1. Introduction

High-accuracy data on prompt fission neutron spectra (PFNS) have traditionally played an important role in nuclear engineering design and technology. Other applications have recently arisen, for example, detection of nuclear materials by both active and passive interrogation methods ^[1]; unfortunately, the data on PFNS are surprisingly scarce. Taking the familiar fissile isotope ²³⁵U as an example, despite its thermal-neutron-induced PFNS having already been extensively studied, there is still active research on this isotope. There are significant discrepancies in the literature ^[2] in ²³⁵U PFNS in the lower and higher energy regions; those in the higher energy region, i.e., above 10 MeV, were also confirmed in integral experiments ^[3,4]. Several experimental datasets ^[5] and the ENDF/B-VII evaluation for the prompt fission spectrum of ²³⁵U (n_th, f) are shown in Figure 1; the discrepancies in the high energy region are apparent, and reactor experiments ^[6] confirm the ENDF/B-VII evaluation problem. Thus, there is a need for new measurements of ²³⁵U PFNS in a pure ²³⁵U context. Additional motivation comes from the high uncertainties in the existing PFNS experiments. To clarify these discrepancies, more reliable and accurate fission spectra are necessary. In previous work, PFNS were mainly measured by neutron time-of-flight (n-TOF) ^[7-9]. Traditional fission detection has used a fission chamber to analyze the fragments released ^[10,11]. However, the TOF technique in PFNS measurements needs a high-powered fission chamber with unambiguous alpha-fission discrimination, excellent time resolution, a low mass of structural material, and a reasonable level of actinides ^[12]; such a chamber is not commonly available. At the same time, the range of the fission fragments in matter is very small, limiting the effective sample thickness and therefore also the fissionable mass available for investigation; the small mass leads to a statistically low number of counts in the measured spectra. This is the main reason for the large uncertainty in the high energy region. Therefore, it is necessary to develop a new method to measure PFNS without a dedicated fission chamber. The recoil proton method ^[13-15], which is frequently used in neutron physics experiments, could also be used in measurements of the PFNS. This paper presents an investigation of the prompt neutron spectra of thermal-neutron-induced fission in ²³⁵U, using the recoil proton method. Technical details of the method, the calculation and validation of the response matrix, and evaluation of the uncertainty are also presented.

Fig.1.Full-screen View

Current experimental data for ²³⁵U(n_th, f): the prompt fission neutron spectrum, expressed as a ratio to the Maxwellian function for T = 1.32 MeV. The basic function and parameters are discussed in [6].

2. Recoil proton method ^[16-18]

The proton method of measuring neutron spectra is based on detecting the proton that recoils when a neutron is elastically scattered in a hydrogenated detector such as a conventional liquid scintillator or one containing stilbene or terphenyl. The energy of the recoil proton E_p is related to the incident neutron energy E_n by the relationship:

where θ is the angle between the incident neutron and the recoil proton directions. Consequently, the simultaneous measurement of proton energy and recoil angle allows the initial neutron energy to be determined. It can be proved that the distribution of recoil proton energies induced by any single neutron energy is rectangular; the actual proton pulse height spectrum induced by a distribution of neutron energies is then a convolution of the single-energy functions. The incident neutron spectrum is unfolded from the measured recoil proton spectrum by using a detector response function to represent the convolution as

where $\stackrel{\rightharpoonup }{\text{N}}$ is a vector whose components are the recoil proton pulse spectrum and R is the response function matrix of the detector, typically obtained from a Monte Carlo simulation such as NRESP ^[19] or O5S ^[20]. The vector $\stackrel{\rightharpoonup }{\Phi }$ containing the incident neutron spectrum is then

where R^-1 is the inverse of the response function matrix.

3. Experimental

The experiments were carried out in a neutron scattering hall at the Institute of Nuclear Physics and Chemistry (INPC), Mianyang, China; a thermal neutron beam from the 20 MW China Mianyang Research Reactor (CMRR) ^[21] was used. The experimental layout is shown in Figure 2. The total neutron flux of the beam for the experiments was about 4 × 10⁶ n s⁻¹ cm⁻²; the measured neutron wavelength was λ = 2 Å, corresponding to the energy of the thermal neutrons; the beam size at the sample position was 3 × 5 cm (Figure 3). The sample was enriched uranium metal with ²³⁵U purity above 90%; the sample shape was a cylinder with dimensions Ф25 mm × 0.47 mm; the total mass of ²³⁵U was 4 g. A block of neutron-absorbing ⁶Li₂CO₃ material was used as a beam stop after the experimental area. A BC501 liquid scintillation detector was used to acquire the neutron spectrum (main neutron detector, MND); this device has a size of Φ76.2 mm × 50.8 mm, and has good linearity, excellent neutron and gamma (n-γ) discrimination, and high light output ^[22-24]. A further feature of the BC501 liquid scintillator is isotropic response, a significant advantage over solid detectors ^[25]. The distance between the center of the ²³⁵U sample and the BC501 detector was 60 cm. The detector was placed in a massive shield consisting of lead and Li₂CO₃-loaded paraffin, as shown in Figure 2. The angle (θ) between the axis of the MND and the beam line was 45°. A copper "shadow bar" with dimensions Ф10 cm × 40 cm was placed in front of the MND to reduce the scattered neutron background. A collimating shield of Li₂CO₃ with a tapered inner bore was placed directly in front of the massive main shield surrounding the MND to further reduce background neutron events.

