Single-event fast neutron time-of-flight spectrometry with a petawatt-laser-driven neutron source

Domain: biology
Published: 2026-04-01
Editorial outcome: major_revision

Abstract
Laser-driven neutron sources (LDNSs) offer unique advantages for fundamental physics and applications: ultrashort pulses providing superior energy resolution, high instantaneous flux, and a reduced footprint. While single-event neutron spectroscopy has been demonstrated with epithermal neutrons, its application for fast neutrons is more challenging and remains unproven. This demands stable multi-shot operation and detectors resilient to this particularly extreme environment. Here, a proof-of-concept experiment at the DRACO PW laser is presented. This setup stably produced ~108 fast neutrons per shot sustained over more than 200 shots at a shot-per-minute rate. Neutron time-of-flight measurements with a diamond detector at only 150 cm from the source resolved individual neutron-induced reactions at a rate consistent with simulations informed by real-time diagnostics of accompanying gammas, ions, and electrons. Combined with the recent advances in the field, this work establishes LDNSs as a promising, scalable platform for future fast neutron-induced reaction studies, particularly those involving short-lived isotopes.

Introduction
Neutron-induced reactions play a crucial role in various research fields, from exploring the origins of elements in our universe1 to understanding the core principles of nuclear physics2,3. These reactions are also relevant to dosimetry4, medicine5,6, space science7, material science8, condensed matter physics9, and nuclear fission and fusion technology10, highlighting their broad scientific, societal, and industrial relevance.

As many research reactors are decommissioned, particle accelerators take the lead in experimental neutron science. To study nuclear structures, fission dynamics, material composition, and nucleosynthesis processes at high resolution and across a broad neutron energy range, accelerator-based neutron sources commonly employ the neutron time-of-flight (ToF) method. Pulsed neutron beams are generated and travel a well-defined flight path to a sample, where they induce nuclear reactions. To measure, e.g., neutron-energy-dependent reaction cross-sections, individual reactions can be detected via promptly emitted radiation. This enables the determination of the flight time—and thus the kinetic energy—of the interacting neutron, with the energy resolution primarily governed by the initial neutron pulse duration and the flight path length.

Nuclear reactions induced by fast neutrons (>1 MeV) are of particular importance for fission, fusion, and dosimetry, as reflected in the Nuclear Energy Agency’s High Priority Request List, where they account for over 90% of the requested nuclear data11. Additionally, more than 25% of requests concern radioactive actinide isotopes. The same applies to neutron capture in astrophysics12, in which the s-process branching points of interest are all radioactive. Here, the pulse intensity is particularly advantageous for measurements on said radioactive samples as it improves the ratio between signal and radioactive background13. As a result, there is increasing interest in exploring alternative sources that can deliver intense, energetic neutron pulses to address these experimental needs.

Even though the world’s largest ion accelerators host proton spallation facilities that provide such neutron pulses at ~Hz repetition rates14–18, the nuclear physics community is looking to expand the range of neutron sources to meet current and future demands. In this context, advanced compaction sources based on laser-plasma acceleration (LPA)—a rapidly advancing technology—have been discussed as drivers of fast neutron sources to complement and extend the existing infrastructure for nuclear physics research using the neutron time-of-flight method19.

In LPA, an ultra-short (fs) high-power (TW to PW) laser pulse interacts with a solid target, generating ultra-short (~ps) ion pulses in a plasma process accompanied by a strong prompt emission of electrons, X-rays, and electromagnetic noise. The acceleration process favors ions with a high charge-to-mass ratio, in particular protons. LPA proton pulses contain up to 1012 protons at MeV energies and exhibit a broad angular distribution and an exponentially decaying energy spectrum with a cut-off toward higher kinetic energies. It has recently been demonstrated that petawatt-class (PW) lasers operating at Hz-level repetition rates can reliably produce intense proton pulses up to several tens of MeV20,21.

Owing to the characteristics of LPA beams, the corresponding laser-driven neutron sources (LDNSs) offer an ultra-high instantaneous flux (e.g., 1011 neutrons/shot22), which presents a dual advantage for nuclear reaction studies with neutron time-of-flight: First, for a given energy resolution, their short pulse duration allows for a short flight path length and therefore compact setup dimensions. Second, as discussed above, a high instantaneous neutron count is particularly advantageous for measurements on radioactive samples.

