Neutron source

The experiments were conducted on the D-T and D-D neutron sources.

A T-Ti target was bombarded with a pulsed deuteron beam accelerated to 300 keV using the CIAE Cockcroft–Walton accelerator, with a beam current of ~20 μA. The beam pulse was repeated frequently at a rate of 1.5 MHz, and its pulse width was as narrow as 2 ns at the full width at half maximum (FWHM). The energy of the pulsed neutron beam was 14.5 MeV with a yield of 2 × 10⁹ n/s. An associated particle system was installed at 12.2° using an Au-Si surface barrier semiconductor detector to monitor the neutron yield. Alpha particles were produced at opposite angles, although the T(d,n)⁴He reaction produces neutrons. The semiconductor detector was used to measure alpha particles in the ΔΩ solid angle at the ϕ angle to the incident deuteron beam, representing the neutron flux in the unit solid angle at the θ angle to the incident deuteron beam, which can be obtained by [32, 33] ${\varphi }_{\text{n}}\left(\theta \mathrm{,}{E}_{\text{d}}\right)=\frac{N_{\alpha }}{\text{Δ}\text{Ω}}\times A_{\alpha }\mathrm{,}$ (1) $\text{Δ}\text{Ω}=\frac{\pi \times r^2}{L^2}\mathrm{,}$ (2) where Nα represents the count of alpha particles measured at ϕ angle, Aα represents the correction factor related to the energy of the deuteron beam and the emission angle of the alpha particles, and ΔΩ represents the solid angle of the semiconductor detector subtending the T-Ti target, with r and L representing the radius of the aperture and the distance between the aperture and the target, respectively.

The relationship between ${\varphi }_{\text{n}}\left(\theta \mathrm{,}{E}_{\text{d}}\right)$, determined using Eq. (1), and the neutron yield from the T(d,n)⁴He reaction is given by $\frac{{\varphi }_{\text{n}}\left(\theta \right)}{N_{\text{n}}}=\frac{\sigma (\theta )}{{\sigma }_{\text{tot}}}\mathrm{,}$ (3) where N_n, σ_tot, and $\sigma (\theta )$ represent the source neutron yield and the total cross-section of T(d,n)⁴He reaction and differential cross section of T(d,n)⁴He reacts at the θ angle, respectively. Substituting Eqs. (1) and (2) into Eq. (3), we can calculate the number of neutrons produced by the T(d,n)⁴He reaction using $N_{\text{n}}=\frac{N_{\alpha }\times A_{\alpha }\times {\sigma }_{\text{tot}}}{\text{Δ}\text{Ω}\times \sigma (\theta )}\mathrm{,}$ (4) The energy of the deuteron beam(E_d) for the D-T neutron source is ~300 keV, alpha particles are measured at 135°(ϕ=135°), neutrons are emitted at 0°(θ=0°), σ_tot is 3984 mb, $\sigma (\theta )$ is 336 mb/sr, and Aα is assumed to be 1.263. The radius of the aperture is ~0.160 cm, and the distance between the semiconductor detector and target was 90 cm. Based on this data, the relationship N_n= Nα × 1.508 × 10⁶ can be obtained.

