Experimental Setup

A neutron capture experiment was conducted at end station 2 (ES#2) of the back-n beamline. The measurement utilized a detection system consisting of four C₆D₆ scintillation detectors, each with a diameter of 127 mm and length of 76.2 mm, housed within a 1.5-mm thick aluminum capsule, and coupled with a photomultiplier tube (ETEL 930 KEB PMT). For the measurement of the neutron capture reaction cross-section, the C₆D₆ detector offers several advantages [24]: (1) It exhibits low sensitivity to neutrons, which is crucial for eliminating background signals in the detection of the final state γ rays from the (n,γ) reaction. This insensitivity significantly reduces the neutron-induced background. (2) The C₆D₆ detector demonstrates a fast time response, with signal responses to neutrons and γ-rays on the order of nanoseconds. Coupled with the response time of the photomultiplier tube, this resulted in a rise time of approximately 10 ns for the entire anode signal, thereby improving the overall time resolution of the detection systems. (3) Through pulse height weighting technique (PHWT), the detection efficiency of C₆D₆ detectors can be independent of decay paths, multiplicity, and energy distribution of γ rays. The physical arrangement and Monte Carlo simulation reconstruction of the detector system and target are presented in Refs. [25], with the detailed layout parameters provided in Ref.[26]. The detector was placed opposite to the direction of the beam. This configuration minimizes the background interference from beam scattering, given that γ-rays emitted by neutron capture reactions are isotropic. The neutron flux was determined using a Li-Si detector based on the ⁶Li(n,α)³H reaction. The energy spectra were obtained from back-n collaboration, with an uncertainty of less than 8.0% for E_n < 0.15 MeV [27]. The Back-n data acquisition system (DAQ) employs a full-waveform data acquisition solution.

In this study, the TOF () method was used to determine the resonance energy of the neutrons. E_n is expressed as follows: $E_{\text{n}}=\frac{1}{2}{m}_{\text{n}}{\left(\frac{L}{t_{\text{n}}}\right)}^2\mathrm{,}$ (1) where m_n is the neutron mass, L is the flight distance, and t_n is the flight time. In the Back-n facility, t_n is determined as $t_{\text{n}}=\left(t_{\text{det}}-t_{\gamma }\right)+\frac{L}{c}$, where t_det is the time when the detector responds to neutrons or γ rays, $t_{\gamma }$ is the time when the γflash arrives at the detector, c is the speed of light [28]. ES#2 is approximately 76 m from the spallation target, and the value of L is 77.26 m in our case. The uncertainty in L is mainly caused by multiple scattering of neutrons inside the spallation target [29].

In the normal operating mode of a CSNS, there are two proton bunches with a time interval of 410 ns for each pulse, which has a repetition frequency of 25 Hz. Because of the superposition of the event distributions corresponding to the two bunches, the resolution of the TOF measurement at back-n is degraded by the double-bunch characteristics if the measured event distribution is used directly without unfolding, particularly in the higher neutron energy region [30]. In this study, we used the analytical method developed by the back-n collaboration to nearly recover the event distribution corresponding to a single proton bunch [31].

The experiment was conducted in May 2019 and involved the preparation of gold (¹⁹⁷Au), carbon (^natC), empty, and natural samarium (^natSm) targets. A total beam time of approximately 49 h was used in this study. The ¹⁹⁷Au(n,γ)¹⁹⁸Au reaction, serving as a standard neutron capture cross section, was initially measured for 13 h at proton power levels ranging from 50.5–51.9 kW to validate previous findings [25], thereby ensuring the integrity of the experimental setup and data acquisition (DAQ). Subsequently, measurements were performed on the carbon and empty targets for 12 h and 8 h, respectively, to assess the neutron-scattering background and environmental interference under beam conditions. Throughout this period, the accelerator exhibited relatively stable performance with a beam power of approximately 50 kW and an uncertainty level below 2%. Finally, the natural samarium target was measured for 16 h at beam power levels between 48.3 and 50.5 kW. Details regarding the target parameters and measurement conditions are presented in Table 1, with diameter measurements obtained using Vernier calipers and the thickness determined by micrometer readings.

Weighting Function

The essence of data analysis is to obtain the counts of neutron capture reactions within the target, which are contingent on the detection efficiency and accuracy of the response of the detector to (n,γ) reactions. The efficacy of C₆D₆ scintillators in detecting prompt γ-ray cascades emitted during neutron capture reactions is contingent on the intricate de-excitation path of the compound nucleus. Consequently, it is imperative that the measured signals undergo the pulse-height weighting technique (PHWT), which renders the detection efficiency independent of the cascade γ-ray energies.

