Neutron source

The neutron source was produced using a 400 kV Cockcroft–Walton accelerator at CIAE, which were generated at the tritium–titanium (T-Ti) target with a surface density of 1.2 mg/cm² via bombardment of a pulsed deuteron (D⁺) beam. During the experiment, the energy and average current were 300 keV and 20 μA, respectively, at a repetition rate of 1.5 MHz. The neutron pulse width was as narrow as approximately 2 ns. The energy of the pulsed neutrons was approximately 14.5 MeV, with a yield of 2×10⁹ n/s at the target. An associated particle system at 135° was established to measure the yield of the neutrons, which majorly included a silicon surface-barrier detector (SSD). Although neutrons are produced through the T(d, n)⁴He reaction, alpha particles are produced at the reverse angle. The silicon detector was used to measure alpha particles in the $\text{Δ}\text{Ω}$ solid angle at angle $\phi$ to the incident D⁺ beam, and ${\varphi }_n\left(\theta ,E_d\right)$ is the neutron flux in the unit solid angle at angle θ to the incident D⁺ beam. These parameters can be calculated using Eqs. (2) and (3) [35, 36]: ${\varphi }_n\left(\theta ,E_d\right)=\frac{N_{\alpha }}{\text{Δ}\text{Ω}}\times A_{\alpha },$ (1) $\text{Δ}\text{Ω}=\frac{\pi \times r^2}{L^2},$ (2) where E_d is the average energy of deuteron ions participating in the reaction to produce neutrons in the T-Ti target, N_α is the count of alpha particles measured at angle $\phi$, A_α is the corrective factor related to the energy of the D⁺ beam and the emission angle of $\text{α}$ particles. $\text{Δ}\text{Ω}$ is the solid angle of the silicon detector subtending the T-Ti target, r is the radius of the aperture to limit the solid angle in front of the silicon detector, and L is the distance between the aperture and the target.

The relationship between the neutron flux in the unit solid angle at angles θ, ${\varphi }_n\left(\theta ,E_d\right)$, expressed by Eq. (1), and the neutron yield is expressed as follows: $\frac{{\varphi }_{\text{n}}\left(\theta \right)}{N_{\text{n}}}=\frac{\sigma \left(\theta \right)}{{\sigma }_{\text{tot}}},$ (3) where σ_tot is the total cross-section of the D-T reaction, σ(θ) is the differential cross-section of the D-T reaction at angle θ. By substituting Eq. (1) into Eq. (3), the yield of neutrons can be obtained using Eq. (4): $N_n=\frac{N_{\alpha }\times A_{\alpha }\times {\sigma }_{\text{tot}}}{\text{Δ}\text{Ω}\times \sigma \left(\theta \right)}$ (4)

Here, the energy of the D⁺ beam was approximately 300 keV, and E_d was approximately 147 keV. The alpha particles were measured at 135° ($\phi =135°$).When the neutron was emitted at 0° ($\theta =0°$), σ_tot was 3984 mb, σ(θ) was 336 mb/sr, and A_α was assumed to be 1.263. The radius of the aperture was approximately 0.16 cm, and the distance between the limiting aperture and T-Ti target was approximately 90 cm. The expression, $N_n=N_{\alpha }\times 1.508\times {10}^6$, can be obtained. Therefore, as long as the number of ⁴He particles is accurately measured, it is logical to calculate the number of neutrons.

Samples

The slab samples used in the experiment included one polyethylene sample and three ²³⁸U samples. Polyethylene was used as a standard sample to test the reliability of the system; its purity was higher than 99.9%.The purity of the ²³⁸U sample was higher than 99.37%. Further descriptions of the ²³⁸U samples are provided in Table 2.

