# Development of a low-background neutron detector array

Y. T. Li  W. P. Lin<EMAIL_ADDRESS>B. Gao<EMAIL_ADDRESS>H. Chen
H. Huang  Y. Huang  T. Y. Jiao  K. A. Li  X. D. Tang  X. Y. Wang  X. Fang  H.
X. Huang  J. Ren  L. H. Ru  X. C. Ruan  N. T. Zhang  Z. C. Zhang  CAS Key
Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern
Physics, Chinese Academy of Sciences, Lanzhou 730000, China  School of Nuclear
Science and Technology, University of Chinese Academy of Sciences, Beijing
100049, China  Key Laboratory of Radiation Physics and Technology of the
Ministry of Education, Institute of Nuclear Science and Technology, Sichuan
University, Chengdu 610064, China  Joint Department for Nuclear Physics,
Lanzhou University and Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  China Institute of Atomic Energy, Beijing
102413, People’s Republic of China  Sino-French Institute of Nuclear
Engineering and Technology, Sun Yat-sen University, Zhuhai, Guangdong 519082,
People’s Republic of China

###### Abstract

A low-background neutron detector array was developed to measure the cross
section of the 13C($\alpha$,n)16O reaction, which is the neutron source for
the $s$-process in AGB stars, in the Gamow window ($E_{c.m.}$ = 190 $\pm$ 40
keV) at the China Jinping Underground Laboratory (CJPL). The detector array
consists of 24 3He proportional counters embedded in a polyethylene cube. Due
to the deep underground location and a borated polyethylene shield around the
detector array, a low background of 4.5(2)/hour was achieved. The 51V(p,
n)51Cr reaction was used to determine the neutron detection efficiency of the
array for neutrons with energy $E_{n}$ $<$ 1 MeV. Geant4 simulations, which
were shown to well reproduce experimental results, were used to extrapolate
the detection efficiency to higher energies for neutrons emitted in the
13C($\alpha$,n) 16O reaction. The theoretical angular distributions of the
13C($\alpha$,n)16O reaction were shown to be important in estimating the
uncertainties of the detection efficiency.

###### keywords:

Underground laboratory , Neutron detector , Low background , 3He Counter

††journal: Nuclear Instruments and Methods in Physics Research Section A

##  1 Introduction

The 13C($\alpha$,n)16O reaction is the dominant neutron source for the slow
neutron capture process (s-process), which synthesized roughly half of the
elements heavier than iron in the Universe [1]. The main site of the s-process
is the “He intershell” of asymptotic giant branch (AGB) stars where the
temperature is 0.1 GK. This corresponds to a Gamow window of 190 $\pm$ 40 keV
for the 13C($\alpha$,n)16O reaction, which is far below the Coulomb barrier.
Theoretical calculations predicted the cross section as low as
$\sim$$10^{-14}$ barn at 190 keV [2, 3]. Meanwhile, the 13C($\alpha$,n)16O
reaction is also the main neutron source for the intermediate neutron capture
process (i-process) with a typical temperature 0.2 GK [4, 5]. A reliable
direct measurement is still missing within the corresponding energy range from
0.2 to 0.54 MeV. To push direct measurements of the cross section towards the
Gamow window, high-intensity beams and low-background neutron detector array
are indispensable.

Present measurements performed at ground laboratories are limited by the
cosmic-ray-induced background. With a typical background counting rate of a
few hundred per hour (e.g. [6, 7]), those measurements only reached a lower
limit of $E_{\alpha}$ $\sim$ 400 keV with a cross section of $\sim$ $10^{-10}$
barn. The China JinPing underground Laboratory (CJPL) [8] with about 2400 m
rock overburden (6700 m water equivalent) shields against most of the cosmic
rays and therefore the backgrounds are much lower comparing to ground
laboratories. The Jinping Underground Nuclear Astrophysics experimental
facility (JUNA) [9, 10] has been initiated to measure important stellar
nuclear reaction rates, taking advantage of the low-background environments in
CJPL. The present JUNA project includes 12C($\alpha$,$\gamma$)16O,
13C($\alpha$,n)16O, 19F(p,$\gamma$)20Ne and 25Mg(p, $\gamma$)26Al reactions
[9, 10]. A high-intensity accelerator capable of delivering proton and
$\alpha$ beams up to 10 mA in the energy range of 0.05 - 0.4 MeV has been
built for JUNA [9]. This made it possible to measure the 13C($\alpha$,n)16O
cross section at the region of the s-process Gamow window if combined with a
high-efficiency and low-background neutron detection system.