Typically, a high detection efficiency is sought after; however, for neutron capture reactions, a low detection efficiency is preferred owing to the phenomenon of γ radiation cascade emission. In the case of neutron-capture cascade emission, it is desirable to detect at most one γ ray in the cascade emission, making a low detection efficiency more suitable. Therefore, the detection efficiency of the capture reaction is approximately equal to the sum of the detection efficiencies of the capture reaction cascade γ. ${\epsilon }_{\text{c}}=1-{\displaystyle \prod }\left(1-{\epsilon }_{\gamma i}\right)\approx {\displaystyle \sum }{\epsilon }_{\gamma i}\mathrm{,}$ (2) where εc is the detection efficiency of the C₆D₆ detector for the capture reaction, εγi is the detection efficiency of the i^th cascade γ ray. Because εγi is sufficiently small, the equal sign of the above formula holds. Equation (2) establishes the relationship between εc and εγi, but it cannot be directly reflected in the output energy spectrum of C₆D₆ detector. We hope to establish a direct relationship between εc and the output energy spectrum of the detector, which is helpful to directly analyze εc from the output signal of the detector and then calculate the neutron capture cross section. If the γ detection efficiency in equation (2) is proportional to the γ energy Eγ, then ${\epsilon }_{\gamma i}=\alpha E_{\gamma i}\mathrm{.}$ (3) Then, ${\epsilon }_c=\alpha {\displaystyle \sum }{E}_{\gamma i}\mathrm{,}$ (4) where α is the scale coefficient and $E_{\gamma }$ is the energy of cascade γ, which can be obtained directly from the pulse height spectrum output by C₆D₆.

For equation (4) to hold, it is necessary to perform mathematical control on the response function of the detection system to realize the relation in (3), which is a pulse-height weighting technique (PHWT). The PHWT was first proposed by Macklin and Gibbons and applied to the C₆F₆ detector to measure the neutron capture cross-section [32]. We anticipate that the energy of each group of cascaded γ-rays will be directly proportional to the weighted detection efficiency. The normalized detection efficiency manifests intuitively in the pulse-height spectrum (PH spectrum) counts. Consequently, the detection efficiency of the detector for γ can be characterized by analyzing the pulse-height spectrum. By introducing a weighted function number, we ensure that the following equation is satisfied: ${\displaystyle {\int }_{EL}^{\infty }}{R}_{\text{d}}\left(E_{\text{d}}\mathrm{,}{E}_{\gamma j}\right)W\left(E_{\text{d}}\right)d\left(E_{\text{d}}\right)=\alpha E_{\gamma j}\mathrm{,}$ (5) where the EL is the threshold of PH spectrum; E_d is an energy bin of PH spectrum; $R\left(E_{\text{d}}\mathrm{,}{E}_{\gamma j}\right)$ is counts of PH spectrum with energy response function in E_d; $W\left(E_{\text{d}}\right)$ is the weight factor corresponding to E_d; $E_{\gamma j}$ is the energy of gamma-ray of group j, here we set the coefficient α =1.

The experimental capture yields were determined using a weighting function (WF) parameterized as a polynomial function of the γ-ray energy. WF can be expressed as $WF\left(E_{\text{d}}\right)={\displaystyle \sum _{i=0}^4}{a}_i{E}_{\text{d}}^i\mathrm{,}$ (6) where ai is the parameters of the WF, which can be determined using the least-squares fit method: ${\chi }^2={\displaystyle \sum }{\left(k{E}_{\gamma j}-{\displaystyle {\int }_{EL}^{\infty }}R\left(E_{\text{d}}\mathrm{,}{E}_{\gamma j}\right)WF\left(E_{\text{d}}\right)\text{d}{E}_{\text{d}}\right)}^2\mathrm{.}$ (7) Each event was weighted by an appropriate WF to ensure that the weighted efficiency of the detector was directly proportional to its excitation energy, as illustrated in Fig. 2. This manipulation of raw data remains valid when the original efficiency is sufficiently low, allowing for the measurement of only one γ-ray per capture event in the C₆D₆ setup [33].

