Neutron source

The 400 kV ns pulsed neutron generator [26] was used to produce pulsed neutrons for the experiment. The generator emits monoenergetic 14.5 MeV fast neutrons through the T(d, n)⁴He reaction, achieved by bombarding a T-Ti target with a D⁺ ion beam. The incident D⁺ ion beam energy was 300 keV, with an average current of 20 μA, pulse width of 2 ns, and pulse frequency of 1.5 MHz. The T-Ti target, with an active zone diameter of 1.6 cm and thickness of 1 mg/cm², generated a neutron yield of approximately 2×10⁹ n/s.

Samples and measured angle

A standard polyethylene sample and three natural Zr (^natZr) slabs were used in the experiment. The dimensions of the polyethylene sample were 30cm × 30cm × 6cm and its density was 0.942 g/cm³. The purity of the Zr sample reached 99.5%; detailed information is provided in Table 1.

Polyethylene was selected as the standard sample to validate the measurement system because of its well-characterized n-p elastic scattering cross-section [27]. The interaction between neutrons and hydrogen involves only the elastic scattering reaction channel (n-p scattering), and the n-p scattering cross-section is internationally recognized as a standard reference. By employing polyethylene, we could effectively validate the experimental system’s reliability, including its data acquisition and processing capabilities before the measurements of the ^natZr samples.

Leakage neutron spectra were measured at six angles to ensure comprehensive data collection. For the 6-cm Zr sample, measurements were conducted at 47°, 61°, 79°, 101°, 119°, and 133°. For the 12 and 18-cm samples, the angles were adjusted to 47°, 58°, 73°, 107°, 122°, and 133° to minimize interference with the monitoring system. The measurements were performed at different angles using an electric platform for precise sample positioning, as illustrated in Fig. 2.

Fig. 2Full-screen View

(Color online) Measured angle and Zr sample movement

Shield and collimator

The shielding and collimation system was designed to minimize the scattered neutron background and ensure the accuracy of the measured data [28]. It consists of three main components: a shadow bar, pre-collimator, and wall collimator. The shadow bar, positioned between the neutron source and pre-collimator, blocks direct neutron interactions with the pre-collimator material, preventing the generation of secondary neutrons. The wall and pre-collimators have a three-layer structure, as summarized below:

This system ensures that only neutrons scattered from the sample within the detector’s solid angle reach the main detector, whereas background neutrons and gamma rays are effectively suppressed.

Detector systems and data acquisition

The experimental setup included an EJ-301 liquid scintillator as the primary detector, two monitor detectors, and an associated particle detector. The EJ-301 detector (diameter: 5.08 cm, thickness: 5.08 cm) measured the leakage neutrons emitted from the sample. Two monitor detectors (diameter: 1.27 cm, thickness: 1.27 cm), respectively positioned at 0° and 90° relative to the beam direction, primarily measured the TOF spectra of the source neutrons. An associated particle detector based on a SiC detector was positioned at 135° to the beam direction to measure alpha particles and protons for neutron yield normalization [29-32].

The neutron yields were calculated using the following relationships:(1)where N_n is the neutron yield, Nα is the alpha particle count, and N_p is the proton count. Kα and K_p are the corresponding normalization coefficients, derived from the relationship between the neutron flux and alpha particle (or proton) flux in the unit solid angle at 135°. These calculations provide critical inputs for normalizing the experimental results.

The data-acquisition system employed was GDDAQ [33], which uses Pixie-16 modules for digital signal processing. The key parameters of the Pixie-16 card are listed in Table 2. The system efficiently handled data collection, enabling the integration of TOF and pulse shape discrimination (PSD) analyses during post-processing.

Figure 3 illustrates the TOF measurement system. The pick-up signal generated by the D⁺ ion beam as it passed through a copper ring inside the tube in front of the target was sent to an acquisition card through a fast pre-amplifier. The signals from the three liquid scintillator detectors and beam pickup signal were processed together to calculate the neutron TOF.

