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Article
Demonstration of shape analysis of neutron resonance transmission spectrum measured with a laser-driven neutron source
Koizumi Mitsuo koizumi.mitsuo@jaea.go.jp

1
Ito Fumiaki 14
Lee Jaehong 1
Hironaka Kota 1
Takahashi Tohn 1
Suzuki Satoshi 1
Arikawa Yasunobu 2
Abe Yuki 2
Lan Zechen 23
Wei Tianyun 2
Mori Takato 2
Hayakawa Takehito 23
Yogo Akifumi 2
1 https://ror.org/05nf86y53 grid.20256.33 0000 0001 0372 1485 Integrated Support Center for Nuclear Nonproliferation and Nuclear Security, Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195 Japan
2 https://ror.org/035t8zc32 grid.136593.b 0000 0004 0373 3971 Institute of Laser Engineering, Osaka University, Suita, Osaka 565-0871 Japan
3 grid.529589.a 0000 0004 7436 1394 Kansai Institute for Photon Science, National Institutes for Quantum and Radiological Science and Technology (QST), 8-1-7 Umemidai, Kizugawa-shi, Kyoto 619-0215 Japan
4 https://ror.org/01g5y5k24 grid.410794.f 0000 0001 2155 959X Present Address: High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba-shi, 305-0801 Japan
19 9 2024
19 9 2024
2024
14 219168 7 2024
11 9 2024
© The Author(s) 2024
2024
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Laser-driven neutron sources (LDNSs) can generate strong short-pulse neutron beams, which are valuable for scientific studies and engineering applications. Neutron resonance transmission analysis (NRTA) is a nondestructive technique used for determining the areal density of each nuclide in a material sample using pulsed thermal and epithermal neutrons. Herein, we report the first successful NRTA performed using an LDNS driven by the Laser for Fast Ignition Experiment at the Institute of Laser Engineering, Osaka University. The key challenge was achieving a well-resolved resonance transmission spectrum for material analysis using an LDNS with a limited number of laser shots in the presence of strong background noise. We addressed this by employing a time-gated 6Li-glass scintillation neutron detector to measure the transmission spectra, reducing the impact of electromagnetic noise and neutron and gamma-ray flashes. Output waveforms were recorded for each laser shot and analyzed offline using a counting method. This approach yielded a spectrum with distinct resonances, which were attributed to 115In and 109Ag, as confirmed through neutron transmission simulation. The spectrum was analyzed using the least-square nuclear-resonance fitting program, REFIT, demonstrating the possibility of using an LDNS for nondestructive areal-density material characterization.

Subject terms

Nuclear energy
Applied physics
Nuclear physics
Techniques and instrumentation
Applied optics
Optical techniques
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pmcIntroduction

The continuous advancement of high-power laser technologies opens new possibilities for ion acceleration and applications using accelerated ions1–3. When a laser beam impacts a thin target, it accelerates ions through short-duration laser–plasma interaction near the target. The ion acceleration is determined by the characteristics of the target and laser, such as type and thickness of the target material, laser wavelength, polarization, and time and space density distributions1,4,5. The mechanisms are categorized into regimes, such as target normal-sheath acceleration (TNSA)6,7, radiation pressure acceleration (RPA)8, breakout afterburner (BOA)9, and collisionless shock acceleration (CSA)4. The maximum energy of the accelerated ions can reach tens of MeV, and even exceed 150 MeV10.

Utilizing laser-accelerated ions, laser-driven neutron sources (LDNSs) attract interest as short-pulse high-intensity neutron generators. These systems generate neutrons via reactions between the accelerated ions and a neutron converter (secondary target) near the laser target3–5,11. The neutrons have a broad energy distribution, with the maximum energy potentially as high as that of the accelerated ions. Furthermore, the size of the neutron converter (neutron source) can be reduced to only a few centimeters, because the laser-driven ion generation occurs in a micrometer-scale region at the target, and the neutron converter is placed near the target. The neutron generation duration is short, aligned with a laser pulse duration of less than a nanosecond, significantly shorter than that of accelerator-driven pulsed-neutron facilities12–14. Except for fast-neutron applications, a moderation system is crucial for extracting neutrons with the desired energy, i.e., epithermal15, thermal16, and cold17. Radiography experiments and nuclear reaction observation have been performed using neutrons of various energies3,18–22.