This paper describes the development and characterization of a low-background
neutron detector array for the cross section measurement of the 13C($\alpha$,
n)16O reaction.

##  2 Design of the detector array

The detector array consists of 24 3He-filled proportional counters
(manufactured by GE-Reuter Stokes) embedded in a 50 $\times$ 50 $\times$ 50
cm3 polyethylene cube. Each proportional counter is filled with 3He and argon
gases, with pressures of 4 bar and 2.4 bar, respectively. The active length of
each counter is 30 cm with a diameter of 2.54 cm. The sketch of the detector
array is shown in Fig. 1. The 24 proportional counters are evenly distributed
in two concentric rings with radius of $R_{1}$ = 8.5 cm and $R_{2}$ = 13 cm,
respectively. The radius of the two rings were optimized using Geant4
simulations, following the same procedure as that in [11], to get the maximum
detection efficiency for 2.0-MeV isotropic neutrons. A central bore hole with
a diameter of 10 cm was created to accommodate the beam line and the target.

Figure 1: (Color online) Schematic view of the detector array. In panel (a),
the borated polyethylene shield (black brick), positions of the 3He counters
(red tubes) and the central bore hole are indicated. Traces of two neutron
events are also shown as green curves. In panel (b), a three-dimensional view
of the detector array is presented.

Neutrons from the 13C($\alpha$, n)16O reaction with energies of 2 - 3 MeV are
first moderated by the polyethylene cube and then captured by the proportional
counters. To shield against environmental neutrons, the polyethylene cube is
wrapped with a 5 cm-thick 7% borated polyethylene layer.

Figure 2: (Color online) (a) Typical energy spectrum measured by the detector.
A cut as shown in panel (b) was applied to select the neutrons (see text). The
dashed lines indicate the regions of interest between 0.64 - 0.8 MeV. The
inset shows an energy spectrum in wider energy range without cuts. (b) Raise
time versus energy two-dimensional plot measured by the detector array. The
$\beta$/$\gamma$-, neutron & alpha- and alpha-regions are indicated in the
plot.

The signal of each detector is processed by a charge-sensitive pre-amplifier
(model CAEN A1422). The output waveforms are digitized and recorded by a XIA
Pixie-16 100 MHz card. Fig. 2 (a) shows a typical energy spectrum measured by
the detector array. The peak at 0.76 MeV corresponds to full-energy events
where the triton and proton produced from the 3He + $n$ $\rightarrow$ $p$ \+
$t$ reaction deposit all their kinetic energies in the sensitive region of the
counter. If the proton or triton hits the wall of the detector before
depositing all their kinetic energies in the sensitive region, the detector
records only part of the reaction $Q$ value. Those are wall-effect events
which correspond to the flat region with lower energies starting from 0.18 MeV
in the spectrum. The argon gas filled in the proportional counters has little
effect on the neutron detection efficiency but can significantly decrease the
track lengths of the produced proton and triton, and therefore reduce the wall
effect. By defining a region of interest around the full energy peak between
0.64 - 0.8 MeV (ROI) as indicated in Fig. 2 (a), we find 81.0$\pm$0.4% of the
detected events are located in it.

##  3 Background measurements

Stainless steel is chosen as the wall material of the proportional counters
because it has much lower $\alpha$ emission rate comparing to aluminum [12,
13]. The inset in Fig. 2 (a) shows an energy spectrum up to 7 MeV. The events
located beyond the neutron full-energy peak are mainly due to $\alpha$
radioactivity from the wall material of the counters. The $\alpha$ spectrum
has a relatively flat distribution below $\sim$ 3 MeV and shows a peak at 5
MeV, a typical energy of $\alpha$ decays from U/Th nuclides. Below 0.3 MeV
energy region, lots of $\gamma$/$\beta$ events exist, overlapping with the
neutron events. Following the procedure described in Ref. [12], the
$\beta/\gamma$ events can be well separated from neutrons in the raise time
versus energy two-dimensional plot as shown in Fig. 2 (b).