LDNSs have been experimentally realized and investigated, most commonly by directing LPA protons or deuterons onto neutron converter targets in various configurations23–25 (see Ref. 26 for the most recent review). Proof-of-concept experiments have shown the use of laser-driven neutrons for radiographic imaging27, material analysis28,29, and as diagnostic tools in laser-plasma physics30–32. Among these, the most studied application compatible with current LDNS capabilities is neutron resonance spectroscopy. This is a non-destructive material analysis technique where the dips in a transmission measurement are unambiguously assigned to a given isotope. The technique has been achieved both in a single shot, operating a neutron detector in current mode33, and by averaging over a few shots, employing single-neutron detection22,34. However, to date, experimental work has been limited to moderated sources delivering epithermal neutrons in the eV range. For unmoderated fast-neutron sources, only prospective studies on resonance spectroscopy or single-neutron detection have been reported29. Consequently, more complex measurements approaching full nuclear-physics experiments remain unexplored. Even if they have been recognized as a key scientific case at upcoming world-class laser facilities like ELI-NP35, their feasibility has yet to be experimentally demonstrated.

To show that a future research program on neutron-induced nuclear reactions with LDNSs is viable, three key capabilities must be established:

(1) It is necessary to obtain as complete information as possible about individual reactions and interaction events (i.e., single-event detection). This high degree of fidelity requires a measurement technique that can resolve individual particle interactions, a key requirement for time-of-flight (ToF) analysis and reaction cross-section studies. Consequently, detection methods that integrate over all interactions within their active volume, such as passive neutron detectors (e.g., bubble detectors36), retrospective activation methods37, or the typical current-mode operation of scintillator detectors38 that are commonly and successfully employed in LDNS experiments for neutron counting and bulk spectrometry, are incompatible with this specific requirement. Thus, a single-event fast neutron detection system, capable of operating in the harsh environment of an LPA, must be established and, what is more difficult, very shortly after the laser shot.

(2) To achieve sufficient statistics for reliable neutron time-of-flight analysis in single-event experiments, individual detector signals must be accumulated over multiple laser shots. The precise number of laser shots required is highly variable and experiment-specific, depending on factors such as the detector’s intrinsic efficiency, the solid angle coverage, the target nuclear cross-section, and the desired energy resolution. For instance, ~200 laser shots are sufficient for the demonstration experiment presented herein, whereas more than 105 proton beam pulses at the CERN n_TOF spallation source have been necessary recently to accurately measure the 12C(n,p/d) reactions up to 25 MeV39. This inherent requirement for accumulation dictates the need for stable, high-repetition-rate source operation and shot-to-shot monitoring of the experimental conditions to ensure data integrity.

(3) Accurate background characterization and subtraction, which is especially critical in LDNS environments. Unlike conventional accelerator-based sources, laser-plasma interactions generate an intense, prompt, and mixed background—including photons, electrons, ions, and scattered or secondary neutrons—whose properties are not yet fully understood or standardized.

These capabilities are demonstrated simultaneously for the first time in this work (see Refs. 40,41 for more details). The experiment discussed herein established the feasibility of studying fast neutron-induced nuclear reactions via neutron time-of-flight using a petawatt-class, ultrashort-pulse laser source operating in a stable multi-shot mode.

A suite of dedicated particle diagnostics enabled shot-to-shot monitoring of neutron, electron, proton, ion, and photon production, demonstrating the required source stability. In parallel, Monte Carlo (MC) simulations were used to model the influence of background radiation components at the detector position, which were also measured. A high-performance diamond detector was placed at a flight path of only 1.5 m, maximizing neutron flux while maintaining sufficient neutron energy resolution.

Signals from individual fast neutron-induced reactions were successfully detected over hundreds of laser shots. The measured time-of-flight spectrum is consistent with MC predictions based solely on the LPA beam diagnostics, overcoming long-standing limitations related to detector suitability, source stability, and background complexity in this challenging environment.

Results
Design and implementation of a time-of-flight setup for an LDNS
Traditional accelerator-based neutron time-of-flight facilities maintain a distinct spatial separation between the neutron source and the detection apparatus. Thick walls equipped with collimators and neutron beam guides define the neutron flight path towards the measuring stations and suppress photon and neutron scattering backgrounds from the neutron production site. This is essential for ensuring accurate and reliable experimental results, but, for now, it remains impractical with current LDNSs, as their multi-purpose laser interaction rooms are not yet optimized for neutron time-of-flight measurements. This implies a short standoff distance of the neutron detection systems not only to the neutron production target, commonly referred to as the catcher, but also to the laser-plasma interaction point, or pitcher. The latter emits a strong pulse of electromagnetic radiation (EMP) in the entire spectrum (THz, optical, X-rays, and hard γ-rays) as well as particles (electrons, protons, heavy ions) across a large solid angle, some of which are energetic enough to produce neutrons and photons not only in the catcher but in other components of the experimental setup and the laser interaction chamber. To address these challenges, a streamlined setup was employed, focusing on three key tasks, as illustrated in Figs. 1–3: (1) Characterizing the laser-plasma interaction to feed MC simulations for (2) predicting neutron generation channels and detection rates in an optimized detector and shielding configuration; and (3) continuous shot-to-shot monitoring of particle beams generated in the LPA process to enable data accumulation, as required by high-precision nuclear physics experiments.