Neutron resonance analysis is a nondestructive assay (NDA) method using pulsed thermal-epithermal neutron beams23–25. This technique relies on neutron time-of-flight (n-TOF). In neutron resonance transmission analysis (NRTA), a sample is positioned between the neutron source and the detector. The neutron flight times from the source to the detector are measured at a known distance, and the neutron energies are deduced. The resulting n-TOF transmission spectrum shows nuclide-specific resonance patterns due to nuclear reactions, such as scattering, capture, and fission. The areal densities of each nuclide are determined by analyzing the spectrum. High-resolving power in NRTA is achieved through a long flight path length, a short neutron pulse duration, or both23,24,26. LDNSs could suit the NRTA measurements because of their ability to generate short neutron pulses. This capability allows for a compact n-TOF system, making NRTA more efficient.

The measurement challenges are high-flux neutron detection in high-background environments, such as the electromagnetic (EM) noise and strong gamma-ray and neutron flashes at the laser shot. The nuclear reactions of neutrons and ions with surrounding materials induce gamma-ray emissions, which can saturate and destabilize the detector output signal and cause after-pulsing in photomultiplier tubes (PMTs)27. A PMT with gated voltage can reduce the impact of the flash signals28–30. Neutron resonance transmission experiments using LDNSs have been reported31–34. Resonant fast-neutron absorption at 3 MeV in a graphite sample was observed using a plastic scintillator connected to a silicon photomultiplier in a noise shield via an optical fiber31. Drops in neutron counts at the neutron resonance energies in a spectrum were observed from 18 laser shots using a borated microchannel plate (MCP) detector, which has low sensitivity to gamma rays32. The changes in neutron transmission at the neutron resonance energies were observed by monitoring the output level of a time-gated 6Li-glass scintillation neutron detector with a single laser shot33. Furthermore, temperature monitoring was demonstrated by observing the broadening of resonance using single-shot neutron pulse beams34. These studies suggested the potential of neutron transmission resonance measurements for determining the nuclear areal densities in a sample.

Herein, we report the first successful nuclear areal-density analysis using neutron transmission spectra obtained by employing an LDNS. These spectra were measured using a time-gated 6Li-glass scintillation neutron detector to reduce the impact of EM noise as well as neutron and gamma-ray flashes. The output waveforms from the detector were recorded for each laser shot. The data were analyzed offline using a counting method to reduce uncertainty in the detector response. A spectrum with distinct resonances was obtained from merely three laser shots. The assignment of the resonances attributed to 115In and 109Ag in the sample was confirmed via simulations, which also ruled out spurious detector responses. The obtained spectrum was analyzed using the least-square nuclear resonance fitting program called REFIT35, demonstrating the feasibility of nondestructive areal-density measurement of nuclides in a sample using an LDNS.

Results

Experimental setup

An experiment was performed using an LDNS33 with the Laser for Fast Ignition Experiment (LFEX)36 at the Institute of Laser Engineering (ILE), Osaka University. Figure 1 shows the experimental setup. The LDNS was placed at the target location of the LFEX, at the center of a stainless steel (Steel Use Stainless: SUS) vacuum chamber with a radius of 0.8 m. The pulse width of the LFEX was approximately 1.5 ps at full width at half maximum (FWHM), and the total energy was approximately 1000 J. The laser intensity at the LDNS target was approximately 1019W/cm2. The laser repetition rate was limited to three shots per day due to the required cooling after each laser shot.Fig. 1 A diagram of the neutron-resonance transmission measurement setup using a laser driven neutron source (LDNS): (a) overview of the experimental setup with the neutron flight path; the sample used in the experiment was a stack of 0.2-mm-thick indium (natIn) and 0.8-mm-thick silver (natAg) plates; (b) a drawing of the LDNS comprising the first target (CD film) for charged-particle acceleration, the second target (neutron converter) for neutron generation, and the polyethylene moderator for neutron deceleration.