Fig. 2Full-screen View

(Color online) (a) C₆D₆ original efficiency. (b) Weighted efficiency. (c) The ratio of weighted efficiency to γ rays energy

The energy deposition of different monoenergetic γ rays in the C₆D₆ detector layout [23] was simulated using the Geant4 Monte Carlo program [34, 35]. The original efficiency curves are presented in Fig. 2(a). Upon applying the weight function to the original efficiency curve, the linear relationship between the detection efficiency and energy is illustrated in Fig. 2(b), with the ratio of efficiency to energy in Fig. 2(c) approaching unity. Below 1.5 MeV, the weighted efficiency does not exhibit proportionality to the energy, necessitating the establishment of a threshold during PH spectrum processing to mitigate any impact from the failure of the weight function.

Background Analysis

To be effective, the WF must be applied to the net pulse-height spectrum. The key to obtaining the net pulse height spectrum is background deduction. For the neutron capture cross-section measurements with C₆D₆ detectors at back-n, the background composition was as follows [36]: $B(t)=B_0+B_{\text{empty}}\left(t\right)+B_{\text{sample}}\left(t\right)\mathrm{,}$ (8) where $B_0$ is the sample- and time-independent background, $B_{\text{empty}}\left(t\right)$ is the time-dependent but sample-independent background, and $B_{\text{sample}}\left(t\right)$ is the sample-dependent background, which is related to the scattering of neutrons and γ rays by the sample. The neutron energy E_n is derived from the time-of-flight t: $B\left(E_{\text{n}}\right)=B_0+B_{\text{empty}}\left(E_{\text{n}}\right)+B_{\text{sn}}\left(E_{\text{n}}\right)+B_{\text{s}\gamma }\left(E_{\text{n}}\right)\mathrm{,}$ (9) where B is the total background, which is related to the neutron energy E_n; $B_{\text{sn}}$ is the background caused by neutron scattering with the target; and $B_{\text{s}\gamma }$ is the background caused by in-beam γ scattering with the target.

The background resulting from environmental activation and delayed γ rays is independent of the sample and time but relies solely on the experimental conditions. In this context, the background is determined by measuring an empty target without a beam to establish $B_0$. However, the background arising from both the beam and the environment is not influenced by the sample but varies with time. This aspect of the background is assessed by measuring an empty target under the beam conditions to determine $B_{\text{empty}}\left(E_{\text{n}}\right)$.

The background caused by neutron scattering typically necessitates a target nucleus with a large neutron scattering cross section in the relevant energy range, while also requiring the neutron capture cross section of the target nucleus to be relatively flat to avoid interfering with the measurement of the Sm target. In this study, we used measurements of the carbon target under beam conditions to determine $B_{\text{sn}}\left(E_{\text{n}}\right)$. Given its low neutron capture cross-section compared to Sm and the absence of a resonance structure in the relevant energy range, lead is an ideal material for evaluating the in-beam γ background $B_{\text{s}\gamma }\left(E_{\text{n}}\right)$ because of its strong γ-ray scattering capability.

In 2019, we failed to recognize the significance of the in-beam γ background, and consequently overlooked this aspect of the data. However, in 2022, we ascertained the general time structure of the in-beam γ background at the back-n facility using various in-beam γ ray experimental findings [23]. Subsequently, we propose a methodology for the comprehensive quantification of in-beam γ rays based on Geant4 simulation. By re-analyzing the 2019 ^natEr target experimental results using this approach, we obtained reliable outcomes that validated its efficacy. Furthermore, employing this method, we processed the 2019 ^natSm target experimental data to determine $B_{\text{s}\gamma }\left(E_{\text{n}}\right)$.

The normalized count spectrum is shown in Fig. 3. The lines $p_0-p_2$ represent the spectra of the natural samarium, carbon, and empty targets, which were normalized to the neutron flux rate detected by the Li-Si detector. Line p₃ corresponds to the in-beam γ-ray background, and its shape is measured using a lead target. As discussed in Ref.[23], there exists a general formula and parameters for expressing its shape at the Back-n facility until significant modifications are made to the beamline that may impact the generation or transportation of in-beam γ rays. We considered the inclusion of a Co filter at the beamline, which exhibits two distinct resonance absorption peaks at energies of E₁ = 132 eV and E₂ = 5.016 keV. When the filter is designed to completely absorb neutrons, only γ rays remain in the beam. Consequently, $A_1\left(B_1\right)$ corresponds to line p₀ at an energy of E₁(E₂), representing the result of natural samarium reacting with neutrons and γ rays, whereas $A_2\left(B_2\right)$ is obtained through simulation, depicting the outcome of a natural samarium target interacting solely with γ rays.