To characterize the background of the detector array, ground- and underground-
measurements were performed at the China Institute of Atomic Energy and the A1
hall of the CJPL, respectively. The neutron events were selected by using the
“neutron & alpha” cut from the raise time versus energy two-dimensional plot
as shown in Fig. 2 (b). Such events also include contributions from $\alpha$
background. To disentangle the $\alpha$ backgrounds from the “neutron & alpha”
events, a flat $\alpha$ energy spectrum is assumed [12, 13] in the energy
range 0.18 - 2.0 MeV. The total background inside the ”neutron & alpha” cut as
shown in Fig. 2 (b) measured at CJPL for the whole array is 4.5(2)/hour, of
which 1.94(5)/hour is from $\alpha$ background. The above $\alpha$ background
is evaluated using the $\alpha$ counts in the energy range 1.0 - 2.0 MeV which
was assumed to have the same $\alpha$ emission rate as 0.18 - 0.8 MeV. This
assumption was verified using a 4He proportional counter which will be
discussed below. The total background is more than two orders of magnitude
lower than the result of 1238(11)/hour obtained from ground-measurement.

A 4He counter, which has exactly the same parameters as the 3He counters but
filled with 4He gas instead of 3He, manufactured by the same supplier was used
to investigate the $\alpha$ background in more detail. The 4He counter is
insensitive to neutrons but expected to have similar $\alpha$ background shape
as the 3He counters. The $\alpha$ background rate, with 28.9-hour measurement
time in CJPL, was found to be 4.24 $\pm$ 0.48 and 4.22 $\pm$ 0.38 MeV-1hour-1,
in 0.18 - 0.8 and 1.0 - 2.0 MeV energy regions, respectively. This justifies
that the two energy regions have indeed the same $\alpha$ emission rates.
However, we found an $\alpha$ emission rate of 2.63(30)/hour by using the same
neutron cut as the 3He counters in the raise time versus energy plot. This is
about a factor of 30 higher than the 3He counters. Note that the $\alpha$
emission rate of 1.94(5)/hour quoted above includes the background of the 24
3He counters while the 2.63(30)/hour is only for one 4He counter. This implies
that the $\alpha$ background could differ significantly even for the same type
of wall material. This has to be carefully investigated at the manufacturing
stage in order to achieve low $\alpha$ background.

To further reduce the $\alpha$ background, one can choose the events within
the ROI only [see Fig. 2 (a)]. As a result, the $\alpha$ background is reduced
by 74% at the cost of losing only about 19% of the neutron detection
efficiency. This corresponds to a background of 2.5(1)/hour, of which
0.50(1)/hour is from $\alpha$ background. A better approach for
$\alpha$-background suppression is to use plastic scintillator as the
moderator, where most of the $\alpha$ background can be eliminated via
coincident measurements [14]. The $\alpha$ background is intrinsic properties
of the proportional counters used in the array which does not change with
environments. However, the neutron background may change with different
environments and therefore should be characterized for each use.

##  4 Efficiency calibration

###  4.1 51V(p, n)51Cr Experiment and simulation

Detection efficiency of the array was calibrated at the nuclear physics
experiment (NPE) terminal of the 3-MV tandetron accelerator [15] at Sichuan
university. Quasi Mono-energetic neutrons were produced using the 51V(p,
n)51Cr reaction (Q = -1534.8 keV) at incident energies between 1.7 and 2.6 MeV
with a step of 0.15 MeV. The 51V(p, n)51Cr reaction is widely used in the
calibration of neutron detectors [16, 17, 18, 19, 20, 21] for its slow
variation of neutron intensity and energy with angle, and the well-known
target preparation and utilization. Fig. 3 shows the emitted neutron energy as
a function of incident proton beam energy. When the incident energy is above
2.33 MeV, neutrons from transitions feeding the first excited state of 51Cr
($E_{x}=$ 749 keV) are mixed with those feeding the ground state. However, as
pointed out in Ref. [16], the contribution from transitions to the first
excited state is negligible for incident energies up to 2.6 MeV [17], which
was also confirmed in the present work (see discussions in the following
sections). The proton beams were focused at the target with a diameter of less
than 5 mm (full width at half maximum). The beam spots were monitored by a
fluorescent target together with a beam position monitor located 1.5 m
upstream the target for each beam energy.

Figure 3:  The emitted neutron energies from the 51V(p,n)51Cr reaction as a
function of proton beam energies. The height of the bars represents the energy
spread of the emitted neutrons. The two components of the neutron energies at
$E_{p}$ = 2.45 and 2.6 MeV correspond to transitions feeding the ground and
the first-excited states of 51Cr.