Collimator

During the experiment, neutrons interacted not only with the ²³⁸U sample, but also with other devices in the laboratory. These neutrons entered the detector after scattering and forming background counts. Shields and collimators were used in the experiment to minimize the influence of the background and scattered neutrons on the experimental results [37]. As shown in Fig.1, a precollimator consisting of iron, polyethylene, and lead was set between the experimental sample and concrete wall along the flight path of the neutrons. The other collimator was placed inside a 2-m-thick concrete wall made of the same materials as the precollimator. A shadow bar was placed between the experimental sample and the precollimator along the flight path of the neutrons to eliminate the scattered background neutrons generated during the interaction between the source and the collimator. By using the shadow bar, precollimator, and wall collimator, the background spectrum (sample-out) measured during the experiment was significantly lower than the effect spectrum (sample-in), and the foreground–background ratio increased significantly (Fig.2).

Fig. 2Full-screen View

(Color online) TOF measurement results at 60° and 120° under sample-in and sample-out conditions

Electronics system and data processing

A simplified diagram of the measurement circuit is shown in Fig. 3. The leakage neutron spectra measurements were conducted using a scintillation detector comprising a BC-501A scintillator with a diameter and thickness of 5.08 and 2.54 cm, respectively. The BC-501Asignal was divided into two outputs. One output entered the analog-to-digital converter as the pulse height (PH), and the other was used to determine the TOF and pulse shape discrimination (PSD). The TOF was derived by considering the anode signal as the start-time signal, and the beam pick-up signal from the accelerator was used as the stop signal after an appropriate delay. The PH was used for energy calibration to determine the detector threshold. The PSD was used for n-γ discrimination to eliminate γ-ray events.

Fig. 3Full-screen View

Block diagram of measuring circuits

Stilbene and BaF₂ scintillation crystals were used to detect the TOF spectra of the source neutrons and TOF spectra of associated gamma rays, respectively. After adequate processing of these spectra, the time distribution of the pulsed neutrons was obtained. The SSD signal was the output of the silicon detector and was used to obtain the alpha-particle count using the associated particle system. Digital data were recorded by event from the CAMAC module and analyzed offline.

In the experimental data processing, the data-taking software, Kmax, was used to obtain the initial TOF spectra of the leakage neutrons after selecting an appropriate PH threshold and neutron events via offline analysis. The initial spectra were then normalized to the neutron yields calculated based on the associated particle counts and BC-501A detector area. Hence, the final TOF spectra were in the neutron flux per unit neutron per unit area (cm^-2).

Description of neutron source

A description of the neutron source, which primarily includes the energy, angular, and pulsed-time distributions, is shown in Fig. 4. One of the calculations was performed using the TARGET [38] code, which was developed by PTB in Germany to express the energy and angular flux distributions of the neutron source. By inputting the values of the incident energy of the D⁺ beam, T/Ti ratio, and T-Ti target thickness, which in this study were 300 keV, 1.8, and 1.2 mg/cm², respectively, a calculated distribution that could be used in the MCNP simulation was obtained. The results are presented in Fig. 4a.

Fig. 4Full-screen View

(Color online) Description of D-T source in Monte Carlo simulation: (a) angular dependence of energy spectrum; (b) pulsed-time distribution

The pulsed-time distribution is a critical input parameter used in the simulation of the TOF spectrum and is described by a TME card in the MCNP code. It was obtained through a fitting process of the neutron spectra from the stilbene scintillation crystal and the γ spectra from the BaF₂ scintillation detector [39]. The fitting results for the pulsed-time distribution are presented in Fig. 4b.

Description of neutron detector (BC-501A)

The description of the BC-501A detector mainly includes the efficiency curve and size of the liquid scintillator detector. The efficiency of the BC-501A detector was determined by following these steps [40]. (1) The relative efficiency of BC-501A was measured using a ²⁵²Cf neutron source. (2) The absolute efficiency was calibrated using a D-D neutron, and the results were used to normalize the relative efficiencies. (3) The efficiency was calculated using the NEFF code[41], and the results were validated using the experimental measurement results presented subsequently. The light output function used in the calculation was calibrated with neutrons generated via the ⁹Be(d, n)¹⁰B reaction using a 2×1.7 MV Tandem accelerator at the CIAE. Figure 5 shows the shapes of the efficiency curves for different threshold values. The calculations are in good agreement with the measurements.

