# Neutron capture measurement and resonance parameter analysis of ^natSm

X.X. Li (李鑫祥)  Shanghai Institute of Applied Physics, Chinese Academy of
Sciences, Shanghai 201800, China  University of Chinese Academy of Sciences,
Beijing 100049, China  L.X. Liu (刘龙祥)  Shanghai Advanced Research Institute,
Chinese Academy of Sciences, Shanghai 201210, China  Shanghai Institute of
Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China  W. Jiang
(蒋伟)  Institute of High Energy Physics, Chinese Academy of Sciences,
Beijing,100049,China  China Spallation Neutron Source, Dongguan, 523803, China
J. Ren (任杰)  China Institute of Atomic Energy, Beijing, 102413, China  H.W.
Wang (王宏伟)111Corresponding author<EMAIL_ADDRESS>Shanghai Advanced
Research Institute, Chinese Academy of Sciences, Shanghai 201210, China
Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai
201800, China  University of Chinese Academy of Sciences, Beijing 100049,
China  G.T. Fan (范功涛)222Corresponding author<EMAIL_ADDRESS>Shanghai
Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210,
China  Shanghai Institute of Applied Physics, Chinese Academy of Sciences,
Shanghai 201800, China  University of Chinese Academy of Sciences, Beijing
100049, China  J.J. He (何建军)  Key Laboratory of Beam Technology of Ministry of
Education, College of Nuclear Science and Technology, Beijing Normal
University, Beijing 100875, China  Institute of Radiation Technology, Beijing
Academy of Science and Technology, Beijing 100875, China  D.X. Wang (王德鑫)
College of Mathematics and Physics, Inner Mongolia Minzu University , Tongliao
028000,China  S.Y Zhang (张苏雅拉吐)  College of Mathematics and Physics, Inner
Mongolia Minzu University , Tongliao 028000,China  Z.D. An (安振东)  Shanghai
Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800,
China  Sun Yat-sen University, Zhuhai, 510275, China  X.G. Cao (曹喜光)  Shanghai
Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210,
China  Shanghai Institute of Applied Physics, Chinese Academy of Sciences,
Shanghai 201800, China  University of Chinese Academy of Sciences, Beijing
100049, China  L.L. Song (宋龙龙)  Shanghai Advanced Research Institute, Chinese
Academy of Sciences, Shanghai 201210, China  Y. Zhang (张岳)  Institute of High
Energy Physics, Chinese Academy of Sciences, Beijing,100049,China  China
Spallation Neutron Source, Dongguan, 523803, China  X.R. Hu (胡新荣)  Shanghai
Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800,
China  University of Chinese Academy of Sciences, Beijing 100049, China  Z.R.
Hao (郝子锐)  Shanghai Institute of Applied Physics, Chinese Academy of Sciences,
Shanghai 201800, China  University of Chinese Academy of Sciences, Beijing
100049, China  P. Kuang (匡攀)  Shanghai Institute of Applied Physics, Chinese
Academy of Sciences, Shanghai 201800, China  University of Chinese Academy of
Sciences, Beijing 100049, China  B. Jiang (姜炳)  Shanghai Institute of Applied
Physics, Chinese Academy of Sciences, Shanghai 201800, China  University of
Chinese Academy of Sciences, Beijing 100049, China  X.H. Wang (王小鹤)  Shanghai
Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800,
China  J.F. Hu (胡继峰)  Shanghai Institute of Applied Physics, Chinese Academy
of Sciences, Shanghai 201800, China  Y.D. Liu (刘应都)  Xiangtan University,
Xiangtan, 411105, China  X. Ma (麻旭)  Xiangtan University, Xiangtan, 411105,
China  C.W. Ma (马春旺)  Henan Normal University, Xinxiang, 453007, China  Y.T.
Wang (王玉廷)  Henan Normal University, Xinxiang, 453007, China  J. Su (苏俊)  Key
Laboratory of Beam Technology and Material Modification of Ministry of
Education, College of Nuclear Science and Technology, Beijing Normal
University, Beijing 100875, China  Beijing Radiation Center, Beijing 100875,
China  L.Y. Zhang (张立勇)  Key Laboratory of Beam Technology and Material
Modification of Ministry of Education, College of Nuclear Science and
Technology, Beijing Normal University, Beijing 100875, China  Beijing
Radiation Center, Beijing 100875, China  Y.X. Yang (杨宇萱)  Shanghai Institute
of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China  W.B.
Liu (刘文博)  Shanghai Institute of Applied Physics, Chinese Academy of Sciences,
Shanghai 201800, China  Henan Normal University, Xinxiang, 453007, China  W.Q.
Su (苏琬晴)  Shanghai Institute of Applied Physics, Chinese Academy of Sciences,
Shanghai 201800, China  Henan Normal University, Xinxiang, 453007, China  S.
Jin (金晟)  Shanghai Institute of Applied Physics, Chinese Academy of Sciences,
Shanghai 201800, China  University of Chinese Academy of Sciences, Beijing
100049, China  K.J. Chen (陈开杰)  Shanghai Institute of Applied Physics, Chinese
Academy of Sciences, Shanghai 201800, China  ShanghaiTech University, Shanghai
200120, China