The LDNS comprised a target, a neutron converter, and a moderator (Figure 1 (b)). The target was a 5-μm-thick deuterated polystyrene (CD) foil, which was evaporated and replaced for each laser shot. The neutron converter comprised two beryllium (Be) rods, each 0.5 cm in diameter and 1 cm in height. The moderator was a 4-cm-thick truncated cone-shaped polyethylene block. When a laser pulse was shot on the CD target, deuterons and protons on the target surface were accelerated through the laser–plasma interaction. Neutrons were generated via the 9Be(d, n) and 9Be(p, n) reactions in the neutron converter, which were subsequently decelerated in the polyethylene moderator.

A neutron flight path was arranged at a horizontal angle of 40∘ to the laser beam injection, and an Al window was set on the vacuum chamber. Collimators with a 5 cm × 5 cm aperture comprising 20% borated polyethylene and Pb blocks (mostly sized 5 cm × 10 cm × 20 cm) were installed along the neutron flight path. A 1-cm-thick Pb plate was placed in the neutron beam path to reduce gamma-ray flashes from the laser plasma. At the end of the beam path, approximately 3.6 m from the moderator surface, a scintillation neutron detector was positioned, within a Pb-shielded space. The neutron detection system is detailed in the Methods section. The collimated neutron beams were directed solely onto the scintillator to prevent gamma rays and neutrons from directly hitting the PMT. The output waveforms from the neutron detector were recorded and analyzed as described in the Methods section.

Neutron transmission spectra

Figure 2 (a) shows the experimentally obtained n-TOF spectrum. In the measurement, a stack of 0.2-mm-thick indium (natIn) and 0.8-mm-thick silver (natAg) plates was used. The samples and their thicknesses were chosen to measure the resonance dips. The recorded shot-by-shot waveforms were analyzed offline to extract the n-TOF spectrum (see Methods). Three resultant spectra were averaged, including one measured on a separate day. The ordinate of the spectrum represents the averaged neutron counts in a 7-μs time bin, with a unit of counts per μs per laser shot. The statistical uncertainty in transmission within a 7-μs time bin obtained by three laser shots was approximately 5%. The energy resolution of the 7 μs time bin corresponds to 1%–7% for resonance energies from 0.5 eV to 25 eV, where the resonance broadening due to the moderator was approximately 1%, as evaluated via the simulation presented in the Methods section.Fig. 2 The n-TOF spectra through a stack of natIn and natAg plates: (a) the experimental and simulated n-TOF spectra; the ordinate represents the averaged neutron counts in a 7-μs time bin, with a unit of counts per μs per laser shot; the filled circles show the experimental data, the black line is to guide the eye, the solid and dashed blue lines show the simulation results with and without the sample, respectively; (b) the neutron transmission spectra; the experimental data points (closed circle) and a blue line connecting the data points obtained by the fitting program, REFIT, are presented; (c) the neutron transmission spectra calculated using nuclear data38; the thickness of the In plate was varied while that of the Ag plate was kept 0.8 mm; the thicknesses of the In plate are indicated on the right-hand side of the panel; the transmission was the averaged value of the 7-μs time bin.

The resonance dips appeared at approximately 110 and 220 μs, where the resonances were attributed to 109Ag (5.19 eV, 2.32 ×104 b) and 115In (1.46 eV, 2.93 × 104 b), respectively. The results correlated with the evaluated values of 114 μs and 215 μs using the nonrelativistic relation, TOF(μs) = 72.3×L/E, where E is the neutron energy in eV, and L is the flight path length (3.6 m). The depth of the resonance dips is approximately half of the counts at the center of the dips, around 170 μs, whereas the neutron yield at the dips in the simulation is less than 10% (see Figure 5 (a) in the Methods section). The neutron-capture gamma-ray background from the neutron source can explain this discrepancy39.

Transmission spectra deduced from the simulated neutron flux presented in the Methods section are also plotted in Figure 2 (a). The gamma-ray background counts were approximated using a linear function passing through the bottom of the dips in the experiential spectrum, and the energy-dependent neutron detection efficiency of the 6Li-glass scintillation detector was calculated using the 6Li(n, t) cross-sections from Japanese Evaluated Nuclear Data Library (JENDL) 4.038. The simulated neutron counts were scaled to match the depth of the experimental ones, evaluating approximately 1011 neutron generation per shot at the LDNS neutron converter. As shown in Figure 2 (a), the simulated spectrum matched the experimental results, confirming the successful observation of resonances without any spurious contribution from neutron and gamma-ray flushes as well as EM noise.Table 1 Result of REFIT.