Fig. 3Full-screen View

(Color online) TOF measurement electronics system

Experimental methods and data processing

2.5.2

Data processing

Energy calibration of the EJ-301 detector was performed using standard gamma sources to ensure energy linearity and to set the measurement thresholds, which were essential for excluding noise signals. Gamma rays were inevitably produced during the interactions of neutrons with matter. The PSD method was employed to distinguish neutron signals from gamma signals by leveraging the differences in their pulse shapes.

A baseline correction was applied to each signal to reduce noise. The PSD value was calculated as the ratio of the slow component integral to the total signal integral. This enabled the effective separation of the neutron signals from the gamma signals. The impact of PSD on TOF spectra is shown in Fig. 4, where improved neutron spectra are evident after eliminating the gamma-ray signals.

Fig. 4Full-screen View

(Color online) PSD discrimination results. (a) PH-PSD two-dimensional spectrum. (b) TOF spectrum of leakage neutrons before PSD discrimination. (c) TOF spectrum of leakage neutrons after PSD discrimination

During the experiment, the source neutrons interacted not only with the sample but also scattered with the air and surrounding structural materials. Because the measured leakage neutron spectrum specifically represents neutrons emitted from the sample after interactions with the source neutrons, the contributions from neutrons scattered by air and other materials had to be eliminated. To achieve this, we performed background measurements with the D-T neutron source present but without the sample. The resulting background spectrum was subsequently compared with the effect spectrum obtained when the sample was in place. The results are shown in Fig. 5, where “sample-in” denotes the effect spectrum measured with the sample, and “sample-out” represents the background spectrum measured without the sample. The effect-to-background ratio reached a peak value of 28 with an integrated effect-to-background ratio of 15 across the entire TOF spectrum.

Fig. 5Full-screen View

(Color online) Measured leakage neutron time-of-flight spectra, illustrating a comparison between the effect and background spectra

Geometric model

Accurate geometric modeling is essential for reliable simulations. Ideally, a detailed model that includes all the experimental structures would produce the most accurate results. However, such models significantly increase the computation time. To balance accuracy and efficiency, it is necessary to remove structures that have minimal impact on the simulation results. This was achieved through a series of simulations.

First, a detailed geometric model of the experimental hall and measurement system was created based on actual dimensions and materials. The leakage neutron spectrum of the polyethylene sample was calculated and used as the reference spectrum in this study. Subsequently, a weighting method was applied to obtain leakage neutron spectra of various sections of the experimental hall. These sections included the front, rear, left, and right walls (with the beam direction as the reference) as well as the ceiling and floor. In these simulations, wall weights were set to zero. Six spectra were generated and compared with the reference spectrum. Finally, the ratios of the studied spectra to the reference spectrum were calculated. The results are shown in Fig. 6(a). This enabled us to analyze the influence of different wall sections on the leakage neutron spectrum. Analysis of the ratios revealed that the ceiling, floor, front, and rear walls had minimal impact on the leakage neutron spectrum, with deviations from the reference spectrum of less than 0.1%. The left wall primarily influenced the low-energy region of the leakage neutron spectrum, whereas the right side wall primarily affected the high-energy region.

Fig. 6Full-screen View

(Color online) Ratio of the study spectra under different wall conditions to the reference spectra

To further investigate the effects of the left and right sidewalls, we divided them into different regions along the central axis of the collimated beam. With the weighting method again, the results showed that only the region within a 75 cm radius from the central axis of the side walls had a significant effect on the simulation results, as shown in Fig. 6(b) and (c).

In summary, except for the regions of the left and right side walls within a radius of 0.75 cm, the influence of the other hall walls on the leakage neutron spectrum can be neglected. These walls were excluded from the calculation model. The model considers only the geometric structure along the neutron path to the detector, which includes the target, sample, shadow bar, pre-collimator, wall collimator, and parts of the left and right walls. A schematic of the simplified model is shown in Fig. 7. The geometric model was constructed using the experimentally measured dimensions and material properties of the target, collimation components, and shielding walls. This approach ensured that the simulation results closely matched the experimental setup, thereby minimizing the discrepancies caused by geometric inaccuracies.