Fig. 3Full-screen View

(Color online) The spectrum of the natural samarium target, empty target, and carbon target (normalized to the neutron flux rate). The in-beam γ ray background is determined by simulation, as described in Ref. [23]

Let $A_3=A_2{\sigma }_1/{\sigma }_2\left(B_3=B_2{\sigma }_1/{\sigma }_2\right)$, where ${\sigma }_1\left({\sigma }_2\right)$ is the γ-ray elastic cross section of the lead and ^natSm target. $p_4=C_1\left(p_1-p_2\right)+C_2\cdot p_3$. C₁ is the ratio of the neutron scattering cross section of samarium to that of carbon. Let points $\left(E_1\mathrm{,}{A}_3\right)$ and $\left(E_2\mathrm{,}{B}_3\right)$ be in line p₄; then, parameter C₂ can be determined.

Neutron Capture Yield

The net PH spectrum was derived by subtracting the background values. Following the application of WFs, the capture yield can be determined as follows: $Y_w\left(E_{\text{n}}\right)=\frac{N_{\text{w}}\left(E_{\text{n}}\right)}{N_{\text{s}}I\left(E_{\text{n}}\right)S_{\text{n}}}\mathrm{,}$ (10) where $Y_{\text{w}}\left(E_{\text{n}}\right)$ is the capture yield, $N_{\text{w}}\left(E_{\text{n}}\right)$ is the weighted pulse height spectrum, Ns is the target area density, $I\left(E_{\text{n}}\right)$ is the neutron flux measured by Back-n collaboration [27], S_n is the target neutron separation energy. For a natural Sm target, each resonance corresponds to a specific isotope and possesses its own separation energy for efficient capture. Consequently, the value of S_n varies across the different resonance peaks. The method used to calculate the value of S_n for the ^natSm target is shown in Fig. 4. Different colors represent different Sm isotopes. Line types (including dotted, solid, and dashed lines) indicate the variations in neutron capture cross-sections of isotopes with incident neutron energy, and dot types represent the different values of the neutron separation energy S_n. Both linear and point patterns are presented in Figure 4 to demonstrate that the value of the natural target S_n is based on the contributions of different isotopes to the resonance peaks. Because S_n ranges from 5.81 MeV (¹⁵⁴Sm) to 8.15 MeV (¹⁴⁷Sm), no significant difference can be observed on the y-axis scale in Fig. 4, and $S_{\text{n}}\times \text{max}(\sigma )$ is employed to reflect the value of natural target S_n at different energies. The dotted lines in Fig. 4 show that, since different isotopes contribute different resonance peaks, the S_n value of the natural target is a piecewise function, which is related to the formant position of different isotopes. The values of S_n for the ^natSm isotopes can be obtained based on a new atomic mass evaluation(AME2020) [37].

Fig. 4Full-screen View

(Color online) The normalized value of cross section for different isotopes and the value of S_n for natural samarium element. Line types (including dot lines, solid lines, and dashed lines) indicate the variations of neutron capture cross sections of nuclides with incident neutron energy, and dot types represent the values of natural S_n at different energies

Uncertainty

The uncertainty in the capture yield encompasses several contributing factors, as outlined in [26]: variability arising from the experimental conditions, data analysis, and statistical error.

The uncertainty arising from the experimental conditions includes variations in the energy spectrum and proton beam power, both of which directly affect the neutron flux at the target. This uncertainty is subsequently propagated into the yield through the term I in Eq. (9). According to the findings of the Back-n collaboration [27], the uncertainty associated with the energy spectrum in the Back-n ES#2 without a lead absorber ranges between 2.3% and 4.5% above 0.15 MeV and less than 8.0% below 0.15 MeV. The uncertainties stemming from the beam power are listed in Table 1. As shown in Table 1, in addition to Sm, the target material also contained trace quantities of other elements, and their contents varied from 0.001% to 0.01%. As the contents of these impurities are sufficiently low, their impact on the measurement results of the Sm neutron capture cross-section is less than 1%.