###### Abstract

Multiple isotopes of samarium element are the isotopes produced by the $s$
process, and ^154Sm is produced by the $r$ process. In addition, ^144Sm is $p$
nuclei in nuclear astrophysics. The measurement of these can help us to better
understand the results of relevant photonuclear reaction experiments. On the
other hand, ^149Sm is a ^235U fission product with a $1\%$ yield, its cross
sections are important to reactor neutronics. In this work, the neutron
capture yield of the natural samarium target was measured at the back-
streaming white neutron beamline (Back-n) of the China Spallation Neutron
Source (CSNS), and the resonance parameters were analyzed by SAMMY code. The
resonance peaks and the neutron separation energies contributed by the
different isotopes are considered individually. The results of the capture
yield found signs of the possibility of two resonance peaks at 8 eV, which
awaits further experimental examination. Cross-section was calculated
according to resonance parameters and was compared with other experimental
results and evaluation databases of ENDF/B-VIII.0 and CENDL-3.2. A clear
difference between ENDF/B VIII.0 and CENDL-3.2 database appears at 23.2 eV,
the experimental result at this energy is smaller than data of ENDF/B VIII.0
database but CENDL-3.2 database. Most of the controversial experimental
results invariably come from the samarium 149 isotope.

##  I INTRODUCTION

The origin of heavy elements has always been a concern in physics. The
elements from carbon to iron can be well explained by the nuclear combustion
process of stars. However, these processes cannot produce nuclei with mass
number $A>64$ bib.01 . Neutron capture reaction is the main way to synthesize
elements heavier than iron, neutron capture processes in astrophysics include
the slow neutron capture process ($s$ process) bib.a1  and the rapid neutron
capture process ($r$ process) bib.a2 , ^147,148,149,150,152Sm are the isotopes
produced by the $s$ process, and ^154Sm is produced by the $r$ process. Their
neutron capture cross sections are of great significance for understanding the
pathways taken during the $s$ process. In addition, about $1\%$ of heavy
element abundances are produced by charged particles and photoinduced
reactions ($p$ process) bib.a3 , ^144Sm is $p$ nuclei in nuclear astrophysics.
It is not produced by neutron capture but rather carry out neutron capture
reactions, the measurement of which can help us to better understand the
results of relevant photonuclear reaction experiments. On the other hand,
^235U is an important raw material for nuclear reactors and samarium 149
isotope is a ^235U fission product with a $1\%$ yield, its cross sections are
important to reactor neutronics.

Few past studies on samarium neutron capture cross sections have focused on
1-50 eV bib.b1 ; bib.b2 ; bib.b3 ; bib.b5 ; bib.b6 ; bib.b7 ; bib.b8 ; bib.b9
. A neutron capture experiment on natural samarium was the work of Chou et al.
in 1973 bib.cjc . Unfortunately, the resonance parameters for one peak in the
resolvable resonance energy region were not analyzed. The latest results came
from Leinweber et al bib.gl . 20 years ago, they measured the neutron capture
cross-section of samarium by using the dilute samples of samarium nitrate in
deuterated water (D_2O) at the Rensselaer Polytechnic Institute (RPI) LINAC
facility, with neutron energies up to 30 eV.

China spallation neutron source (CSNS) is the first spallation neutron source
in China, and it has important applications in the fields of materials
science, physics, chemistry, life sciences, resources and environment, and new
energy CSNS1 ; CSNS2 ; CSNS3 . The back-streaming white neutron beamline
(Back-n) was built in 2018, and it is mainly used for neutron data
measurements backn.01 ; backn.02 . So far, a number of neutron capture
reaction experiments have been carried out on the Back-n beamline lxx.hjs ;
hxr.nst ; rj.cpc ; wdx.aps ; jb.cpb ; lxx.prc ; lxx.cpb .

This work reports the neutron capture cross-section of natural samarium in the
energy region between 1 eV and 50 eV measured at the Back-n beamline.
Resonance parameters are extracted by SAMMY code for each peak contributed by
individual isotope in this energy region. The experimental methods, data
processing and uncertainty analysis are presented.

