clusion regarding the Cu in the absence of such data. We
are preparing better experimental studies to address this
question.
VI. CONCLUSION
As double-beta decay experiments become more sen-
sitive, the potential background must be constrained to
ever-lower levels. Much progress has been made in reduc-
ing naturally-occurring radioactive isotopes from mate-
rials from which the detector is constructed. As these
isotopes that have traditionally limited the experimen-
tal sensitivity are eliminated, rarer processes will become
the dominant contributors. Here we have considered
neutron-induced processes and have quantified them. Re-
actions involving neutrons can result in a wide variety of
contributions to the background. That is, no single com-
ponent is likely to dominate. Therefore, tell-tale signa-
tures for neutrons are needed and were identified in this
work.
In addition to the general continuum background
that neutrons might produce, two specific dangerous
Pb(n, n′γ) lines were identified. These two backgrounds
can be significantly reduced using depth and/or an inner
layer of Cu within the shield. In particular, the 3062-
keV transition in 207Pb has a double escape peak at the
endpoint energy for double-beta decay in 76Ge. A com-
parison of past double-beta decay data indicates the rate
of this transition is too small to explain a claim of double-
beta decay.
VII. ACKNOWLEDGMENT
We thank R.L. Brodzinski for discussions regarding the
historical production of 207Bi and its possible presence in
the environment. We thank John Wilkerson and Jason
Detwiler for useful suggestions and discussion. Finally,
we also thank Alan Poon and Werner Tornow for use-
ful discussions and a careful reading of the manuscript.
This work was supported in part by Laboratory Directed
Research and Development at Los Alamos National Lab-
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