Fig.2.Full-screen View

Experimental arrangement for the prompt fission neutron spectrum measurement of ²³⁵U(n_th, f). The copper shadow bar was used only during background measurements.

Fig.3.Full-screen View

Distribution of thermal neutron flux at the sample position

A schematic of the electronics for measuring the prompt fission neutron spectra is shown in Figure 4. The dynode signal from the MND is fed into a preamplifier (ORTEC 113) and an amplifier (ORTEC 572). The discrimination of neutrons from gammas was realized by a zero-crossing method ^[20]. The neutron signal was selected by the time-to-amplitude converter (ORTEC 567) and used as coincidence input to a linear gate and stretcher (ORTEC 542); the amplifier (ORTEC 572) output signal was used to record the recoil proton pulse height spectra. Due to the restricted range of linearity of the BC501A scintillator, the proton pulse height spectra were divided into a low-energy and a high-energy region; the low-energy region was from 0.5 to 3 MeV with a lower threshold setting of 0.4 MeV, while the high-energy region was from 2 to 16 MeV with a lower threshold of 1.75 MeV. The lower energy threshold was set by calculating and adjusting the lower-level discriminator of a timing single-channel analyzer (ORTEC 551) accordingly, based on the value of the neutron energy. A standard monoenergetic gamma source (²²Na) with the two energies 0.511 (annihilation peak) and 1.274 MeV (gamma decay) was used to calibrate the system for the two energy ranges. The neutron flux was monitored in-line and in real-time by two detectors: a ³He proportional counter and a ²³⁵U fission chamber; the proportional counter was positioned in the neutron beam upstream of the experiment, while the fission chamber was positioned downstream from the ²³⁵U sample. During the course of the experiment, the thermal neutron flux in the beam was held stable; consequently, the two energy regions could be connected and time-normalized to form the complete proton-recoil spectrum. The experimental parameters are summarized in Table 1.

Fig.4.Full-screen View

Electronics schematic for measurement of the fission neutron spectrum. A zero-crossing method is used to discriminate neutrons from gammas.

4. Results and discussion

4.1 Response matrix

The proton-recoil spectra are unfolded to obtain the incident neutron energy spectra by using a neutron response matrix; the matrix is derived from the response function for monoenergetic neutrons. Several Monte Carlo codes including O5S ^[20], SCINEFLU ^[26], and MCNP ^[27,28] have been used to calculate the response functions of liquid scintillators; in this work, we use the software code NRESP7 ^[19], which was developed at the Physikalisch-Technische Bundesanstalt (PTB) Institute in Germany, to calculate the response function of the BC501 detector. In our analysis, several realistic factors are taken into account: neutron scattering in the aluminum detector housing and in the light pipe, neutron scattering from carbon nuclei, anisotropy of the (n, p) reaction for neutron energy above 10 MeV, and nonlinearities in the light output. For convenience in unfolding the spectra, an energy interval of 0.25 MeV is used. The results of the calculation are shown in Figure 5. The monoenergetic neutron response functions shown have not been convoluted with the detector resolution, producing a steep edge and a rectangular shape.

Fig.5.Full-screen View

Response functions of the BC501 detector to monoenergetic neutrons (see the legend), calculated by the NRESP7 code

To validate the calculated response function, we performed a simple experiment using a D-T neutron source to measure the BC501 detector response. The experiment was carried out at INPC in a spacious experiment hall of length 26 m, width 11 m, and height 14 m. Neutron generation was by the T(d, n)⁴He reaction using a 134 keV deuteron beam. The neutron yield was monitored by counting the associated alpha particles with an Au-Si surface-barrier detector located at an angle of 178° from the deuteron beam line. The BC501 detector was placed 10 m away from the D-T source in the 0° direction, where the neutron energy was 14.8 MeV. The measured response function compared with the calculation is shown in Figure 6. To facilitate comparison with the experiment, the simulated response function was convoluted with the detector resolution. The comparison graph showing the quantity (Calculated/Experimental – 1) is presented in Figure 7. It can be seen that the calculated response function and the measurement are in good agreement at energies above 4 MeV; however, below 2 MeV, the measured values are higher than calculated. There are two main reasons for the discrepancy: one is the influence of gamma rays. In the measurements, the n-γ discrimination in the low-energy region is worse than in the high-energy region. A small fraction of gamma events is recorded as neutron events in the recoil proton spectra, leading to a measured value that is higher than that calculated. A second contributor to the discrepancy is scattered neutrons. Although we have taken several measures to reduce their effect, some scattered neutrons are also recorded in the measured spectra. The recoil proton spectra were unfolded to obtain the incident neutron spectra by the inverse matrix method described above; the results for the D-T neutron source are shown in Figure 8. The neutron energy of the peak is 14.78 MeV, in good agreement with data from the accelerator manual ^[29]. It should be mentioned that only one energy (14 MeV) has been experimentally validated, and other experiments will be carried out in the future to improve this situation.