Fig. 7Full-screen View

(Color online) Schematic diagram of the calculation model for the shielding integral experiment measurement system

Source neutron parameters

The source neutron parameters, including the energy-angle distribution and pulse time distribution, play crucial roles in simulations. Accurate descriptions of these parameters are vital to ensuring consistency between simulated and experimental leakage neutron spectra. Any deviations in their description can lead to significant discrepancies.

In experiments using a D-T neutron source, not all incident D⁺ ions react with the tritium in the target. Unreacted D⁺ ions are deposited on the target, leading to subsequent D-D reactions. Over time, as the tritium in the target is depleted and more D⁺ ions accumulate, the neutron source becomes a mixed field of D-T and D-D neutrons with dynamically changing yields. The energy-angle distributions of the D-T and D-D neutrons were calculated using the TARGET program, which incorporates the geometry and material parameters of the target. The ratios of the D-T and D-D neutron yields were determined from the measured alpha particle and proton ratios obtained from the associated particle detectors. These distributions were combined to produce source neutron spectra that accurately reflected the experimental conditions.

The pulse time distribution of source neutrons was influenced by beam dynamics, such as initial energy dispersion, high-voltage ripple during acceleration, and deviations caused by beam clustering. These factors introduced slight changes in the source neutron emission profile over time. The TOF spectrum of the source neutrons, measured by the monitor, was combined with the simulated response matrices to calculate the pulse time distribution through inverse convolution, as shown in Eq. (2).(2)where Ni represents the measured TOF spectrum, R is the response matrix (with elements Rij), and Φ_j is the pulse time distribution. This approach provided a precise representation of the source neutron emission profile for subsequent simulations.

Detector efficiency curve

The energy distribution of the neutrons leaking from the sample spans a broad range and requires a comprehensive understanding of the efficiency of the detector over this wide energy region. Because of the limited availability of monoenergetic neutron sources, experimentally measuring the detection efficiency across the entire energy spectrum is impractical. Instead, the NEFF program was used to calculate the efficiency curves based on the geometric parameters of the detector, photoresponse curve, and energy threshold. These calculated efficiency curves were validated against the available experimental data for similar systems, ensuring their reliability for TOF spectrum normalization.

Simulation of leakage neutron TOF spectrum

To evaluate the accuracy of Zr isotope data in various nuclear data libraries, we replaced the ^natZr material cards in the MCNP simulations. ^natZr consists of isotopes ⁹⁰Zr, ⁹¹Zr, ⁹²Zr, ⁹⁴Zr, and ⁹⁶Zr, with proportions of 51.54%, 11.22%, 17.15%, 17.38%, and 2.8%, respectively. Evaluated nuclear data for these isotopes were sourced from the CENDL-3.2, ENDF/B-VIII.0, JEFF-3.3, and JENDL-5 libraries. The ENDF/B-VIII.0 library was used for all other materials, including Cu in the target structure, polyethylene, Fe, and Pb in the collimation system, etc. This ensured that any differences in the TOF spectra originated solely from ^natZr nuclear data.

After normalization using the calculated detector efficiency curves, the simulated TOF spectra were directly compared with the experimental results, providing insights into the accuracy of the nuclear data evaluations.

Verifying the system with a standard sample

To ensure the reliability of the experimental measurement and data acquisition systems, we conducted a validation study by comparing the simulated and experimental results of the n-p scattering peaks using a polyethylene sample. The leakage neutron spectra from the polyethylene sample were experimentally measured at scattering angles of 47°, 61°, and 79°. The measured spectra were compared with the simulated results obtained using four evaluated nuclear data libraries: CENDL-3.2, ENDF/B-VIII.0, JEFF-3.3, and JENDL-5. The results are shown in Fig. 8. The close agreement between the experimental measurements and simulated results confirmed the accuracy and reliability of the measurement system, data acquisition setup, and subsequent data processing procedures employed throughout the study.