##  II Experimental Method

The neutron capture experiment was carried out at the end station 2 (ES#2) of
the Back-n beamline. The measurement uses the C_6D_6 detection system. It
consists of four C_6D_6 scintillation detectors, approximately 76 m away from
the spallation target. Each C_6D_6 scintillator has 127 mm in diameter and
76.2 mm in length, and contained in a 1.5-mm thick aluminum capsule which was
coupled with a photomultiplier tube of ETEL 9390 KEB PMT rj.8 . The physical
layout and Monte-Carlo reconstruction of the detector system and target are
shown in Fig. 1(a) and (b) ( see Ref. lxx.prc  for details). Detector
placement is backwards relative to the beam direction as shown in Fig. 1(c).
This is because the $\gamma$ rays emitted from the ($n,\gamma$) reaction are
isotropic, and the backward layout can effectively avoid the influence of
neutron scattering without significantly reducing the detection efficiency.
The neutron flux was measured by a Li-Si detector at neutron trash, which is
based on the ^6Li($n,\alpha$)^3H reaction. Here, the used neutron spectrum was
provided by the Back-n collaboration cyh.epja . Back-n data acquisition system
(DAQ) adopts a full waveform data acquisition solution.

Figure 1: (color online) (a) A picture of the detector layout. (b) Monte Carlo
simulation reconstruction of the detector system and target. (c) A side view
of the layout.

The experiment was carried out in May 2019. A gold (^197Au) target, a carbon
(^natC) target, an empty target and a natural samarium target are prepared.
The total beam time was about 49 h. The ^197Au ($n,\gamma$) ^198Au reaction
standard neutron capture was firstly measured for 13 h in proton power between
50.5 and 51.9 kW to reproduce the previous results lxx.hjs . Carbon and empty
targets were used to determine the background of neutron scattering and
environmental background under beam conditions, and they were measured for 12
h and 8 h, respectively. During this period, the accelerator was relatively
stable and the beam power was about 50 kW, with an uncertainty less than
$2.0\%$. Finally, the natural samarium target was measured for 16 h in beam
power of 48.28–50.45 kW. Normalized spectra for the 1 eV–100 keV energy region
are shown in Fig. 2. The parameters of the targets and measurement conditions
are shown in Table 1, where diameter was measured by vernier caliper and
thickness was measured by micrometer.

Table 1: Information of experimental targets Target |  | Impurities |  | Diameter (mm) | Thickness (mm) | Beam Power (kW)
---|---|---|---|---|---|---
^natSm | $\omega(\ce{Mo})=0.002\%$ | $\omega(\ce{Ti})=0.002\%$ | $\omega(\ce{Tb})=0.001\%$ | $50.00\pm 0.02$ | $1.000\pm 0.005$ | $49.37\pm 1.08$
$\omega(\ce{Fe})=0.01\%$ | $\omega(\ce{Ca})=0.005\%$ | $\omega(\ce{C})=0.01\%$
$\omega(\ce{si})=0.01\%$ | $\omega(\ce{Mg})=0.005\%$ | $\omega(\ce{Nb})=0.002\%$
$\omega(\ce{Al})=0.005\%$ | $\omega(\ce{Cl})=0.005\%$ | $\omega(\ce{Ta})=0.002\%$
$\omega(\ce{La})=0.001\%$ | $\omega(\ce{Ce})=0.001\%$ | $\omega(\ce{Pr})=0.002\%$
^natC |  | $<0.100\%$ |  | $50.00\pm 0.02$ | $1.000\pm 0.005$ | $50.00\pm 1.00$
^197Au |  | $<0.100\%$ |  | $30.00\pm 0.02$ | $1.000\pm 0.005$ | $51.20\pm 0.70$
Figure 2: (color online) Raw spectra for different targets, normalized to the
Li-Si detector results.

##  III Data Analysis

The data analysis uses the pulse height weighting technique (PHWT). PHWT was
originally applied by Macklin and Gibbons in the measurement of neutron
capture cross section by the C_6F_6 detector bib.b6 . This method has shown
suitable for the detector systems in Back-n beamline lxx.hjs ; hxr.nst .

The experimental capture yields are obtained with a weighting function ($WF$)
parameterized as a polynomial function of $\gamma$-ray energy. $WF$ can be
expressed as

$WF(E_{d})=\sum_{i=0}^{4}a_{i}E_{d}^{i}$ (1)

where $WF$ is the weight function, $E_{d}$ is an energy bin of pulse height
spectrum, $a_{i}$ is the parameter of weight function and can be determined by
the least squares fit.