The D-D neutron source was obtained by replacing the T-Ti target with a D-Ti target. The deuteron beam current was~30 μA with an energy of ~360 keV. The energy of the pulsed neutron beam was ~3.2 MHz with a yield of 4.5 × 10⁷ n/s. The neutron yield was measured using an associated particle system. For the D(d,n)³He reaction, the associated protons were measured using competing D(d,p)T reactions [34]. This is because the protons produced in the D(d, p)T reaction are easier to detect compared with the ³He from the D(d,n)³He reaction. The accompanying ³He particles have very low energy, approximately 0.9 MeV, making them easily drowned out by noise, whereas protons have relatively higher energy, approximately 3 MeV, which allows them to be completely separated from the noise. A semiconductor detector was used to measure protons in the ΔΩ solid angle at ϕ angle to the incident deuteron beam, representing the neutron flux in the unit solid angle at the θ angle to the incident deuteron beam, which can be obtained by [35] ${\varphi }_{\text{n}}\left(\theta \mathrm{,}{E}_{\text{d}}\right)=\frac{N_{\text{p}}}{\text{Δ}\text{Ω}}\times A_{\text{p}}\mathrm{.}$ (5) The neutron yield from the D(d,n)³He reaction is obtained by substituting Eq. (5) and (2) into Eq. (3). $N_{\text{n}}=\frac{N_{\text{p}}\times A_{\text{p}}\times {\sigma }_{\text{tot}}}{\text{Δ}\text{Ω}\times \sigma (\theta )}\mathrm{,}$ (6) where N_p represents the count of protons measured at ϕ angle and A_p represents the correction factor related to the energy of the deuteron beam, the emission angle of the protons, and the ratio of proton to neutron reaction cross-sections. σ_tot represents the total cross-section of the D(d,n)³He reaction, and $\sigma (\theta )$ represents the differential cross-section of the D(d,n)³He reaction at the θ angle.

For the D-D neutron source, the energy of the deuteron beam is ~360 keV, the associated particles are measured at 135°(ϕ=135°), with neutrons emitted at 0°(θ=0°), ${\sigma }_{tot}$ is 40.300 mb, $\sigma (\theta )$ is 6.800 mb/sr, and A_p is assumed to be 2.557. Consequently, the relationship N_n= Nα × 1.526 × 10⁶ can be obtained.

Sample

The slab samples used in the experiment included a polyethylene sample and three ^natPb samples. Polyethylene was used as a standard sample to test the reliability of the system, and its purity was ~>99.9%. Information on the ^natPb samples is listed in Table 1, and its purity is greater than 99.99%.

Collimator

The neutrons interacted with the ^natPb sample and several other devices in the laboratory. The shields and collimators used in the experiment reduced the effects of scattered neutrons and environmental background on the experimental results[36]. Figure 2 shows a pre-collimator comprising iron, polyethylene, and Pb set between the sample and detector. A shadow bar made of copper was fixed between the source neutrons and pre-collimator to eliminate the scattered neutron background generated by the interaction between the source neutrons and pre-collimator. Another collimator system was installed inside a concrete wall with a thickness of 2 m. Using a shadow bar, precollimator, and wall collimator, the background spectrum (sample-out) measured during the experiment was found to be significantly lower than the foreground spectrum (sample-in), as shown in Fig. 3. This effectively improved the foreground/background ratio by increasing it to approximately 20:1.

Fig. 3Full-screen View

(a)D-T and (b)D-D ToF spectra measured under the sample in and sample out conditions

Detectors, electronic system, and data processing

An electronic circuit diagram is shown in Fig. 4. The leakage spectra were measured using a BC501-A detector. The output of the BC501-A detector was split into two channels: the first channel was sent to an analog-digital converter as pulse height (PH) information, whereas the second channel was used to determine details about the ToF and pulse shape discrimination (PSD). The start-time signal obtained from the anode signal of the detector was used to determine the ToF, whereas the stop signal was produced with an appropriate delay using the pulse pick-up signal from the accelerator. In the offline analysis, PH and PSD were used to determine the detection threshold and distinguish between the n and γ signals, respectively.

Fig. 4Full-screen View

Electronic circuit diagram for the experiment

An SSC and BaF₂ scintillation crystal were used to detect the ToF spectra of the source neutrons and the associated gamma rays, respectively. By appropriately processing these spectra, the pulsed time distribution of the source neutrons was obtained. The SSD signal was the output of the semiconductor detector, which was used to obtain the count of associated particles as alpha particles or protons. All events from these detectors were recorded using the CAMAC data acquisition system. The Kmax software was used to obtain the initial leakage neutron ToF spectra after selecting an appropriate PH threshold and selecting neutron events by offline analysis. The initial spectra were normalized using neutron yields calculated from the count of the associated particles and the area of the BC501-A detector.