Fig. 5Full-screen View

(Color online) Detection efficiency curves of BC-501A liquid detector with different thresholds

Detector size refers to the area and thickness of the detector. The detector can be regarded as a surface detector because its thickness was only 2.54 cm, which is significantly shorter than the flight distance of 8 m. Therefore, a ring detector estimator with a diameter of 5.08 cm was used in the MCNP-4C code.

Simulation of MCNP program

The benchmark model for the two measured angles used in the simulation is shown in Fig.6[42].When calculating the leakage neutron spectra transmitted at 60°, the material of the sample cell at 120° was described on a material card assigned to air, whereas the sample cell at 60° was assigned to air for 120° calculations. Both sample cells were assigned to air for background simulation.

Fig. 6Full-screen View

(Color online) Geometry for MCNP simulation

The MCNP program was adopted to simulate the experiment and test the latest data of ²³⁸U in CENDL-3.2, ENDF/B-VIII.0, JENDL-5.0 and JEFF-3.3, with data files of other materials, such as targets, collimators, shields, and air taken from the ENDF/B-VIII.0 library. The ACE format data suitable for the MCNP code were processed using the NJOY99 program[43]. The number of simulated histories was 10⁹, making the statistical uncertainty for the calculation slower than 1% for each time bin. Based on these comparisons, it was easy to determine the differences between the four evaluated libraries.

Experimental system test on standard samples

The leakage neutron spectra measurements on standard sample (polyethylene) with measurement angles of 45° and 60° were first conducted to verify the reliability of data acquired using this experimental system [44]. The polyethylene sample was a rectangular slab with a 30 cm square base and 6 cm thickness.

The MCNP program was used to obtain the corresponding simulated results, and the data file was obtained from the ENDF/B-VIII.0 library. The results were analyzed to examine the simulations after background deduction and return. The results are plotted in Fig. 7, and the count values are listed in Table 3. The experimental results of the n-p elastic peak satisfactorily replicated the simulated results. This indicates that the processing of the experimental data is reasonable, and the system measurement data are reliable.

Fig. 7Full-screen View

Comparison between calculation results for polyethylene at 45° and 60° and experimental results

Uncertainty analysis of experimental data

Normalization of the initial experimental spectra can be performed not only based on the number of associated particles, but also based on the ratio of the area of the n-p elastic peak between the experimental and simulated results. The normalized coefficient, B¹, can be determined using Eq. (5): $N_{\text{n}}=\frac{N_{\text{p}}^{\text{e}}}{N_{\text{p}}^{\text{c}}}=B^1\times N_{\alpha }^{\text{p}},$ (5) where ${\text{N}}_{\text{p}}^{\text{e}}$ is the count of neutrons (n-p scattering) on polyethylene, $N_{\text{p}}^{\text{c}}$ is the count of neutrons (n-p scattering) on polyethylene calculated using MCNP (unit source neutron), and $N_{\alpha }^{\text{p}}$ is the count of associated $\alpha$ on polyethylene.

The initial experimental spectra on ²³⁸U sample can be normalized using Eq. (6): $\frac{N_{\text{U}}^{\text{e}}}{N_{\text{n}}}=\frac{N_{\text{U}}^{\text{e}}}{B^1\times N_{\alpha }^{\text{p}}}=\frac{N_{\text{U}}^{\text{e}}\times N_{\text{p}}^{\text{c}}\times N_{\alpha }^{\text{p}}}{N_{\alpha }^{\text{U}}\times N_{\text{p}}^{\text{e}}},$ (6) where $N_{\text{U}}^{\text{e}}$ is the count of neutrons on ²³⁸U (unit time bin), and $N_{\alpha }^{\text{U}}$ is the count of associated $\alpha$ on ²³⁸U.

Most systematic uncertainties in ²³⁸U measurements can be eliminated by normalizing the experimental data with the standard sample, as expressed by Eq. (6), which includes uncertainties in the absolute efficiency of the BC-501A detector (3%) and the ambiguity of the solid angle for associated particle detection. Finally, the total uncertainty of the experimental results consisted of the remaining systematic and statistical uncertainties. The statistical uncertainty from the neutron count from ²³⁸U was better than 3% over 80% points. The others are listed in Table 4.