$\chi^{2}=\sum\left(E_{\gamma j}-\int_{EL}^{\infty}R(E_{d},E_{\gamma
j})WF(E_{d})dE_{d}\right)^{2}$ (2)

where $E_{\gamma j}$ is the $\gamma$-ray energy of group $j$,
$R(E_{d},E_{\gamma j})$ is the counts of pulse height (PH) spectrum with
energy response function in $E_{d}$, $EL$ is the threshold of PH spectrum,
$dE_{d}$ is the differentiation of $E_{d}$. Each event is weighed by the
proper $WF$ to ensure that the detector weighted efficiency is proportional to
their excitation energy as shown in Fig. 3.

The cascaded $\gamma$-rays in ($n,\gamma$) reactions were simulated using the
Geant4 bib.geant4  Monte-Carlo program. Since the simulation directly affects
the uncertainty of the PHWT method, the target system and detector system are
completely reconstructed as shown in Fig. 1(b) and (c). Here, the internally
converted electron emission is also considered in the simulation.

Figure 3: (color online) (a) The C_6D_6 original efficiency. (b) Weighted
efficiency. (c) The ratio of weighted efficiency to $\gamma$-ray energy. Below
1.5 MeV, the weighted efficiency is not ideally proportional to the energy,
and hence a threshold is set here when processing the PH spectrum.

The capture yield ($Yw$) can be determined using the following formula bib.yw
:

$Y_{w}(E)=\frac{N_{w}}{N_{s}IS_{n}}$ (3)

where $N_{w}$ is the weighted PH spectrum count, $N_{s}$ is the sample area
density, $S_{n}$ is the neutron binding energy of the target, and $I$ is the
neutron beam flux.

For an admixture of different isotopes, $S_{n}$ needs to be determined
individually according to different resonance peaks, because each individual
resonance belongs to one specific isotope and has its own separation energy
for the capture efficiency. Fig. 4 shows the values of $S_{n}$ at different
resonance peaks. Star point indicates normalized value of $S_{n}$ and solid
line indicates normalized value of cross-section. Different colors indicate
different isotopes. Note that both the $S_{n}$ and cross-section values are
normalized to 0–1 for the convenience of showing the effect of the resonance
peaks contributed by different isotopes on the value of $S_{n}$. Values of
$S_{n}$ for different isotopes are shown in Table 2.

Figure 4: (color online) The values of $S_{n}$ at different resonance peaks, star point indicates normalized value of $S_{n}$ and solid line indicates normalized value of cross-section. Different colors indicate different isotopes. Note that both the $S_{n}$ and cross-section values are normalized to 0–1 for the convenience of showing the effect of the resonance peaks contributed by different isotopes on the value of $S_{n}$.  Table 2: Values of $S_{n}$ for different isotopes  Reaction |  $S_{n}$ (MeV) |  Uncertainty ($\%$)
---|---|---
^144Sm$(n,\gamma)$^145Sm | $6.76$ | 0.003
^147Sm$(n,\gamma)$^148Sm | $8.15$ | 0.002
^148Sm$(n,\gamma)$^149Sm | $5.88$ | 0.002
^149Sm$(n,\gamma)$^150Sm | $7.99$ | 0.002
^150Sm$(n,\gamma)$^151Sm | $5.60$ | 0.002
^152Sm$(n,\gamma)$^153Sm | $5.87$ | 0.002
^154Sm$(n,\gamma)$^155Sm | $5.81$ | 0.003

The uncertainty in the capture yield mainly includes the following factors
lxx.prc : uncertainty from experimental conditions and data analysis, and
statistical error.

Uncertainty from experimental conditions includes uncertainty of energy
spectrum and the proton beam power. They directly affect the neutron flux in
front of the target, and the uncertainty is passed into the yield through the
$I$ term in Eq. (3). According to the Back-n collaboration cyh.epja , the
uncertainty of the energy spectrum in Back-n ES#2 at the mode of without lead
absorber is between 2.3% and 4.5% above 0.15 MeV and less than 8.0% below 0.15
MeV. Uncertainty from beam power is listed in Table 1.

Uncertainties in data analysis are mainly caused by the PHWT method and
neutron binding energy of each reaction. The former will affect the
uncertainty of the capture yield through $N_{w}$ in Eq. (3), while the latter
will affect it through $S_{n}$ in Eq. (3). In 2002, Tain et al. compared the
neutron width PHWT treatment results of a 1.15 keV peak in 56Fe with
experimental results, and found that the systematic error of PHWT was
$2.00\%$–$3.00\%$ bib.phwt . This uncertainty is only attainable if the proper
threshold, conversion electron, and $\gamma$-ray summing effects are taken
into account. We completely reconstructed the target system and detector
system in the simulation. At the same time, a cascade $\gamma$ emission
program including a model of internal conversion process is used in the
simulation. These works can minimize the additional uncertainty when we
applied PHWT to our results. The values of $S_{n}$ for different reactions are
adopted from the new atomic mass evaluation (AME2020) ame2020  and NuDat-3.0
database, each uncertainty is shown in Table 2. On the other hand, the
uncertainty from the normalization method to determine the absolute value of
$I$ in Eq. (3) will also affect the capture yield uncertainty The Ref. lxx.prc
provided two normalization methods: Gaussian fitting of one of the resonance
peak (usually the first peak in the experimental energy region is chosen,
which for ^natSm target is the peak at 3.4 eV). The normalized coefficient is
calculated by comparing the fitted curve with the evaluation data, and the
CENDL-3.2 database was chosen in this work. Another method is to compare the
energy bins one by one. For different targets, the value of normalized
uncertainty is different, and for ^natSm, it is less than 1.3%.