Fig. 8Full-screen View

(Color online) Comparisons of the measured and simulated leakage TOF spectra from the polyethylene sample

Uncertainties analysis

The experimentally measured TOF spectrum of leaked neutrons must be normalized before it can be compared with simulation results; the normalized TOF spectrum is given by Eq. (3):(3)where

Therefore, the main sources of error include the following:

Measurement results of the Zr samples

The leakage neutron TOF spectra of ^natZr samples with three thicknesses at six angles were measured in the experiment, resulting in 18 sets of data. The results for the three thicknesses are shown in Figs. 9, 10, and 11 for comparison with the leakage neutron spectra simulated by MCNP based on CENDL-3.2, ENDF/B-VIII.0, JEFF-3.3, and JENDL-5 libraries.

Fig. 9Full-screen View

(Color online) Comparison between calculated and measured leakage spectra of the 6 cm ^natZr sample

Fig. 10Full-screen View

(Color online) Comparison between calculated and measured leakage spectra of the 12 cm ^natZr sample

Fig. 11Full-screen View

(Color online) Comparison between calculated and measured leakage spectra of the 18 cm ^natZr sample

By comparing the calculated and experimental leakage neutron spectra, the following observations were made:

1. At approximately 156 ns, the simulation results of the CENDL-3.2 library slightly underestimated the experimental results at small angles (below 79°) but significantly overestimated them at large angles.

2. At approximately 164 ns, the simulation results of CENDL-3.2 and JEFF-3.3 libraries were higher than the experimental results across all angles, whereas the simulation of ENDF/B-VIII.0 library was lower than the experimental results at small angles (47°, 58°, and 61°).

3. The simulation results for CENDL-3.2 and JEFF-3.3 libraries were lower than the experimental results for 300 ns–500 ns.

4.3.1

Change in C/E values with TOF

C/E values were obtained by dividing the simulation results from the CENDL-3.2 library by the experimental data. The variation in C/E with TOF is shown in Fig. 12. As indicated, between 145 and 160 ns at small angles (47°, 58°, and 61°), the simulation results were slightly lower than the experimental values, whereas at larger angles, they were clearly higher. Near 164 ns, the simulation results exceeded the experimental values; however, between 250 and 550 ns, the simulation results were lower than the experimental values.

Fig. 12Full-screen View

(Color online) C/E values calculated from the simulation results of the CENDL-3.2 library

Similarly, C/E values were obtained by dividing the simulation results from the ENDF/B-VIII.0 library by the experimental data. The variation in C/E with TOF is shown in Fig. 13. As the figure shows, between 145 and 160 ns, the simulation results are higher than the experimental values; however, between 160 ns and 250 ns, most of the simulation results were lower than the experimental values.

Fig. 13Full-screen View

(Color online) C/E values calculated from the simulation results of the ENDF/B-VIII.0 library

For the JEFF-3.3, the variation in C/E with TOF is shown in Fig. 14. As shown, between 145 and 160 ns, the simulation results were higher than the experimental values, particularly at smaller angles (≤79°). Between 300 and 500 ns, the simulation results were lower than the experimental values, and this discrepancy was even more pronounced at larger angles.

Fig. 14Full-screen View

(Color online) C/E values calculated from the simulation results of the JEFF-3.3 library

For the JENDL-5 library, the variation in C/E with TOF is shown in Fig. 15. As shown, between 145 and 150 ns, at smaller angles (<101°), the simulation results exceeded the experimental values. Between 220 and 400 ns, at larger angles (>119°), the simulation results were lower than the experimental values.

Fig. 15Full-screen View

(Color online) C/E values calculated from the simulation results of the JENDL-5 library

4.3.2

Comparison of C/E values in different energy regions

Discrepancies exist between simulations from different libraries and experimental results. These differences are caused by variations in the reaction cross-sections related to secondary neutron production in each library. Analyzing these discrepancies can help identify potential limitations within libraries.