Results and analysis

Leakage neutron spectra measurements were performed at 60° and 120° on slab ²³⁸U using D-T neutrons. The measurements were compared with the predictions of the MCNP calculations using four evaluated neutron libraries. The comparison showed that differences existed between the simulation and measurement results. In particular, the simulation with the CENDL-3.2 library was significantly higher than the experimental results between 200 and 400 ns (Fig. 8).

Fig. 8Full-screen View

(Color online) Comparison between calculated and measured leakage spectra on ²³⁸U sample with thicknesses of 3, 6, and 9 cm at 60° and 120°

The discrepancies between the calculated and experimental results are considered to be attributed to the reaction cross-sections associated with the production of secondary neutrons in different libraries. NDplot was used to plot the experimental and evaluated data in the neutron libraries. The ND-plot program is a simple and efficient software application for nuclear data [45]. By inputting the proton number, mass number, incident particle type, energy, and other information about the target nucleus, experimental and evaluated data, such as the reaction cross-section, secondary particle angle distribution, secondary particle energy distribution, and secondary particle energy angle distribution, can be obtained. The secondary neutrons produced through the interaction between the D-T neutrons (approximately 14.5MeV) and²³⁸U are presented in Fig. 9, which generally consist of neutrons scattered via elastic and inelastic scattering, and neutrons produced through fission reactions (n, f), (n, 2n), and (n, 3n).

Fig. 9Full-screen View

(Color online) Energy spectra of secondary neutrons after interaction between14.5MeV neutronsand²³⁸U sample at (a) 60° and (b) 120°.The data was retrieved from the CENDL-3.2 library

Based on the different energy regions mainly contributed by different reactions, the neutron energy spectra can be divided into four energy regions: (1) 12 < E_n < 16 MeV, which consist of neutrons scattered by elastic (n, el) and inelastic discrete-level ((n, inl)d) reactions; (2) 8.5 < E_n < 12 MeV, in which the neutrons are mainly from inelastic continuum scattering ((n, inl)C) and total fission reaction (n, f); (3) 3 < E_n < 8.5 MeV, which consists of emitted neutrons from (n, f) and production of two-neutron (n,2n) reactions; (4) 0.8 < E_n < 3 MeV, which consists of emitted neutrons from (n, f), (n,2n), and (n, 3n) reactions and multiple neutron scattering.

The simulated and experimental results of the leakage neutron spectra were integrated according to the above four energy regions, and the C/E ratios of the different libraries were obtained by comparing the simulated and experimental results. The C/E ratios of the four nuclear data libraries are listed in Table 5.

Based on the C/E ratios, some deviations were observed between the simulated and experimental results.

(1) In the 12 < E_n < 16 MeV region, the neutrons from elastic scattering were predominant at 60°, whereas at 120°, the neutrons from inelastic discrete-level scattering were predominant. The simulations with CENDL-3.2 yielded considerable overestimations in both directions, particularly in the direction of 120°, which reached approximately 80%. The simulations with JEFF-3.3 and ENDF/B-VIII.0 satisfactorily reproduced the measurements at 60°; however, in the direction of 120°, overestimations of approximately 20% and 30% were obtained, respectively. The simulations with JENDL-5.0 accurately predicted the experimental values at both angles.

(2) The angular distributions of secondary neutrons from (n, el) and (n, inl)d reactions after the interaction of the 14.5-MeV neutron with the²³⁸U sample are shown in Fig.10a and 10b, respectively, and the cross-sections of different libraries at 60° and 120° are listed in Table 6.The (n, el) and (n, inl)d cross-sections at 14.5 MeV in the CENDL-3.2 file are larger than those from the other three libraries at both angles. In particular, the data for the (n, el) reaction reaches 7.86×10^-3 b at 120°, which is significantly higher than that in the JENDL-5.0 file (2.50×10^-3 b). The larger (n, inl)d cross-section (9.42×10^-3 b) in the ENDF/B-VIII.0 file results in the overestimation of the calculations at 120° in this region. The overestimation of the calculations with the JEFF-3.3 file at 120° is principally because of the larger (n, el) cross-section (3.51×10^-3 b) in it.