The in-beam $\gamma$-ray background at Back-n is a non-negligible noise
component. Unfortunately, it was not fully understood in the early stages of
the Back-n beamline experiment. After 2020, some in-beam background analyses
at Back-n have been reported rj.nima ; rj.aps , and we also analyzed in-beam
background in detail in the 2021 experiment lxx.cpb . Although the importance
and measurement methods of the in-beam background are well understood, they
are not effective in improving the experimental results in 2019 because of the
changes in experimental conditions. Because there is no evidence that this
does not have a significant effect on the in-beam $\gamma$ background. In
addition, quantification of in-beam $\gamma$ background is also a problem.
Based on the above reasons, the current feasible method is to select the part
with little influence of the in-beam $\gamma$ background, and introduce it
into the experimental results as uncertainty, as done in reference lxx.prc .
The cross-section of ^natSm is significantly lower than that of ^natEr, which
leads to a more significant effect of the in-beam $\gamma$ background.
Therefore, we have to be careful to choose the lower energy region for
analysis, because the in-beam $\gamma$-rays mainly exist in the energy region
greater than 20 eV, and becomes larger with increasing neutron energy up to
around 1 keV lxx.cpb . The processing method is the same as in Ref. lxx.prc ,
but the energy region is limited below 50 eV to control the uncertainty.
Contribution of in-beam $\gamma$ background is shown in Fig. 5 for the ^natSm
target.

Figure 5: (color online) Where the in-beam $\gamma$ background measured in
Ref. lxx.cpb  was normalized to the neutron flux of this experiment. The ratio
of ^natSm counts and in-beam $\gamma$-ray counts show the contribution of in-
beam $\gamma$-ray background. The energy region is limited below 50 eV to
control the uncertainty less than 10%. According to the results of Ref.
lxx.cpb , the in-beam $\gamma$-ray background starts at 20 eV.

Finally, the statistical uncertainty of the experiment was smaller than 0.68%.
All error sources and their estimates are summarized in Table 3.

Table 3: The statistical error and systematic error of the experiment $\sigma$ | Meaning | Value
---|---|---
Experimental Conditions
$\sigma({BeamPower})$ | Uncertainty from beam power |  see Table 1
$\sigma({I_{2}})$ | Uncertainty from energy spectra below 0.15 MeV | $<8.00\%$
Data Analysis
$\sigma({PHWT})$ | Uncertainty from PHWT method | $<3.00\%$
$\sigma({Normalized})$ | Uncertainty from normalized | $<1.30\%$
$\sigma({In-Beam})$ | Uncertainty from counts of in-beam BKG |  see Fig. 4
$\sigma({S_{n}})$ | Uncertainty from binding energy |  see Table 2
Statistical error
$\sigma({Statistic})$ | Uncertainty from mathematical statistics | $<0.68\%$

##  IV Result and Discussion

We should admit that past analyses lxx.prc ; lxx.cpb  are subject to
unpredictable uncertainties. Because we used to deal with the cross-section
directly according to the following Eq. bib.xc :

$Y_{w}(E)=(1-e^{Nt\sigma_{t}(E)})\frac{\sigma_{c}(E)}{\sigma_{t}(E)}$ (4)

where $\sigma_{c}$ is the neutron capture cross section, $\sigma_{t}$ is the
neutron total cross section, $N$ is the atom density, and $t$ is the target
thickness.

In fact, this formula is ideal, which does not take into account the
experimental effects. These neglected effects, such as Doppler broadening,
energy resolution functions, etc., can cause errors in the experimental
results. However, these uncertainties are difficult to assess. Therefore, the
cross-section is not directly calculated by Eq. 4 in this work. In order to
obtain more accurate data we analyzed here, the capture yield by an $R-$Matrix
SAMMY code bib.sammy .