Description of the neutron source

The neutron source characteristics include the energy spectra, angular flux, and pulsed time distributions. The T/Ti or D/Ti ratio, energy of the incident deuteron, energy distribution, and angular flux distribution were calculated based on the thickness of the T-Ti or D-Ti target using the TARGET [37] program developed by PTB in Germany. The thickness of the T-Ti and D-Ti targets used in the experiment was ~1 mg cm^-2, the T/Ti and D/Ti ratios were ~1.8, and the incident energy of the deuteron beam was 300 keV(D-T) or 360 keV(D-D). The results calculated using the TARGET program are shown in Fig. 5a and b.

Fig. 5Full-screen View

(Color online) (a) The angle dependent energy distributions of D-T source (b) The angle dependent energy distributions of D-D source (c) The distributions of pulsed time (d) The neutron efficiency curves of BC501A

The MCNP process requires an accurate pulse time distribution in the TME card. The accuracy of the pulse time distribution is extremely important for the final simulation of the ToF spectrum. Figure 5(c) shows the neutron ToF spectrum measured using stilbene and the gamma ToF spectrum measured using BaF₂. A new curve was fitted with an iterative algorithm using the SAND-II algorithm and the GRV-MC32 unfolding program [38]. In the processing procedure, the neutron ToF spectrum measured by the SSC detector served as the input spectrum, wherein the FWHM was larger than the actual pulse width owing to the structural characteristics of the neutron energy spectrum at 0°. The gamma ToF spectrum detected by the BaF₂ detector was used as the default spectrum in the iterative algorithm. The fitting results were compared with the input and default spectra in Fig. 5(c), demonstrating that the bottom shape is similar to that of the input shape, whereas the peak shape of the fitting spectrum is similar to that of the default shape [39]. The final fitting spectrum provides a better description of the neutron pulse time distribution.

Description of the detector

This section describes the efficiency curve calibration and size specifications of the BC501-A liquid detector. The efficiency curve was determined experimentally using the following method [40]: (1) The relative efficiency curve was obtained using a ²⁵²Cf neutron source. (2) The absolute efficiency value was calibrated using the D-D neutron source, and the result was used to normalize the relative curve. (3) The efficiency curve was calculated using an MC program with the NEFF code [41]. Figure 5(d) shows the efficiency curves for the different threshold values. The calculated results agree well with the experimental results. This study used a threshold value of 0.8 MeV. Detector size refers to the area and thickness of the detector. The detector can be defined as a surface detector in MCNP because its thickness is only 2.540 cm, which is significantly less than the flight distance of 8.000 m. Therefore, a ring detector estimator with a diameter of 5.080 cm was used to tally the ToF spectra in the MCNP-4C program.

Simulated data

Two angles are calculated for the simulated model shown in Fig. 6(a) [42]. During the 60° and 120° simulations, the left and right sample cells were filled with air, as with the background simulation. The evaluated nuclear data of the Pb isotopes from CENDL-3.2, JEFF-3.3, JENDL-5, and ENDF/B-VIII.0 were used to compare the simulated results from different libraries with the experimental results. The ACE libraries [43] were generated using the NJOY99 code [44]. The data for other materials, such as the target, collimators, shield, and air, were obtained from ENDF/B-VIII.0. Discrepancies can be easily identified by comparing the nuclear data evaluations described in the libraries above.