Fig. 10Full-screen View

(Color online) Angular distribution of secondary neutron from different reactions for²³⁸U at 14.5 MeV, retrieved from four data files: (a) elastic scattering (n, el), (b) inelastic discrete-level scattering (n, inl)d, and (c)inelastic continuum scattering (n, inl)C

(3) In the 8.5 < E_n < 12 MeV region, the simulations with the CENDL-3.2 file showed a good agreement with the measured spectra at 60° but yielded an overestimation of approximately 30% at 120°. However, the simulations with ENDF /B-VIII.0 was consistent with the measurements at 120° but yielded an underestimation of approximately 20% at 60°. The calculations with the JENDL-5.0 file somewhat replicated the measured spectra at 60° but gave a slight overestimation at 120°. The calculations with the JEFF-3.3 files lightly underestimated the measurements at 60° but accurately predicted the measurement results at 120°.

(4) The angular and energy distributions of secondary neutrons from the (n, inl)C reaction after the interaction of the 14.5-MeV neutron with ²³⁸U are shown in Figs.10c and 11a. The angular distribution and energy spectrum provided by the CENDL-3.2 file at 120° were lower than those of JENDL-5.0, but the calculations using CENDL-3.2 appeared to overestimate the production of neutrons more than the JENDL-5.0 calculations. This effect mainly resulted from the contribution by neutrons partly scattered by the (n, el) reaction in the 8.5–12 MeV energy region owing to the wider width of the pulsed beam from the measurements. The angular distribution of the secondary neutrons at 120° obtained by the CENDL-3.2 file was higher than those of the other libraries (Fig.10a).

Fig. 11Full-screen View

(Color online) Energy spectra of secondary neutrons from several reaction channels for ²³⁸U at 14.5 MeV, retrieved from four data files: (a) continuous-level elastic scattering (n, inl)C, (b) fission reaction (n, f), and (c) (n, 2n) reaction

(5) In the 3.0 < E_n < 8.5 MeV region, the simulations with ENDF/B-VIII.0, JENDL-5.0, and JEFF-3.3 libraries show good agreements with the measured leakage spectra. However, the results obtained with CENDL-3.2 significantly overestimated the measurement results at both 60° and 120°. The discrepancy between the measured spectrum and that calculated with the CENDL-3.2 file is mainly because the energy distributions of secondary neutrons from fission and the (n, 2n) reactions are harder than those in the other three libraries. As shown in Figs.11b and 11c, the shape of the energy spectrum of secondary neutrons from the fission reaction in CENDL-3.2was higher than those from other files in the 3–8 MeV energy interval but lower in the 0.8–3 MeV interval. Moreover, the spectrum from the (n, 2n) reaction in CENDL-3.2 was higher than those from other files in the 3.5–8 MeV interval but lower in the 1–3.5 MeV region.

(6) In the 0.8 < E_n < 3.0 MeV region, calculations performed using the four libraries accurately predicted the measurement results.

(7) Across the entire energy region (0.8–16 MeV), the calculation values obtained with the CENDL-3.2 file were slightly higher than the measurement values, and the C/E ratios were closer to 1 with an increase in sample thickness.

(8) A comparison between the measured spectra and those calculated with the CENDL-3.2 and JENDL-5.0 files was performed at each time bin, and the C/E ratios were plotted (Fig. 12). The C/E ratios of the leakage spectra calculated with the CENDL-3.2 file to the measured spectra tended to deviate from 1 over the high-energy region; however, the ratios became closer to 1with decreasing energy. The C/E ratios of the spectra calculated with the JENDL-5.0 file to the measured spectra are generally very close to 1 in most energy regions, except for those that are slightly higher than 1 at approximately 10 MeV.

Fig. 12Full-screen View

(Color online) C/E ratios for leakage neutrons leaking from ²³⁸U with transport calculations obtained usingCENDL-3.2 and JENDL-5.0 evaluated data files