In this work, we concerned about the neutron capture yield of natural samarium
target measured in the resonance energy range of 1–50 eV. Fitting yields are
more accurate than fitting cross-sectional data directly because various
experimental effects, such as broadening, self-shielding, and multiple
scattering, are explicitly considered by the SAMMY code.

Resolution broadening refers to the combined effects of the CSNS proton burst
width, the time delay in the moderator, the TOF channel width, and the effect
of the detector system. Resolution function of CSNS was studied in Ref.
jb.nima . Self-shielding correction accounts for the attenuation of the
incident beam in the sample. Multiple-scattering correction accounts for the
increase in the observed capture yield due to capture of neutrons scattered at
higher energies. Both corrections were applied in SAMMY for all capture
analyses.

The experimental yields and SAMMY fitting results are shown in Fig. 6. It can
be seen that for the resonance peaks in higher energy (above 42 eV), the
fitting effect seems not very good, which may be caused by the gradual
increase of the in-beam background. A probable contribution is the in-beam
$\gamma$ background. According to the previous results lxx.cpb , the
contribution of the in-beam $\gamma$-rays increases between 20 eV and about 1
keV. It is worth noting that for a 1-mm samarium target, the capture yield at
8 eV should saturate (the value of the capture yield should reach 1) but in
fact does not, and show signs of two peaks (see Fig. 6). At present, it cannot
be directly concluded that there are two resonance peaks there, perhaps it is
also due to the lack of measurement time. Therefore, they are treated
cautiously as one peak. This requires further experimental verification.
Resonance parameters are shown in Table 4.

Table 4: Resonance parameters extracted from the $R$-matrix analysis and compared with they are from evaluation database of ENDF/B-VIII.0 and CENDL-3.2. As analyzed in text, the results of $E_{R}=8.0$ eV and $E_{R}>42$ eV were interfered by the shortage of measurement time and in-beam $\gamma$-rays, thus, these results have been removed. Mass | J | g | $E_{R}$(eV) | ENDF/B-VIII.0 | CENDL-3.2 | Present Work
---|---|---|---|---|---|---
$\Gamma_{\gamma}$ (meV) |  $\Gamma_{n}$ (meV) |  $\Gamma_{\gamma}$ (meV) |  $\Gamma_{n}$ (meV) |  $E_{R}$(eV) |  $\Gamma_{\gamma}$ (meV) |  $std(\Gamma_{\gamma})$ (meV) |  $\Gamma_{n}$ (meV) |  $std(\Gamma_{n})$ (meV)
147 | 3.0 | 0.44 | 3.40 | 65.00 | 1.30 | 67.00 | 1.40 | 3.39 | 48.48 | 2.81 | 1.17 | 0.04
27.16 | 79.00 | 6.80 | 69.00 | 7.00 | 27.14 | 58.12 | 3.69 | 5.67 | 0.12
29.74 | 73.00 | 14.70 | 71.00 | 14.70 | 29.73 | 93.32 | 3.37 | 19.64 | 0.49
40.71 | 73.40 | 5.10 | 69.00 | 5.40 | 40.80 | 45.18 | 4.07 | 4.26 | 0.31
4.0 | 0.56 | 18.32 | 70.00 | 69.30 | 72.00 | 71.90 | 18.31 | 309.56 | 11.84 | 19.05 | 0.48
32.10 | 68.00 | 38.20 | 62.00 | 39.00 | 32.11 | 41.70 | 1.27 | 55.05 | 1.42
39.64 | 67.00 | 70.20 | 60.00 | 71.30 | 39.72 | 292.67 | 4.38 | 30.08 | 0.57
149 | 3.0 | 0.44 | 6.43 | 66.00 | 0.80 | 68.00 | 1.20 | 6.46 | 116.01 | 10.09 | 1.55 | 0.09
12.01 | 65.50 | 1.90 | 62.00 | 1.80 | 11.99 | 5.01 | 0.46 | 2.88 | 0.25
15.88 | 85.00 | 0.40 | 62.00 | 0.40 | 15.89 | 48.96 | 5.08 | 0.35 | 0.02
25.27 | 61.50 | 15.70 | 69.00 | 16.00 | 25.25 | 89.04 | 4.99 | 16.46 | 0.44
28.01 | 40.00 | 0.50 | 62.00 | 0.60 | 27.92 | 26.69 | 2.75 | 0.78 | 0.04
29.80 | 62.00 | 3.30 | 62.00 | 3.20 | 30.30 | 94.66 | 9.33 | 0.80 | 0.06
40.20 | 56.00 | 26.70 | 62.00 | 28.30 | 40.21 | 66.00 | 5.86 | 20.92 | 0.88
4.0 | 0.56 | 0.87 | 60.80 | 0.70 | 62.70 | 0.80 | 0.84 | 92.55 | 6.81 | 0.73 | 0.05
4.94 | 64.00 | 1.90 | 59.00 | 2.10 | 4.94 | 58.58 | 4.14 | 1.65 | 0.07
8.93 | 66.50 | 9.50 | 70.00 | 11.80 | 8.98 | 196.42 | 15.55 | 8.42 | 0.55
14.91 | 66.00 | 5.60 | 65.00 | 5.60 | 14.87 | 44.70 | 2.78 | 6.74 | 0.27
17.16 | 89.00 | 2.00 | 62.00 | 2.00 | 17.13 | 84.48 | 5.98 | 2.43 | 0.08
23.25 | 72.00 | 7.90 | 62.00 | 0.90 | 23.20 | 151.06 | 7.40 | 1.21 | 0.02
24.72 | 40.00 | 0.30 | 62.00 | 0.30 | 24.71 | 43.10 | 4.16 | 0.63 | 0.03
26.11 | 49.00 | 3.30 | 62.00 | 3.20 | 26.08 | 35.09 | 3.32 | 3.46 | 0.08
30.80 | 66.00 | 9.40 | 60.00 | 9.50 | 30.81 | 85.72 | 5.47 | 8.77 | 0.16
33.90 | 55.00 | 5.60 | 62.00 | 5.60 | 33.88 | 5.27 | 0.40 | 5.10 | 0.12
150 | 0.5 | 1.00 | 20.65 | 60.20 | 47.90 | 60.20 | 47.70 | 20.53 | 176.34 | 5.22 | 9.42 | 0.17
Figure 6: (color online) The experimental capture yields fitted by the SAMMY
code. It is worth noting that for a 1-mm samarium target, the capture yield at
8 eV should saturate but in fact does not, and show signs of two peaks. Since
it is currently uncertain whether these results arise from insufficient
measurements or a new phenomenon, it is cautious to treat them as one peak.
This requires further experimental verification. As the influence of the in-
beam $\gamma$ background increases, the results for the energy region beyond
42 eV may have large errors, which brings challenges to the fitting.