Using NDPlot [38] software developed by the China Nuclear Data Center, we obtained the secondary neutron energy spectra and energy spectra of different reaction channels produced by 14.5 MeV neutrons incident on ^natZr samples from the CENDL-3.2 library. The results, shown in Fig. 16, were derived by inputting the proton number, mass number of the target nucleus, and the energy of the incident particle.

Fig. 16Full-screen View

(Color online) Secondary neutron energy spectrum produced by 14.5 MeV incident neutrons on ^natZr sample from the CENDL-3.2 library

According to the contribution of different reaction channels to the total cross-section, the entire energy region can be divided into the following intervals:

Elastic scattering interval (n, el): 13.4-15MeV.

Discrete energy level inelastic scattering interval (n, inl)D: 10.6-13.4MeV.

Continuous energy level inelastic scattering interval (n, inl)C: 4.0-10.6MeV.

(n, 2n) reaction interval: 0.8-4.0MeV.

These energy intervals correspond to TOF intervals at different angles, as listed in Table 3.

Table 3Full-screen View

TOF regions of each reaction channel at different angles

Angle (°)	(n, el) (ns)	(n, inl)D (ns)	(n, inl)C (ns)	(n, 2n) (ns)
47	147–155	155–173	173–277	277–610
58	147–156	156–174	174–279	279–616
61	148–156	156–174	174–280	280–618
73	148–157	157–175	175–282	282–623
79	149–157	157–176	176–283	283–626
101	151–159	159–178	178–287	287–635
107	152–160	160–179	179–288	288–638
119	154–162	162–182	182–292	292–644
122	154–163	163–182	182–293	293–646
133	157–166	166–185	185–297	297–654

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To analyze the cross-section data of different reaction channels, we calculated the C/E values for the measurements of samples with different thicknesses at different angles and compared them with the simulation results of CENDL-3.2, ENDF/B-VIII.0, JEFF-3.3, and JENDL-5 libraries, as shown in Table 4.