Variables	Fitted	
Areal density of 109Ag [10-3 at/b]	3.0 ± 0.8	
Areal density of 115In [10-3 at/b]	0.9 ± 0.2	
Flight length [m]	3.57 ± 0.06	
Initial delay [μs]	–5.4 ± 2.2	

Resonance shape analysis

The present experimental data was analyzed using a least-square fitting program, REFIT35. Figure 2 (b) shows measured neutron transmission data points (closed circle) and the fitting result (blue line). The experimental transmission was calculated by applying the background linear function, which was used for the adjustment of simulated spectra to the experimental data, and a linear function fitted for the simulated spectrum without the samples (see Figure 2 (a)). The error bars on the experimental data points were from experimental statistics. The uncertainty from the background subtraction and normalization were disregarded, assuming they were measured separately with good statistics. The fitting was performed for determining the areal densities of 109Ag and 115In, the flight length, and the initial delay of the n-TOF spectrum. As the contributions of 107Ag and 113In to the spectrum are comparably smaller than those of 109Ag and 115In, their areal densities were fixed to prevent unexpected effect on the fitting. Instead, their areal densities were manually adjusted to maintain consistent isotopic abundance. The fitting was repeated until the changes in the variables settled within their errors. Table 1 shows the resultant fitting values of REFIT. The flight length is consistent with our experimental setup. The initial delay correlate with the expected value of –3.5 μs, due to the bunching of the spectrum for 7 μs. The resultant areal densities correlated within the errors with the areal densities: 2.25 ×10-3 at/b for 109Ag and 0.734 ×10-3 at/b for 115In. The uncertainty of the determined areal densities is approximately 25%. These results confirm the viability of an LDNS for neutron resonance transmission measurements, demonstrating areal density determination with minimal laser shots.

Discussion

For real sample measurements, additional measurements are required, i.e., a measurement without a sample to determine neutron transmission, and a measurement with filtering plates to evaluate the gamma-ray background by resonantly blocking neutrons. In parallel, the neutron yield is measured using a neutron flux monitor placed elsewhere to normalize the obtained spectra. This method, NRTA, applies to an areal density measurement of nuclides with resonances in an appropriate energy range, typically from thermal to epithermal ranges, where characteristic resonances are observed. These nuclides are mostly heavy elements including nuclear materials.

Figure 2 (c) shows the neutron transmission spectra using different stacks of natIn and natAg plates calculated using nuclear data38. The transmission data points are averaged in 7-μs time bins, which is the same as the present n-TOF spectrum time resolution. As the thickness of the In plate increases, the resonance depth of 1.46 eV (29.3 ×103 b at peak) increases, saturates, and then broadens, showing the applicability of the employed system for measuring the natIn areal density relevant to thicknesses from 0.01 mm to 2.0 mm. Resonance dips with comparably low cross-sections at 3.82 eV (0.952 ×103 b) and 9.07 eV (1.50 ×103 b) appear with sample thicknesses greater than 0.5 mm, and the resonances of 109Ag (5.19 eV) and 115In (3.82 eV) form superimposed dips.

The uncertainty of this system can be reduced by increasing the statistics. Acceptable neutron detection numbers in the same energy range can be increased by extending the flight path, which prolongs the arrival time of neutrons within a specific energy range. This allows the use of a more efficient detector with sufficient thickness and a larger detection area. Furthermore, detectors capable of managing high count rates, such as segmented detectors, are effective. In the future, the repetition rate of laser systems should increase. A diode laser excitation method will enhance the repetition rate and reduce the size of the laser system. Petawatt-class lasers with 1–10Hz repetition rates are being developed40–44. The advancement of laser power density should increase neutron flux per laser shot. The target must be replaced quickly to catch up with the laser frequency because a single strong laser shot evaporates it. Target systems using target arrays, liquid targets, and other approaches, are proposed and being actively developed45–47.