The experiment utilized the DRACO Petawatt (PW) laser at Helmholtz-Zentrum Dresden-Rossendorf. The laser system is capable of delivering pulses of up to 18 J (on target) with a pulse duration of 30 fs42. These pulses were directed on the pitcher target at an oblique incidence angle of 50° using an f/2.3 parabolic mirror, achieving a peak intensity of ~5×1021 W/cm2. To improve the laser pulse’s temporal contrast, and thereby optimize acceleration performance and stability, a single plasma mirror setup was employed20. This, however, restricts the experiment’s repetition rate to about one shot every ten seconds and the daily shot count to approximately 200. The experiment employed plastic foils with a thickness of about 250 nm as pitcher targets, with protons and carbon ions being the most abundantly accelerated species. These ions were emitted along the normal to both the rear and front sides of the target through the well-established Target Normal Sheath Acceleration (TNSA) mechanism43.

The ion beam generated at the target’s rear was characterized using a suite of detectors, each based on different detection principles. These measurements were used to determine the contributions responsible for neutron generation in the catcher (details in the “Methods” section). A Thomson Parabola Spectrometer (TPS) was placed along the target’s normal to analyze particle spectra from the rear surface of the pitcher (forward direction, fwd) with high energy resolution. It featured a microchannel plate readout for cut-off energy detection and a Gd2O2S:Tb (GOS, on plastic support layer) scintillating screen for the absolute quantification of particle numbers44. To complement the spectral analysis, another GOS scintillating screen was positioned ~10 cm behind the pitcher target to measure lateral beam profiles of accelerated protons above a discrete threshold energy of 40 MeV. Alongside the TPS, the profiler was employed to optimize the beam daily, following the protocol in Ref. 20. A magnetic spectrometer adapted from45 was used to estimate the proton cut-off energy coming from the front side (laser incident side) of the pitcher (backward direction, bwd) by differentiating between protons and heavier ions with aluminum filters. For selected shots, stacks of radiochromic films (RCFs) were placed to map the energy-resolved spatial dose distribution delivered by the proton beam. Electrons and bremsstrahlung radiation were measured along the laser propagation direction. This was achieved by combining a magnetic electron spectrometer equipped with a GOS screen readout inside and an imaging-plate (IP)-based bremsstrahlung calorimeter46,47 placed outside the vacuum chamber. The calorimeter contained a sequence of absorber plates of different materials with increasing thickness. These plates enabled the formation of a secondary particle shower, which was recorded by the IPs as active layers.

Figure 1b summarizes the particle beam spectra retrieved from the detector suite and used as input for the MC simulations. The proton energy spectrum directed towards the catcher is shown in the top panel. It exhibits the typical quasi-exponentially decaying spectral shape with well-defined cut-off energy of about 50 MeV, surpassing by far the 1.9 MeV, 2.2 MeV and 4.2 MeV thresholds of the 7Li, 63Cu, and 65Cu (p,n) reactions. With yields of about 5×1011 protons/shot for energies above 2 MeV, the setup enables prolific fast-neutron generation. Regarding carbon ions (not shown), cutoff energies of Emax = 13 MeV/u were measured, and a total number of ~3×109 ions (>1 MeV) was estimated for use in the simulations by scaling the energy deposition measured in the detector according to the stopping power difference between protons and carbon ions; a conservative estimate was adopted, as the detector was not absolutely calibrated for these species. The contribution of oxygen ions was not examined but deemed negligible for this analysis. The backward-emitted spectrum from the front face of the pitcher is reconstructed using the RCF data from the rear side and the cutoff energy of about 35 MeV measured with the magnetic spectrometer (not shown), assuming a TNSA scenario48. During the laser-plasma interaction, electron and bremsstrahlung emission are strongest in the laser-forward direction, where respective energy spectra were measured (middle and bottom panels of Fig. 1b). To estimate their contribution to the neutron background, the simulations assumed isotropic emission characteristics and conservatively scaled the absolute numbers of electrons and photons, based on experimental measurements.