Vanadium targets with a thickness of 110 $\mu g/cm^{2}$ were used in the
measurements. They were produced by evaporating natural vanadium on 1-mm thick
tantalum disks with a diameter of 30 mm. The target thickness corresponds to
an energy loss of 8$\sim$11 keV for proton beams with energies of 1.7 - 2.6
MeV. The beam intensity varied from 4 $\mu$A to 120 nA as the beam energy
increased from 1.7 to 2.6 MeV, making the counting rate of the detector array
stay around $10^{4}$/s with a dead time being less than 1% for all beam
energies. A direct water cooling of the reaction target was used to reduce the
sputtering and target loss. The possible contribution of beam induced
background was investigated with a blank tantalum target at the beam energy of
2.0 MeV. The background contribution was found to be less than 1%.

The total number of emitted neutrons was determined based on the activation
method as described in Ref. [16]. The number of radioactive product 51Cr
equals to the number of emitted neutrons in the reaction. 51Cr decays by
electron capture with a half-life of $T_{1/2}$ = 27.7025(24) days and has a
branching ratio of $B$ = 9.91(1)% to decay to the first excited state of its
daughter nuclei 51V, which is followed by the emission of a 320-keV $\gamma$
ray. The off-line measurement of this $\gamma$ ray was carried out with a GEM
series HPGe detector whose relative efficiency is 30%. The absolute efficiency
of the HPGe detector was measured at a distance of 20 cm using 137Cs
[1.534(19)$\times$105 Bq] and 152Eu [5.72(6)$\times 10^{4}$ Bq] $\gamma$-ray
sources. The distance of 20 cm is large enough to avoid pileups of cascading
$\gamma$ rays from the sources. A 51Cr $\gamma$ source was produced by the
51V(p, n)51Cr reaction. Its activity was measured at the position of 20 cm and
then used to determine the efficiency for the 320-keV $\gamma$ line at the
position of 10.2 cm ($\eta_{320}$), where all the irradiated targets were
placed for off-line measurements. $\eta_{320}$ was determined to be 0.498(7)%
at 10.2 cm. As beam current was stable within the irradiation time, the number
of emitted neutrons was then determined by the off-line measurement of the 320
keV $\gamma$ ray with the activation formula [16]

$N_{R}=\frac{N_{\gamma}}{B\cdot\eta_{320}}\cdot\frac{e^{\lambda
t_{w}}}{1-e^{-\lambda t_{c}}}\cdot\frac{\lambda\cdot t_{i}}{1-e^{-\lambda
t_{i}}},$ (1)

where $N_{\gamma}$, $t_{i}$, $t_{c}$ and $t_{w}$ are the number of detected
320-keV $\gamma$ rays, the activation time, the counting time, and the waiting
time elapsed between the end of irradiation and the start of the counting.
$\lambda$ = ln(2)/$T_{1/2}$ is the decay constant of 51Cr. After dead time
correction, the detection efficiency of the neutron detector is calculated as

$\eta_{n}=\frac{N_{n}}{N_{R}},$ (2)

where $N_{n}$ is the detected number of neutrons by the detector array.

Since the energy of the neutrons emitted in the 51V(p, n)51Cr reaction is only
up to $\sim$1 MeV, it is still far below that from 13C($\alpha$, n)16O
reaction. The Monte Carlo simulation code Geant4 [22, 23] of version 10.4.2
was used to determine the neutron detection efficiency at neutron energies
above 1 MeV. The detailed detector setup used the simulation is shown in Fig.
4. The beam pipe, target backing and water cooling loops were included in the
simulation, which resembles the real physical setups. An overestimation of the
neutron detection efficiency was obtained from the simulation compared to the
experimental results. Similar overestimations have also been observed in
several other setups [16, 18]. This overestimation is interpreted as that some
of the neutrons are absorbed by small contaminants in the moderating
polyethylene. Instead of using a normalization factor, we added a small amount
of boron into the moderating polyethylene in the simulation to take into
account the neutron absorption effects. Fig. 5 (a) shows the reduced
$\chi^{2}$, obtained by comparing the simulated and measured detection
efficiencies, as a function of boron mass fraction. The minimum of $\chi^{2}$
was found at the boron mass fraction of 0.060% by fitting the curve using a
parabola. The simulated total, inner ring and outer ring detection
efficiencies are shown in Fig. 5 (b) .