Table 4Full-screen View

C/E value of each reaction channel for four libraries

Thickness–Angle	Reaction channel	CENDL-3.2	ENDF/B-VIII.0	JEFF-3.3	JENDL-5
6 cm–47°	(n, el)	0.923 ± 0.030	1.183 ± 0.039	1.152 ± 0.037	1.093 ± 0.036
	(n, inl)D	1.106 ± 0.038	0.764 ± 0.026	1.128 ± 0.038	1.040 ± 0.035
	(n, inl)C	0.902 ± 0.029	0.908 ± 0.029	0.998 ± 0.032	1.032 ± 0.033
	(n, 2n)	0.917 ± 0.029	0.980 ± 0.031	0.940 ± 0.030	1.002 ± 0.032
6 cm–61°	(n, el)	0.853 ± 0.028	1.217 ± 0.040	1.192 ± 0.039	1.107 ± 0.036
	(n, inl)D	1.208 ± 0.041	0.816 ± 0.028	1.199 ± 0.041	1.061 ± 0.036
	(n, inl)C	0.930 ± 0.030	0.944 ± 0.030	1.029 ± 0.030	1.075 ± 0.035
	(n, 2n)	0.933 ± 0.030	1.008 ± 0.032	0.950 ± 0.030	1.017 ± 0.032
6 cm–79°	(n, el)	1.243 ± 0.044	1.377 ± 0.048	1.275 ± 0.045	1.233 ± 0.043
	(n, inl)D	1.084 ± 0.038	0.820 ± 0.029	1.043 ± 0.037	0.986 ± 0.035
	(n, inl)C	0.980 ± 0.032	1.000 ± 0.032	1.020 ± 0.033	1.068 ± 0.035
	(n, 2n)	0.942 ± 0.030	1.039 ± 0.033	0.951 ± 0.030	1.026 ± 0.033
6 cm–101°	(n, el)	1.226 ± 0.044	1.178 ± 0.042	1.128 ± 0.040	1.064 ± 0.038
	(n, inl)D	1.254 ± 0.048	0.893 ± 0.034	1.240 ± 0.045	1.140 ± 0.043
	(n, inl)C	1.016 ± 0.033	1.036 ± 0.034	0.984 ± 0.032	1.022 ± 0.033
	(n, 2n)	0.969 ± 0.031	1.056 ± 0.033	0.968 ± 0.031	1.047 ± 0.033
6 cm–119°	(n, el)	1.394 ± 0.050	1.202 ± 0.043	1.113 ± 0.041	1.087 ± 0.039
	(n, inl)D	1.180 ± 0.044	0.826 ± 0.031	1.120 ± 0.042	0.964 ± 0.036
	(n, inl)C	0.984 ± 0.032	0.977 ± 0.032	0.911 ± 0.029	0.937 ± 0.030
	(n, 2n)	0.924 ± 0.029	0.991 ± 0.031	0.916 ± 0.029	0.988 ± 0.031
6 cm–133°	(n, el)	1.477 ± 0.057	1.188 ± 0.046	1.155 ± 0.045	1.100 ± 0.042
	(n, inl)D	1.327 ± 0.053	0.866 ± 0.035	1.135 ± 0.046	0.972 ± 0.039
	(n, inl)C	0.950 ± 0.031	0.953 ± 0.031	0.869 ± 0.028	0.884 ± 0.029
	(n, 2n)	0.900 ± 0.029	0.958 ± 0.030	0.896 ± 0.028	0.957 ± 0.030
12 cm–47°	(n, el)	0.965 ± 0.031	1.220 ± 0.040	1.147 ± 0.037	1.087 ± 0.035
	(n, inl)D	1.090 ± 0.038	0.822 ± 0.028	1.152 ± 0.040	1.090 ± 0.038
	(n, inl)C	0.917 ± 0.030	0.928 ± 0.030	0.990 ± 0.032	1.018 ± 0.033
	(n, 2n)	0.910 ± 0.029	0.997 ± 0.032	0.928 ± 0.029	0.989 ± 0.031
12 cm–58°	(n, el)	0.906 ± 0.030	1.215 ± 0.040	1.172 ± 0.039	1.096 ± 0.036
	(n, inl)D	1.180 ± 0.042	0.851 ± 0.030	1.204 ± 0.043	1.123 ± 0.040
	(n, inl)C	0.887 ± 0.029	0.929 ± 0.030	0.972 ± 0.031	1.006 ± 0.032
	(n, 2n)	0.883 ± 0.028	0.976 ± 0.031	0.899 ± 0.028	0.965 ± 0.031
12 cm–73°	(n, el)	0.972 ± 0.032	1.168 ± 0.039	1.132 ± 0.038	1.059 ± 0.035
	(n, inl)D	1.037 ± 0.036	0.774 ± 0.027	1.079 ± 0.038	1.037 ± 0.036
	(n, inl)C	0.931 ± 0.030	0.984 ± 0.032	1.004 ± 0.032	1.019 ± 0.033