The resonance parameters are used to calculate the single-level and multi-
level Breit-Wigner cross-sections. For both single-level and multi-level
cases, the capture cross section is given by SLBW

$\sigma_{\ce{capture}}=\frac{\pi}{k^{2}}\sum_{J}g_{J}\sum_{c}\sum_{\lambda}\frac{\Gamma_{\lambda
c}\Gamma_{\lambda\gamma}}{D_{\lambda}}$ (5)

where $k$ is the center-of-mass momentum, $\Gamma_{c}$ is the resonance width
of incident channels, $\Gamma_{\gamma}$ is the $\gamma$ width, $g_{J}$ is the
statistical $g$ factor given by

$g_{J}=\frac{2\boldsymbol{J}+1}{(2\boldsymbol{s}+1)(2\boldsymbol{I}+1)}$ (6)

where $\boldsymbol{s}=1/2$ is the neutron spin, $\boldsymbol{I}$ is the ground
state spin of the target nucleus. Here
$\boldsymbol{J}=|\boldsymbol{L}+\boldsymbol{S}|$,
$\boldsymbol{S}=\boldsymbol{s}+\boldsymbol{I}$, with $\boldsymbol{L}$ the
orbital angular momentum. The denominator $D_{\lambda}$ in Eq. (5) represents

$D_{\lambda}=(E-E_{\lambda})^{2}+(\Gamma_{\gamma}/2)^{2}$ (7)

where $E$ is the center-of-mass incident energy, $E_{\lambda}$ is the
resonance energy, and $\Gamma_{\gamma}=\sum_{c}\Gamma_{\lambda
c}+\Gamma_{\lambda\gamma}$.

The resonance parameters obtained in this work are applied to Eq. 5, and the
present cross sections are calculated as shown in Fig. 7(a). The existing
experimental data and the evaluation database of ENDF/B-VIII.0 and CENDL-3.2
are also shown for conparision. It should be noted that Ref. bib.gl  did not
directly provided the absolute cross section, we calculated the cross sections
by using their resonance parameters. To better evaluate the effect of SAMMY
fitting, resonance kernels $R_{k}$ for different experiments and evaluation
databases are calculated by the following Eq. (8) wdx.aps  and displayed in
Fig. 7(b).