Fig.6.Full-screen View

Comparison of response functions: calculated (black rectangles) and experimental (red circles), at an energy of 14.8 MeV

Fig.7.Full-screen View

Comparison of calculated and experimental response functions. The quantity (Calculated/experimental – 1) is plotted, indicated as (C/E-1).

Fig.8.Full-screen View

Spectrum of D-T neutron source, obtained by unfolding measured results using the inverse response matrix.

4.2 PFNS & uncertainty

The measurements of the PFNS proton-recoil pulse height spectra were divided into low- and high-energy regions. In the low-energy region, the statistical count level in the recoil-proton spectra could be improved, but the measurement time was only several h. In the high-energy region, as a result of the smaller number of high energy neutrons, the data took about 50 h to acquire. After the measurements of the source spectra, the background spectra measurement of the two energy segments were carried out using the copper shadow bar described in Figure 2. It took corresponding amounts of time to complete background spectra measurements in the low- and high-energy regions. The pure or clean recoil proton spectra were obtained by subtracting the background spectra. Based on the recoil proton spectra, the PFNS of ²³⁵U(n_th, f) was obtained using the inverse of the calculated response matrix. The experimental results are summarized in Figure 9. The ratio of the spectra was obtained by comparing the measured spectra with the Maxwellian function for a temperature T = 1.32 MeV, as described in the literature. It can be seen from the figure that the lower threshold in the experimental spectra was set at 1 MeV, limited by the neutron-gamma discrimination for neutron energies below that. Because the uranium sample emitted an elevated level of gamma rays after irradiation by the neutron beam, the n-γ discrimination below 1 MeV was not satisfactory, and in addition, the main parts of the experimental spectra in the low-energy region agreed with previous work and the ENDF/B-VII library. We believe the small differences are caused by delayed neutrons and scattered neutrons from the uranium sample. While the prompt and delayed neutrons could not be discriminated in the recoil proton method here, we took measures (the copper shadow bar and collimator) to reduce scattered neutrons from the environment; however scattered neutrons from the uranium sample itself could not be eliminated. In the high-energy region (above 10 MeV), however, our experimental spectrum is higher than the results of Starostov, Wang, Vorbyev, and the ENDF/B-VII library. Our results are similar to those of Kornilov, especially if the statistical uncertainties are included. These uncertainties result from, for example, the counting statistics in the recoil proton spectra (σ₁), the calculation of the response matrix (σ₂), the neutron/gamma discrimination (σ₃), and the energy calibration by a standard γ source (σ₄). The statistical uncertainty of the counts is obtained from

Fig.9.Full-screen View

Experimental spectra of PFNS for ²³⁵U(n_th, f) (black circles) compared with other reports and the ENDF/B-VII library. Comparison with a Maxwellian function for T = 1.32 MeV is shown.

${\sigma }_1=1/\sqrt{\text{N}},$ (4)

where N is the number of counts in the recoil proton spectra. In our measurement, the statistical uncertainty at 10 MeV is 11%, while the value at 12 MeV is 23%. The uncertainty σ₂ of the response matrix is obtained by the simulated code NRESP7; from the calculations, the relative uncertainty in the low-energy region is 3% - 4%, while in the high-energy region it is 4% - 5%. The uncertainty σ₃ of neutron/gamma discrimination above 1 MeV was about 1%. In the high-energy region, the source neutron calibrating spectra contributes an uncertainty σ₄ about 1%, while in the low-energy region, calibrating by a ¹³⁷Cs source contributes an uncertainty of about 2%. Because the uncertainties in the measurement are independent, the total uncertainty is given by:

${\sigma }_{\text{total}}=\sqrt{{\sigma }^2{}_1+{\sigma }^2{}_{\text{2}}+{\sigma }^2{}_{\text{3}}+{\sigma }^2{}_{\text{4}}}.$ (5)

As a result, the total uncertainty in the high energy region from 10 − 12 MeV was 13 − 24%. Although our final uncertainty remains high, it has been reduced considerably relative to some previous work. It can be seen from the uncertainty budget that the greatest contribution to the uncertainty comes from the counting statistics. Consequently, an effective method to reduce uncertainty would be to increase the count numbers by improving the neutron detector’s efficiency, using a larger quantity of fissile materials, and extending the measurement duration when machine time permits. In addition, using a neutron source with less energy spread will improve the accuracy of the response function. These are areas we plan to explore in the near future.

5. Conclusion

An experiment was performed to obtain the prompt fission neutron spectrum induced by thermal neutrons in ²³⁵U using the recoil proton method. The measured spectrum in the low-energy region is in good agreement with previous work and with the ENDF/B-VII library except for minor differences. In the high-energy region, however, the measured spectrum is higher in comparison. The uncertainty in the energy region from 10 MeV to 12 MeV is 13 − 24%, which is an improvement over previous work. The experimental results show the recoil proton method can be used to measure prompt fission neutron spectra and does not require a dedicated fission chamber.