Fig. 6Full-screen View

(Color online) Simulation model and the ToF results from standard samples. (a) Simulation model for the MCNP calculations. (b) Comparsion between experimental and simulated results of ToF spectra from the polyethylene sample

Measured data

The sample moved along the direction of the neutron detector collimation line (dashed line 1 in Fig. 2), transforming the measured angles owing to changes in the angle of the incident neutrons. In the data storage process, we adopted a method of cyclic measurements involving both samples and the background; for example, samples were measured for 2 h, followed by background measurements for another 2 h. This measurement prevented experimental deviations caused by beams or electronic fluctuations. The measured spectra need to be processed as follows before comparing the calculated spectra: (1) To verify the accumulated single experimental data, normalize each spectrum from the same sample and angle using the counts of the associated alpha or proton. (2) Compare each spectrum and discard the spectra that are noticeably different from those of the other rounds. (3) Utilize the remaining data to derive the summed foreground and background ToF spectra and normalize to one neutron using the neutron yield obtained from Eq. (4) or Eq. (6). (4) The background-corrected spectra can be obtained by subtracting the normalized background spectra from the normalized foreground spectra.

Test of the experimental system with standard samples

Leakage neutrons from two standard samples (polyethylene) were measured to verify the reliability of the measured data from the experimental system. A 30 cm×30 cm×6 cm polyethylene sample was selected as the standard sample for the experiment with the D-T source, and the ToF spectra were measured in an orderly manner at 45° and 60°. Another polyethylene sample with dimensions of 30 cm×30 cm×2 cm was selected as the standard sample in the experiment with the D-D source, and the measurements were conducted at 60°[45].

The corresponding simulation results were obtained using the model shown in Fig. 6(a); the evaluated data were all obtained from ENDF/B-VIII.0. The experimental and simulated results were compared after background rejection. The results are shown in Fig. 6(b), and their counts in the n-p scattering peak are listed in Table 2. The experimental results of the n-p scattering peak agree well with the simulated results, indicating that the processing of the experimental data is reasonable and that the system measurement data are reliable.

Uncertainty analysis of the experimental data

The initial experimental spectra can be normalized by the associated alpha or proton counts and by the ratio of the n-p scattering peak area between the experimental and simulated results. The normalized coefficient B¹ can be obtained using $N_{\text{n}}=\frac{N_{\text{p}}^{\text{e}}}{N_{\text{p}}^{\text{c}}}=B^1\times N_{\alpha }^{\text{p}}，$ (7) where $N_{\text{p}}^{\text{e}}$ represents the sum of the neutron counts in the n-p scattering peak and $N_{\text{p}}^{\text{c}}$ represents the area of the n-p scattering peak calculated by MCNP. Furthermore, $N_{\alpha }^{\text{p}}$ represents the count of associated particles detected in the standard sample. The initial experimental spectra from the ^natPb sample can be normalized using $\frac{N_{\text{Pb}}^{\text{e}}}{N_{\text{n}}}=\frac{N_{\text{Pb}}^{\text{e}}}{B^1\times N_{\alpha }^{\text{Pb}}}=\frac{N_{\text{Pb}}^{\text{e}}\times N_{\text{p}}^{\text{c}}\times N_{\alpha }^{\text{p}}}{N_{\alpha }^{\text{Pb}}\times N_{\text{p}}^{\text{e}}}\mathrm{,}$ (8) where $N_{\text{Pb}}^{\text{e}}$ is the count of neutrons (per time bin) and $N_{\alpha }^{\text{Pb}}$ is the count of associated particles detected from the experiment with the ^natPb sample.

After normalizing the experimental data using Eq. (8), most systematic uncertainties, such as the uncertainty of the absolute detection efficiency (3%), were eliminated. Finally, the uncertainties in the experimental results comprised other systematic and statistical uncertainties. The systematic uncertainties include the relative detection efficiency (≤3%) and scattering angle ambiguity (≤1%), while the statistical uncertainties include the uncertainties of $N_{\text{Pb}}^{\text{e}}$, $\left(N_{\text{p}}^{\text{c}}\le 0.5\%\right)$, $\left(N_{\text{p}}^{\text{e}}\le 0.5\%\right)$, $\left(N_{\alpha }^{\text{p}}\le 0.5\%\right)$, and $\left(N_{\alpha }^{\text{Pb}}\le 0.5\%\right)$.