Uncertainties in the data analysis were primarily attributed to the PHWT method. In 2002, Tain et al. compared the neutron-width PHWT treatment results of a 1.15 keV peak in ⁵⁶Fe with the experimental results, revealing a systematic error of 2.00%–3.00% [38]. This level of uncertainty can only be achieved if proper consideration is given to the threshold, conversion electrons, and γ-ray summing effects. Our simulation involved a complete reconstruction of the target and detector systems, while also incorporating a cascade γ emission program that included a model of the internal conversion processes. These efforts served to minimize additional uncertainty when applying PHWT to our results.

By contrast, the uncertainty stemming from the normalization method used to determine the absolute value of the term I in Eq. (9) affects the precision of the capture yield. The two normalization methods are provided in Refs. [26]: Gaussian fitting of one of the resonance peaks (typically, selecting the first peak in the experimental energy region for a ^natSm target is 3.4 eV). The normalized coefficient is calculated by comparing the fitted curve with evaluation data, and CENDL-3.2 database was utilized in this study. Another approach involves comparing energy bins individually. The normalized uncertainty varies for different targets and is less than 1.3%

The ^natSm experiment was concluded in 2019, and the experimental data for the in-beam γ-ray background were unfortunately not available. Therefore, we employed the methodology outlined in Ref. [36] to analyze the in-beam γ-ray background. The uncertainty within the energy range of 20–300 eV was less than 10.5%.

The statistical uncertainty of the experiment was less than 0.68%. All error sources and their estimates are summarized in Table 2.

Neutron Resonance Parameters

The neutron capture yield of a natural Sm target was measured within the resonance energy range of 1-300 eV. Capture yield data were obtained using Eq. 10 and subsequently fitted using the R-Matrix code SAMMY, accounting for various experimental effects such as Doppler broadening, self-shielding, and multiple scattering. The resonance parameters ^natSm(n,γ) were extracted accordingly. The fitting results are shown in Fig. 5. In the resonance energy region, each peak is attributed to a specific nuclide. Thus, the resonance information of each isotope can be extracted from the results of natural targets based on the resonance energy. Furthermore, Table 3 presents a detailed comparison of the differences between the different evaluation databases (DB#1-5 representing CENDL-3.2, ENDF/B-VIII.0, JEFF-3.3, JENDL-4.0, BROND-3.1).

Fig. 5Full-screen View

(Color online) Experimental capture yields and the fitted ones obtained with the SAMMY code

A comparison of the findings of the current study with those of various evaluation libraries is illustrated in Fig. 6 (¹⁴⁷Sm) and Fig. 7 (¹⁴⁹Sm). For the ¹⁴⁷Sm isotope, the parameter Γ_n remains consistent at 107.0 eV across the different evaluation databases, and our experimental results agree with all of them. However, at the energy points of 139.4 eV, 241.7 eV, and 257.3 eV, the parameter Γ_n in the CENDL-3.2 database aligns with the JENDL-4.0 database but diverges from the ENDF/B-VIII.0, JEFF-3.3, and BROND-3.1 For these energy points, our experimental results were consistent with the evaluations in the ENDF/B-VIII.0, JEFF-3.3, and BROND-3.1 databases. The value of parameter Γ_γ for ¹⁴⁷Sm in the CENDL-3.2 database is 69 meV at 107 eV compared to 82 meV in the other four databases; however, our current experimental result is 85.5 ± 8.0 meV.

Fig. 6Full-screen View

(Color online) Comparison between the Γ_n and Γ_γ values of ¹⁴⁷Sm obtained from the different databases and this study

Fig. 7Full-screen View

(Color online) Comparison between the Γ_n and Γ_γ values of ¹⁴⁹Sm obtained from the different databases and this study

For the ¹⁴⁹Sm isotope, the discrepancy in the parameter Γ_n across different evaluation databases was minimal, and the experimental findings aligned closely with the assessment databases at most energy levels. Specifically, our experiment yielded a value of 25.8±2.5 meV at an energy of 248.4 eV, whereas the four evaluation databases reported values ranging from 36.6 meV to 39.7 meV. The Γ_γ value in the CENDL-3.2 database aligns with that in the JENDL-4.0 database at the energy points 23.2, 24.6, 26.1, and 28.0 eV. However, it diverges from the evaluation databases of ENDF/B-VIII.0, JEFF-3.3, and BROND-3.1. At the energy points of 51.5, 75.2, 90.9, 125.3, and 248.4 eV, the experimental results are consistent with those in the ENDF/B-VIII.0, JEFF-3.0, JENDL-4.0, and BROND-3.1 databases.