	(n, 2n)	0.897 ± 0.028	0.997 ± 0.032	0.911 ± 0.029	0.981 ± 0.031
12 cm–107°	(n, el)	1.199 ± 0.041	1.130 ± 0.039	1.099 ± 0.038	1.018 ± 0.035
	(n, inl)D	1.109 ± 0.038	0.863 ± 0.030	1.109 ± 0.038	0.998 ± 0.034
	(n, inl)C	0.970 ± 0.031	0.995 ± 0.032	0.935 ± 0.030	0.965 ± 0.031
	(n, 2n)	0.904 ± 0.029	0.993 ± 0.031	0.905 ± 0.029	0.980 ± 0.031
12 cm–122°	(n, el)	1.178 ± 0.041	1.048 ± 0.036	1.016 ± 0.035	0.965 ± 0.033
	(n, inl)D	1.185 ± 0.043	0.875 ± 0.032	1.095 ± 0.040	0.988 ± 0.036
	(n, inl)C	0.893 ± 0.029	0.917 ± 0.029	0.839 ± 0.027	0.864 ± 0.028
	(n, 2n)	0.859 ± 0.027	0.931 ± 0.029	0.859 ± 0.027	0.925 ± 0.029
12 cm–133°	(n, el)	1.542 ± 0.057	1.258 ± 0.046	1.211 ± 0.045	1.138 ± 0.042
	(n, inl)D	1.168 ± 0.042	0.815 ± 0.030	1.034 ± 0.038	0.896 ± 0.033
	(n, inl)C	0.892 ± 0.029	0.913 ± 0.029	0.834 ± 0.027	0.837 ± 0.027
	(n, 2n)	0.856 ± 0.027	0.920 ± 0.029	0.854 ± 0.027	0.916 ± 0.029
18 cm–47°	(n, el)	0.958 ± 0.031	1.203 ± 0.039	1.107 ± 0.036	1.084 ± 0.035
	(n, inl)D	1.088 ± 0.037	0.776 ± 0.027	1.113 ± 0.038	1.063 ± 0.036
	(n, inl)C	0.886 ± 0.029	0.940 ± 0.030	1.003 ± 0.032	1.021 ± 0.033
	(n, 2n)	0.902 ± 0.029	1.014 ± 0.032	0.919 ± 0.029	0.984 ± 0.031
18 cm–58°	(n, el)	0.978 ± 0.032	1.282 ± 0.042	1.187 ± 0.039	1.129 ± 0.037
	(n, inl)D	1.164 ± 0.040	0.838 ± 0.029	1.181 ± 0.041	1.082 ± 0.037
	(n, inl)C	0.862 ± 0.028	0.912 ± 0.029	0.951 ± 0.031	0.985 ± 0.032
	(n, 2n)	0.851 ± 0.027	0.959 ± 0.030	0.865 ± 0.027	0.927 ± 0.029
18 cm–73°	(n, el)	0.955 ± 0.031	1.208 ± 0.040	1.158 ± 0.038	1.055 ± 0.035
	(n, inl)D	1.042 ± 0.035	0.786 ± 0.027	1.095 ± 0.037	1.043 ± 0.035
	(n, inl)C	0.946 ± 0.030	1.004 ± 0.032	1.030 ± 0.033	1.053 ± 0.034
	(n, 2n)	0.925 ± 0.029	1.038 ± 0.033	0.942 ± 0.030	1.009 ± 0.032
18 cm–107°	(n, el)	1.288 ± 0.043	1.261 ± 0.042	1.208 ± 0.041	1.105 ± 0.037
	(n, inl)D	1.181 ± 0.041	0.900 ± 0.031	1.162 ± 0.040	1.036 ± 0.036
	(n, inl)C	0.975 ± 0.031	1.013 ± 0.032	0.973 ± 0.031	0.990 ± 0.032
	(n, 2n)	0.941 ± 0.030	1.048 ± 0.033	0.945 ± 0.030	1.021 ± 0.032
18 cm–122°	(n, el)	1.205 ± 0.040	1.120 ± 0.038	1.056 ± 0.035	0.996 ± 0.033
	(n, inl)D	1.212 ± 0.042	0.893 ± 0.031	1.148 ± 0.040	1.016 ± 0.036
	(n, inl)C	0.939 ± 0.030	0.965 ± 0.031	0.891 ± 0.029	0.918 ± 0.029
	(n, 2n)	0.897 ± 0.028	0.980 ± 0.031	0.896 ± 0.028	0.969 ± 0.031
18 cm–133°	(n, el)	1.525 ± 0.054	1.259 ± 0.045	1.197 ± 0.043	1.141 ± 0.041
	(n, inl)D	1.222 ± 0.044	0.884 ± 0.033	1.135 ± 0.041	0.997 ± 0.036
	(n, inl)C	0.931 ± 0.030	0.956 ± 0.031	0.869 ± 0.028	0.883 ± 0.028
	(n, 2n)	0.885 ± 0.028	0.958 ± 0.030	0.883 ± 0.028	0.949 ± 0.028