Neutrons were generated using two different catcher configurations: 3 mm thick Cu and 10 mm thick LiF. Inside the catcher material, fast neutrons are mainly produced via (p,n) reactions and emitted isotropically with MeV energies, exhibiting an exponential behavior inherited from the incident proton beam. To study neutron-induced nuclear reactions—with time-of-flight measurements being the most demanding case—it is essential to detect individual interaction events and extract relevant observables, such as timing and deposited energy. This requires detectors capable of operating in single-event mode with high temporal resolution. A detector suited to this task must combine fast response (to resolve signals separated by nanoseconds), radiation hardness (to withstand the prompt electromagnetic and particle emissions), and insensitivity to gamma and X-ray backgrounds (to avoid blinding or pile-up effects). Additionally, low intrinsic detection efficiency is beneficial to minimize pile-up in high-flux conditions.

To meet these requirements, a single-crystal diamond detector was selected and deployed in time-of-flight configuration (marked in light blue in Fig. 1a). These detectors are known for their sub-ns response time, robustness under radiation, low sensitivity to photons, and proven suitability for neutron-induced reaction studies in harsh environments. Indeed, these detectors have previously been employed successfully in ToF nuclear physics experiments involving neutron-induced reactions, such as (n,α) and fission49,50. Their demonstrated performance in demanding radiation environments—such as the n_TOF-NEAR station at CERN51 and the planned neutron diagnostics at ITER52,53—supports their suitability for use in LPA sources as well.

In previous LDNS experiments, detection systems have mostly operated in current or integral mode (relying on a fast neutron scintillator signal proportional to the total instantaneous rate of interactions) or relied on passive detectors such as activation foils or bubble dosimeters. While these bulk-integrated approaches are valid for characterizing the source, providing essential data such as total neutron yields and source stability estimates, they fundamentally lack the temporal resolution and event-specific fidelity necessary for time-of-flight measurements and the analysis of individual neutron reaction kinematics as pursued in this work. Furthermore, in LDNS measurements, the scintillators are normally surrounded by massive shielding, as in the experiment presented herein, which heavily affects the detector response to both neutrons and photons.

Nonetheless, such conventional detectors remain useful as auxiliary diagnostics. For shot-to-shot neutron monitoring, a standard EJ-232Q liquid scintillator38 coupled to a PMT was placed at 3.6 m from the source and shielded by up to 15 cm of lead and polyethylene. Although limited to providing an integrated signal proportional to the total neutron production, this is sufficient to assess the relative stability of the source on a shot-to-shot basis. Additionally, passive bubble detectors from Bubble Technology Industries54 were used to determine the absolute fast-neutron yield.

Secondary neutron sources. Contrary to conventional accelerator-based sources, particles other than protons are also produced in the laser-pitcher interaction and are emitted in different directions. The impact of these is strongly dependent on the specifics of the experimental setup and, to the best of the author’s knowledge, has not been addressed in current LDNS literature, where the focus often remains on the primary proton beam. In this work, their contribution was assessed using MC simulations. As illustrated in Fig. 2a, it turns out that a small but non-negligible fraction of the neutrons originates from reactions other than proton-induced interactions in the catcher. This secondary contribution is dominated by carbon ions for neutrons above a few MeV, and electrons for neutrons below 1 MeV.

Photon background. Since all charged particles are absorbed either by the catcher, the wall, or the shielding, only direct or secondary photons can reach the detector and induce additional signals to those from neutrons. Their contribution at the diamond detector position is displayed in Fig. 2b alongside the simulated neutron yield: the photon background, produced predominantly by electrons, is only significant at short flight times, i.e, in the region just before the arrival of the highest-energy neutrons (over 30 MeV).

Scattered (indirect) neutrons. A crucial aspect in ToF experiments is the fraction of neutrons reaching the detector indirectly after being scattered or produced in secondary processes by the surrounding elements of the setup. Kinetic energies and arrival times of the neutrons reaching the diamond detector were simultaneously scored, and the corresponding heat map plot is displayed in Fig. 2c, on top of which the dashed red line indicates the expected relationship for neutrons traveling from the catcher to the detector without interacting along the way. All signals far from this kinematic region can be attributed to scattered or secondary neutrons, i.e., neutron background. The direct and background components can be distinguished better in the inset: all signals differing from the expected behavior by more than the 3 ns duration of the ion pulse can be attributed to background. According to the simulations, in our setup, the fraction of direct neutrons at the diamond detector is still dominant over the background at 65%. In comparison, the fraction of signal versus background amounts to 48% for the bubble detector (closer to the catcher but surrounded by structural material, and more sensitive to background due to its relatively flat efficiency down to low neutron energies), and only 9% for the scintillator (further from the catcher, surrounded by massive shielding and close to the hall walls).