The neutron generation of this experiment was evaluated approximately 1011 n/shot, whereas the references indicate 1.6 ×1010 n/shot32 and 2–3 ×1011 n/shot33. The difference in the neutron yields resulted from the target–converter–moderator combination and laser power density. The neutron generation is equivalent to or more than those of the electron accelerator-driven n-TOF facilities, such as the Geel Electron Linear Accelerator (GELINA; 3.4 ×1013 n/s, 800 Hz; equivalent to 4.3 ×1010 n/shot)12 and the Hokkaido University Neutron Source facility (HUNS; 1.6 ×1012 n/s, 100 Hz; equivalent to 1.6 ×1010 n/shot)14. The neutron generation yield with LDNSs can be increased with laser power. A relation proposed for neutron generation n (neutron/shot) using an LDNS is n∝I4, where I is the laser power density (W/cm2)33.

An advantage of LDNSs is the compactness of the system due to the small size of the area of accelerated particle generation, neutron converter, and moderator, all placed nearby. For example, the neutron generator of the KURRI-LINAC facility, which uses accelerated-electron-induced bremsstrahlung gamma rays to generate neutrons by the (γ, n) reaction, comprising a water-cooled tantalum neutron converter (ϕ50 mm ×60 mm) and a water tank for neutron moderation (an octagonal ring of 300 mm × 300 mm × 100 mm), where the neutron converter is placed in the center of the moderator13. An n-TOF measurement system with a small moderator reduces the bore radius of the neutron flight path, reducing the volume of the collimator and shielding materials required. The short-pulse width of neutron generation, facilitated by subnanosecond laser pulses, enhances the time resolution of the n-TOF system, allowing for a shorter flight path to achieve a specific energy resolution, thereby increasing neutron flux. Another notable feature of LDNSs is that optical devices are used to transport laser beams, which are likely easier to control and tune than the heavy electromagnetic devices used in accelerator-driven neutron sources.

In conclusion, this study demonstrated the observation of a neutron resonance transmission spectrum using neutron beams from an LDNS with only three laser shots. The resonance spectrum was successfully analyzed, yielding the sample areal densities. This highlights the potential of a new approach to neutron-based nondestructive material characterization using an LDNS with advanced laser and target systems.

Methods

Neutron beam measurement

Figure  3 (a) shows the neutron detector system schematically. A 6Li-glass scintillator (KG2, 50 mm × 50 mm × 1 mm) was used due to its short decay time (18–62 ns), where the density of KG2 was 2.42 g/cm3 and included 7.5 wt% of Li (95% 6Li enriched)48. The thickness was chosen to achieve a suitable detection efficiency of 30%–6% for the 0.5–15 eV neutrons and to ensure that the detector responded to high-flux neutrons. A fused quartz plate (SiO2, 50 mm × 50 mm × 4 mm) was used for a light guide, whereas an acrylic light guide was avoided to minimize neutron scattering. The scintillator and the glass plates were surrounded by reflector foil (aluminized Mylar), stored in a 1.5-mm-thick Al cap, and mounted on a PMT (R5113-02, a discontinued product of Hamamatsu), with a high-voltage divider and a transistor-switched gating circuit (C1392-11 MOD (normally on type), a discontinued product of Hamamatsu)28,29. The PMT was a 51-mm-diameter head-on type with a silica glass window. The photocathode was bialkali with an effective area of 46 mm in diameter, and the response wavelength was 160–650 nm.Fig. 3 (a) Schematic of the detector system. The neutron beams passed through a 6Li-glass scintillator (KG2, 1 mm thick) with a light guide (fused silica (SiO2), 4 mm thick). The components were stored in an Al cap and mounted on a photomultiplier tube (PMT) with a transistor-switched gating circuit (normally on type). Two high-voltage power supplies (HVPSs) were used for the detector system. The positive voltage was imposed on the cathode using the gating circuit to suppress photoelectron multiplication. The detector output waveform was recorded using an oscilloscope. The measurement timings were controlled using a logic synthesizer. (b) A part of the recorded waveform from –20 to 200 μs. The PMT output saturation by gamma-ray and neutron flashes was avoided using the gated circuit of the detector at the beginning, and the elimination lasted at approximately 42 μs. The signals appeared after the gate period. The baseline shift and destabilization of the signal gradually recovered. (c) A part of an expanded waveform of Fig. 3 (b) between 160 and 164 μs. The gray line is the raw waveform. The black line is a corrected waveform using moving averages. The negative pulse signals under the threshold given by the dashed line are counted.