Figure 4: (Color online) The detector setup used in the simulations for the
51V(p, n)51Cr reaction.

The boron contaminant affects not only the total efficiency, but also the
ratio $R_{in/out}$ of the detection efficiencies of the inner and the outer
ring detectors. With the boron mass fraction obtained above, the measured
ratio $R_{in/out}$ is also well reproduced by the simulation (see Fig. 5 (c)).
Except for the first point, the simulation results are 3%-4.5% lower than that
of the experiment at $E_{p}<$ 2.4 MeV. For $E_{p}$ = 2.45 and 2.6 MeV, the
discrepancy between the simulated and measured $R_{in/out}$ ratios starts to
increase to 4.0% and 7.5%, respectively. This is due to the opening of the
decay channel to the first excited state in 51Cr (see Fig. 3), the effect of
which on the total detection efficiency have been evaluated for $E_{p}$ = 2.6
MeV in the following way. The contribution of the decay channel to the first
excited state can be obtained from the deviation of the measured $R_{in/out}$
from the general trend of the simulated curve. Then we obtained the total
detection efficiencies from our simulation by both considering and not
considering the contributions from the decay channel to the first excited
state, resulting in a difference of only 2.6% in the total detection
efficiencies. The contributions from the decay channel to the first excited
state is negligibly small regarding the total detection efficiency though its
effects on the $R_{in/out}$ is larger. The total, inner ring and outer ring
detection efficiencies for mono-energetic neutrons up to 3 MeV with an
isotropic angular distribution were also simulated and shown in Fig. 5 (d).

Figure 5: (Color online) (a) The reduced $\chi^{2}$, obtained by comparing the
simulated and measured total detection efficiencies, as a function of boron
mass fraction. The curve is a parabola fitting of the reduced $\chi^{2}$. (b)
Measured and simulated total, inner ring and outer ring detection efficiencies
as a function of proton beam energy in the 51V(p, n)51Cr reaction. (c)
Measured and simulated inner-to-outer-ring ratios $R_{in/out}$ at different
proton beam energies. (d) Simulated total, inner ring and outer ring detection
efficiencies for mono-energetic neutrons with an isotropic angular
distribution.  Figure 6: (Color online) Detection efficiencies of the total
(solid squares), the inner ring (solid circles) and the outer ring (solid
triangles) detectors as a function of the target position. The statistical
errors are smaller than the symbol size. Solid, dashed and long dashed curves
are those from the Geant4 simulations.

The dependence of detection efficiency on the source position was measured by
placing the detector array at different positions along the beam line ($Z$
axis) using the 51V(p, n)51Cr reaction at $E_{p}$ = 2 MeV. The position $Z$ =
0 corresponds to the target being at the center of the array. Moving the
detector array forward in the beam direction corresponds to positive $Z$
values and backward corresponds to negative $Z$ values. The relative
efficiencies at different positions were normalized using integrated incident
beam currents on the target. The results for the total, inner ring and outer
ring detectors are shown in Fig. 6 together with the Geant4 simulations. In
Fig. 6, the measured total efficiency at $Z$ = 0 was normalized to the
simulated value. Overall good agreements were found between the measurements
and the simulations.

Taking into account all the above experimental data, the difference between
the simulations and the experiment results is 3%, which reflects one of the
systematic uncertainties of our simulation.

###  4.2 Extrapolating the detection efficiency for the study of the
13C($\alpha$, n)16O reaction at stellar energies

It should be noted that the simulated efficiency in Fig. 5 cannot be directly
applied to the 13C($\alpha$, n)16O reaction in which the emitted neutrons are
neither mono-energetic nor isotropic. The asymmetry in the efficiency curve
shown in Fig. 6 indicates that the simulation predicts a slightly higher
detection efficiency for neutrons emitted at backward angles than that at
forward angles. Since the angular distribution of the 13C($\alpha$, n)16O
reaction is not measured at low energies close to the Gamow window,
theoretically predicted angular distributions were used in our simulations.
Legendre polynomials up to the third order were used in calculating the
angular distributions.Fig. 7 shows the Legendre polynomials coefficient
$\alpha_{1}$ used in the angular distributions of the 13C($\alpha$, n)16O
reaction as a function of beam energies in (a) and the representative angular
distributions obtained at beam energies of 0.2, 0.7, 1.048 and 1.2 MeV in (b).
Adopting the angular distributions in Refs. [24, 25], the angular distribution
effect on the efficiencies is corrected in our Geant4 simulations.