$R_{k}=g_{J}\Gamma_{\gamma}\Gamma_{n}/(\Gamma_{n}+\Gamma_{\gamma})$ (8)

Figure 7: (color online) (a) Comparison of theoretical cross-section
calculated by resonance parameters with other experimental data and evaluation
databases of ENDF/B-VIII.0 and CENDL-3.2. It should be noted that reference
bib.gl  does not directly provided the absolute cross section, this work
calculates the theoretical cross section by applying their resonance
parameters to Eq. (5). A clear difference between ENDF/B VIII.0 and CENDL-3.2
database appears at 23.2 eV, the existing experimental results may be more in
consistent with CENDL-3.2 database. Most of the controversial experimental
results invariably come from the samarium 149 isotope. (b) $R_{k}$ values of
different experiments and evaluation databases, different colors represent
different experimental and evaluation results.

Fig. 6 can explain the strange result at 8 eV in Fig. 7. From the results of
the capture yield, the resonance peak of the samarium 152 isotope at 8 eV may
be contributed by two small resonance peaks. Another possible reason is the
lack of measurement time. For 1-mm thick samarium target, the neutron capture
yield should saturate here, but it does not. Since the measurement of the
samarium target is scheduled at the end, the measurements of the background
and the gold target squeezed the time that should belong to samarium target. A
hindsight experience is that gold target doesn’t need to be paid so much
attention as a test. Therefore, we cannot completely rule out a cause from
measurements, and hence we recommend a further experiment to check this
result.

The experimental results are good between 20 and 42 eV according to Fig. 7. At
23.2 eV, there is a clear divergence between the ENDF/B VIII.0 and CENDL-3.2
databases, and it also can be seen form the results of $R_{k}$ in Fig. 7(b).
The results of both experiments suggest that the resonance peak at 23.2 eV
contributed by samarium 149 isotope may be lower than ENDF/B-VIII.0 database,
but close to CENDL-3.2 database. At 27.1 eV, our $R_{k}$ values are
significantly smaller than the results of Leinweber et al. but evaluation
database.

At 30-50 eV, only one set of published experimental data exists and cannot be
used to evaluate resonances bib.cjc . The resonance at 34 eV is different, and
the value of $R_{k}$ provided by the experiment is significantly smaller than
that of the evaluation databases. It may not come from background or
statistics. The $R_{k}$ results for the peaks above 42 eV are significantly
smaller than evaluation database. Because of a significant increase in the in-
beam background, we can’t rule out the reasons for the experiment. Thus, we
plan to conduct more experiments to determine it.

Interestingly, most of the controversial experimental results invariably come
from the samarium 149 isotope. It is the fission product of ^235U, and its
neutron capture cross section plays an important role in the design and
construction of nuclear reactors. According to the EXFOR database, few
experiments have focused on the neutron capture cross-section of ^149Sm target
in the resonance energy region. It deserves further study.

##  V summary and conclusions

We have measured the neutron capture cross yield of the natural samarium
target in the 1–50 eV energy region at the Back-n beamline of CSNS. Resonance
parameters are extracted and cross sections are calculated accordingly. We
found a clear difference between ENDF/B VIII.0 and CENDL-3.2 database at 23.2
eV, the existing experimental results may be more in consistent with CENDL-3.2
database. The difference between different experiments is obvious at 27.1 eV,
however, the two evaluation databases are almost identical here. The
experimental results at 30-50 eV are new data and mostly consistent with the
evaluation database except for the resonance peak at 34 eV. The resonance
width analyzed from the experimental data is significantly smaller than that
from evaluation database. The reason is less likely due to background or
statistics.

Two important lessons learned from this experiment. One is about the time
allocation of measurements for gold target and background, especially for gold
target. The gold target as the main target was fully measured in January 2019,
and the result was published elsewhere lxx.hjs ; hxr.nst . In subsequent
experiments, the gold targets were only measured as validation data to ensure
the correctness of each experimental setup and data analysis. Exact data are
not necessary, so it shouldn’t take too much beam time. On the other hand, the
in-beam $\gamma$ background has always been a priority issue. It directly
determines the accuracy of the data and limits the energy range that can be
reported. We have published data from 1-100 eV in the analysis of Er targets
lxx.prc , and data only from 1 to 50 eV can be considered reliable and are
provided in this work. Because for higher energy region, the influence of the
in-beam $\gamma$ background may greater than $10\%$. Although we did detailed
measurement and analysis later lxx.cpb , this is not universal. Fortunately,
related work is underway. More precise data is to be expected.

###### Acknowledgements.

We appreciate effective technical support from Dr. Yi-Jie Wang at Tsinghua
University, Dr. Yu-Chao Xu at General Electric, and the efforts of the staff
of the CSNS and Back-n collaboration. This work was supported by the National
Natural Science Foundation of China under Grant Nos. 11875311, 11905274,
1705156, U2032146, 11865010, 11765015, and 1160509, Natural Science Foundation
of Inner Mongolia under Grant Nos. 2019JQ01 and 2018MS01009, and the Strategic
Priority Research Program of the CAS (No. XDB34030000).

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