The neutron detector system was driven by two high-voltage power supply systems (HVPS) (3002D, Canberra): one for photoelectron multiplication and the other for the gating circuit. The photoelectron multiplication voltage imposed on the PMT was reduced from the recommendation of –2.0 kV to –1.4 kV to enhance the over-current resistance caused by a rush of signals. A logic synthesizer (Broad3, Bee Beans Technologies) triggered the gating circuit of the detector and a 12-bit analog-to-digital converter oscilloscope (MSO 58, Tektronix). The start timing signal was sent from the LFEX facility. The gating circuit of the PMT blocked the response of the detector for a fixed time of approximately 10 μs. To avoid the saturation of the PMT output by the laser-induced flashes, the gate period was extended by repeating 10 consecutive gate signals every 4 μs. The detector output waveforms were recorded using the oscilloscope in a 0.5 V full-scale range for 1 ms, with a sampling rate of 1.25 GS/s. The achieved waveform was analyzed offline.

Figure 3 (b) shows a part of the measured waveform. The gate circuit of the detector eliminated the output signal at the beginning of the waveform. The strong spike signal at the laser shot (t=0μs) was from the EM noise, and the other spikes were attributed to the gating circuit. The detector signal appears after the gate period (t>42μs), and the shifted and destabilized baseline gradually recovered. The gray line in Figure 3 (c) shows an expanded part of Figure 3 (b). The output amplitudes of the neutron signals were not significantly larger than the electronic noises. Therefore, in this analysis, the electronic noises were reduced using two moving averages, where the averaged values were assigned to the center of each averaging window. One moving average was calculated over 6.4 μs to remove the long-range baseline shift. The other was a short-range moving average over nine data points in 7.2 ns to remove the sharp electric noise.

The neutron detection timing was determined using the leading-edge method instead of constant fraction discrimination because the leading-edge method is straightforward, and the detector signal was fast enough to achieve the required time resolution (microsecond range). Negative pulse signals exceeding a threshold level were counted, indicated by the dashed line in Figure 3 (c). The threshold level was set to make the resonance dips appear clearly in the observed spectrum, resulting in a high threshold level to minimize noise signal counting. A 40-ns software dead time after pulse detection was imposed to avoid double counting the pulse signals. This time range was sufficient to cover the tip of the peak of a neutron pulse signal, where a decay time of 90%–10% of the signal of KG2 is 93 ns48. Figure 2 (a) shows the resultant spectrum.

The neutron counting rate increases as the flight time decreases (i.e., as the neutron energy increases), as shown in the spectra of Figure 2 (a). This makes it challenging to measure high-energy neutron resonances due to the high event rate. The maximum neutron energy available with this system was approximately 25 eV (corresponding to ∼50 μs), where the baseline level of the PMT output stabilized (Figure 3 (b)). One can measure neutron resonances at higher energies by increasing the flight path length to delay the measurement timing or replacing the neutron detector with one that is noise-resistant and capable of managing high count rates.