Figure 7: (Color online) (a) Legendre polynomials coefficient $\alpha_{1}$
used in the angular distributions of the 13C($\alpha$, n)16O reaction as a
function of beam energies. The red curve is from Paris/Hale ENDF-8 [Bro18] and
the black dots are from Ref [24]. (b) Representative angular distributions
obtained at beam energies of 0.2, 0.7, 1.048 and 1.2 MeV. Figure 8: (Color
online) (a) Simulated detection efficiencies using isotropic (red solid line)
and theoretically predicted (blue dashed line) angular distributions. (b)
Simulated ratios $R_{in/out}$ using both isotropic (red solid line) and
theoretically predicted (blue dashed line) angular distributions. Solid
triangles are the measured $R_{in/out}$ from Ref. [26].

Detection efficiencies were simulated using both isotropic and calculated
angular distributions in the incident $\alpha$ energies between 0.2-1.6 MeV.
In the simulation, the narrow resonances are ignored. Fig. 8 (a) shows
simulated efficiencies using isotropic and calculated angular distributions.
For $\alpha$ energies between 0.3-0.8 MeV, the difference is 0.6% - 2% which
is relatively small. However, above 0.8 MeV, the difference becomes larger
with a maximum of 7%. To evaluate the effect for the sharp resonance, we also
simulated the detection efficiency at the energy where the $a_{1}$ coefficient
reaches its maximum around E = 1.048 MeV, as shown in Fig. 7 (a). The
resulting efficiency is 13% less than the efficiency with an isotropic
isotropic angular distribution. Therefore, the angular distribution effect
needs to be evaluated carefully for the experiments aiming to a high
precision.

The effects of the angular distributions were further investigated by
comparing the simulated and measured ratios of the inner ring and outer ring
detection efficiencies $R_{in/out}$. As shown in Fig. 8 (b), the $R_{in/out}$
is insensitive to the angular distribution and the simulations in both case
agree reasonably well with the measured values from Ref. [26]. The difference
between measured and simulated $R_{in/out}$ values is $\sim$ 4%. An
alternative way of extrapolating the total detection efficiency was carried
out as follows. The inner-ring detection efficiency is extrapolated to the
neutron energy range relevant to the 13C($\alpha$, n)16O reaction. Then the
total detection efficiency is obtained using the measured $R_{in/out}$ values
from Ref. [26]. The difference in the total detection efficiency between the
two extrapolation methods is $\sim$ 2.5%, which is counted as another
systematic uncertainty.

Taking into account the uncertainties of the Geant4 simulations (3%), the
extrapolation (2.5%), the neutron angular distributions (2%) and the detection
efficiency of HPGe detector (1.5%), the overall uncertainty of the detection
efficiency for the 13C($\alpha$, n)16O reaction in the energy range
$E_{\alpha}$ = 300 - 800 keV is determined to be 5%.

##  5 Summary

A high-efficiency and low-background neutron detector array consisting of 24
3He proportional counters embedded in a polyethylene moderator has been
developed for the cross-section measurement of the 13C($\alpha$, n)16O
reaction at the China JinPing underground Laboratory. As a result of the deep
underground location and a 5-cm thick borated polyethylene shield, a low
background of 4.5(2)/hour was achieved, of which 1.94(5)/hour was from the
internal $\alpha$ radioactivity. The 51V(p, n)51Cr reaction was used to
calibrate the neutron detection efficiency of the array for neutrons with
energies $E_{n}$ $<$ 1 MeV. For $E_{n}$ $>$ 1 MeV, the Monte Carlo simulation
code Geant4 was used to extrapolate the detection efficiency. Specifically, an
energy dependent detection efficiency, which can be directly applied to the
13C($\alpha$, n)16O reaction, was obtained from the simulation. The effects of
the angular distribution of the 13C($\alpha$,n)16O reaction on the detection
efficiency, which were overlooked in previous works, were investigated in the
present work and shown to be non-negligible.

## Acknowledgments

The authors thank the staff of the 3MV tandetron accelerator facility of
Sichuan University for their support during the experiment. The authors also
thank the assistance of Carl Brune in estimating the corrections of the
neutron angular distribution. This work was supported by the National Natural
Science Foundation of China under Grants No. 11490564 and 11805138.

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