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4.3.3

Variation in C/E values with angles

The variation in the C/E values with angle for different reaction channels of various thicknesses is illustrated in Fig. 17, from which the following can be observed.

Fig. 17Full-screen View

(Color online) Variation in C/E values with angles

1. In the elastic scattering energy range, the C/E values for ENDF/B-VIII.0, JEFF-3.3, and JENDL-5 libraries showed little variation with the angle. In contrast, the C/E values from the CENDL-3.2 library increased as the angle increased. Although initially lower than those of the other three databases at smaller angles (47°, 58°, 61°, and 73°), the C/E values of CENDL-3.2 library eventually surpassed those at larger angles.

2. In the discrete-level inelastic scattering energy range, the C/E values from the ENDF/B-VIII.0 library were noticeably lower than those from the other three libraries at all angles. Except for 122° and 133°, the C/E values of the CENDL-3.2 and JENDL-5 libraries remained close to each other and exceeded 1 across all angles.

3. In the continuous-level inelastic scattering energy range, the C/E values of the CENDL-3.2 and ENDF/B-VIII.0 libraries exhibited a slight increasing trend with angle, whereas those of the JEFF-3.3, and JENDL-5 libraries exhibited a slight decreasing trend. At 101° and 107°, the C/E values from all the four libraries were the most similar.

4. In the (n, 2n) energy range, the C/E values of all four libraries exhibited little angular dependence. Compared with the ENDF/B-VIII.0 and JENDL-5 libraries, the C/E values from the CENDL-3.2 and JEFF-3.3 libraries were relatively lower.

4.3.4

Analysis and discussion

To further analyze the causes of the discrepancies in the C/E values observed across different databases, we employed the NDplot program to obtain secondary neutron energy spectra, double-differential cross-sections, and angular distributions for various reaction channels resulting from 14.5 MeV neutrons incident on ^natZr, as illustrated in Fig. 18.

Fig. 18Full-screen View

(Color online) Information of secondary neutron generated by 14.5 MeV neutrons incident on ^natZr. (a) (n, el) reaction channel angular distribution. (b) (n, inl)D reaction channel angular distribution. (c) (n, inl)C reaction channel angular distribution. (d) (n, 2n) reaction channel energy spectrum

1. The angular distribution curves of the (n, el) reaction were extracted from all four libraries and compared (Fig. 18(a)). At smaller angles, the cross-section values from the ENDF/B-VIII.0, JENDL-5, and JEFF-3.3 libraries were significantly higher than those from the CENDL-3.2 library. However, at larger angles, the CENDL-3.2 library exhibited higher cross-section values than the other three. This was likely the main reason why, in the elastic scattering energy range, the simulations from all libraries, except for the CENDL-3.2 library, overestimated the experimental results at small angles, and all four libraries overestimated at larger angles.

2. Figure 18(b) shows the angular distribution curves of the (n, inl)D reaction extracted from the four libraries. The (n, inl)D reaction cross-section was obtained by summing the cross-sections of the 40 reaction channels (MT = 51 to 90). At all angles, the cross-section values from the CENDL-3.2 and JEFF-3.3 libraries were relatively high, whereas those from the ENDF/B-VIII.0 library were the lowest. This likely explains why the simulation results from the CENDL-3.2 and JEFF-3.3 libraries in the discrete-level inelastic scattering energy range were higher than the experimental values, whereas those from the ENDF/B-VIII.0 library were lower.

3. The angular distribution curves of the (n, inl)C reaction extracted from the four libraries are shown in Fig. 18(c). The cross-section values of the JEFF-3.3 library decreased noticeably with increasing angle. This was likely the main reason the simulations from JEFF-3.3 library underestimated the experimental results at large angles in the continuous-level inelastic scattering energy range.

4. Figure 18(d) shows the (n, 2n) reaction energy spectra extracted from the four libraries. The cross-section values from the CENDL-3.2 and JEFF-3.3 libraries were lower than those from the ENDF/B-VIII.0 and JENDL-5 libraries. This is likely the main reason why the simulation results from the CENDL-3.2 and JEFF-3.3 libraries were lower than the experimental results in the (n, 2n) energy range.