Simulation of the neutron resonance transmission experiment

To evaluate the performance of the present n-TOF system, a neutron transmission simulation was conducted using the Particle and Heavy Ion Transport code System (PHITS) Ver. 3.1237, with the Japanese Evaluated Nuclear Data Library (JENDL)-4.038. The neutron energy distribution from the neutron converter (Figure 4(a)) employed in the simulation was based on the results of a simulation reported in a previous study49, wherein neutrons were generated from a 5-mm Be neutron converter placed 2 mm apart from a DC target via interaction with incident protons and deuterons with experimentally obtained energy distributions49. The uniformly generated neutrons from the neutron converter were slowed down in the moderator, and then flew to the 5 cm × 5 cm detector (Figure 1). This simulation included a stainless-steel vacuum chamber, Al window, Pb plate, and parts of the polyethylene (20% borated) and Pb collimators (Figure 1). Figures  4 (b) and (c) show the neutron energy distribution at the detector, while Figure  4 (c) shows the thermal to epithermal energy region. Figure 5 (a) shows the resultant n-TOF spectra with and without the sample, comprising a stack of 0.2-mm-thick indium (natIn) and 0.8-mm-thick silver (natAg) plates. Strong resonance dips of 1.46 eV of 115In and 5.19 eV of 109Ag were observed, where the transmissions fell below 10%. Approximately 10-10 neutrons per source per μs were expected in a 25 cm2 neutron detector area.Fig. 4 The energy distributions of neutrons. (a) The incident neutron energy distribution at the entrance of the moderator of the LDNS used for this PHITS simulation study. This distribution was obtained from the results of a simulation described in ref.49, which involved a 5-mm thick Be neutron converter positioned 2 mm from a DC target, and incident protons and deuterons with energy spectra derived from an experiment conducted at LFEX. Approximately, 50% of neutrons are less than 3 MeV and 80% are less than 5 MeV. (b) The neutron energy distribution from 0 MeV to 12 MeV at the detector position. (c) The neutron energy distribution from 0 eV to 25 eV at the detector position.

Fig. 5 Results of simulation of the Particle and Heavy Ion Transport code System (PHITS) 3.1237. (a) Neutron time -of-flight (n-TOF) spectra simulated with 3 × 1011 neutron generations. The red line indicates the neutron flux (sample-out). The black line indicates the neutron flux through a sample (sample-in), i.e., the transmission n-TOF spectrum. All the fluxes are normalized by one neutron generation at the source. Assignments of strong resonances are given. (b) Time distribution of neutrons with same kinetic energies coming out from the moderator surface after the laser shot. The peak heights were normalized. The full width at half maximums (FWHMs) of the time distribution of 0.5, 1, 10, 100, and 1000 eV are 1.8, 1.3, 0.39, 0.13, and 0.042 μs, respectively.

The energy resolution in a neutron resonance-spectrum measurement can be expressed by ΔEn/En=2Δt/t=2Δt2E/mn/L, where En and ΔEn are the neutron kinetic energy and its width, respectively, t and Δt are the neutron flight time and its broadening, respectively, mn is the neutron mass, and L is the flight path length. The time broadening (Δt) is determined by the duration of neutron generation (less than nanosecond for LDNSs), the neutron moderation, and the geometrical flight path differences (∼ΔL/v, where ΔL and v are the flight path difference and the neutron velocity, respectively). Neutron moderation contributes the most to the time broadening of LDNS.

Figure 5 (b) shows the simulated time structure of neutrons with identical kinetic energies at the front surface of the moderator (Figure 1). The width of the time distribution narrows as the neutron energy increases. The FWHMs of the time distribution of 0.5, 1, 10, 100, and 1000 eV are 1.8, 1.3, 0.39, 0.13, and 0.042 μs, respectively. The broadenings were used to evaluate the energy resolutions at a flight path of 3.6 m to be approximately 1% for neutron energies from 0.5 eV to 1 keV. This result correlates with the experimental value of ΔEn/En=2.3% for a 5.2-eV resonance dip measured with a 1.8-m flight path using the same LDNS33. This resolution, achieved using a short-pulse laser and a compact neutron moderator, is sufficient for resolving resonances in a spectrum for general purposes.

Acknowledgements

This work was implemented under the subsidy for “promotion of strengthening nuclear security and the like” of the Ministry of Education, Culture, Sports, Science, and Technology-Japan. The simulation work was conducted using the supercomputer HPE SGI8600 in the Japan Atomic Energy Agency.

Author contributions

M.K., F.I., and J.L. conceived the experiment. M.K., F.I, J.L., K.H., T.T., and S.S. conducted the n-TOF experiment. M.K. supervised the experiments. Y.Ar., Y.Ab., Z.L., Z.L., T.W., T.M., T.H., A.Y., supported the experiments and provided neutrons using the LDNS. A.Y. supervised the operation of the LDNS. J.L. performed the simulation study. M.K. and F.I. analyzed the data. M.K., F.I., and J.L. wrote the manuscript. All authors reviewed the manuscript.

Data availability

The data that support the findings of this study are available from the corresponding author, M. K., upon reasonable request.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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