These observations highlight the complexity and limitations of using scintillator setups and integrating detectors as bubble detectors for neutron yield characterization or comparative studies between different LDNS, when discriminating signal origins is essential.

The simulation results in Fig. 2 illustrate the key design trade-offs to consider when optimizing a time-of-flight setup. A shorter flight path generally increases the neutron flux while reducing the neutron energy resolution. In this context, the neutron flux in the detector needs to be high enough to provide a sufficient count rate to allow for a measurement of the reaction yield, given the mentioned limit in the number of laser shots per day, but avoiding both signal pile-up and superposition of the γ-flash and the neutron signals. In this work, at the chosen distance, the simulations predict a reasonable energy resolution—on the order of a few percent, assuming a neutron production time of approximately 3 ns—with only minimal overlap between photon and neutron events. The expected count rate in the diamond detector is a few signals per laser shot, which is sufficient to keep pile-up under control while still providing adequate statistics within the ~200 shots-per-day limit imposed by the use of the plasma mirror.

Shot-to-shot monitoring
Stability and reproducibility of the laser acceleration performance are essential for multi-shot nuclear physics experiments at LDNS, given that such sources exhibit fluctuations in energy and intensity. This has been a major concern for multi-shot applications of LPA, such as radiation therapy for cancer research, and can only be addressed through reliable shot-to-shot monitoring.

As illustrated in Fig. 3, all employed diagnostics—including proton cut-off energy, proton yield, and high-energy electron production—indicate stable performance of the LPA source and subsequent neutron production under optimized conditions throughout a single shot day.

Quantitatively, the relative standard deviations (RSD) obtained across the 193 consecutive laser shots with the Cu target (unshaded region in Fig. 3) were: 7% for the proton cut-off energy (Ep,max = 54(4) MeV), 24% for the proton yield (Np,TPS = 4(1)×1012 p/shot), 26% for the proton beam profiler signal, 19% for the high-energy electron signal, and 26% for the neutron signal measured by the scintillator detector.

These values demonstrate that, despite the inherent shot-to-shot fluctuations in laser-plasma acceleration, the system maintained adequate stability to enable the accumulation of statistically significant single-event neutron data.

Two dedicated subsets of shots indicated in Fig. 3 further demonstrate that the scintillator-based neutron diagnostic can effectively assess LDNS stability: (i) inserting a PE beam dump that fully absorbs the ion beam (eliminating neutron production), which leaves only a residual background signal on the scintillator, and (ii) during the tuning phase of the LPA (for best focus and optimized spectral phase, following the protocol in 20), where the neutron signal closely follows the evolution of the primary particle beams.

It is important to note that there is no widely established benchmark for these RSD values in high-power laser plasma acceleration experiments, as traditionally such experiments have been conducted in a single-shot regime with extensive preparation for each individual shot23. Typically, only one or very few shots per day were performed. Therefore, the significance of our reported RSDs lies not necessarily in their absolute magnitude, but rather in the ability to maintain consistent and repeatable fluctuations across hundreds of consecutive laser shots. This stable, multi-shot operation enables effective shot-by-shot monitoring, allowing the identification and exclusion of non-optimal shots or experimental drifts, which is essential for accumulating statistically meaningful data in nuclear physics applications.

Single-event-based fast neutron time-of-flight spectrometry
In this work, a fast neutron and particle detector with low efficiency and low gamma sensitivity—a single-crystal diamond detector from CIVIDEC Instrumentation55—was successfully operated at only 1.5 m from the LDNS target. This short flight path, chosen to maximize the neutron flux, represents a challenging scenario due to the intense prompt electromagnetic and particle background generated by the laser-plasma interaction. Despite these conditions, the detector was able to register signals from individual interactions of fast neutrons with the carbon atoms in the detector material50, demonstrating the feasibility of single-event spectrometry in the immediate vicinity of a petawatt-class neutron source.

A trace from the diamond detector corresponding to a single laser shot is shown in Fig. 4a, obtained after optimizing the acquisition conditions. The plot illustrates the trace before (raw trace, gray) and after applying quality improvements by subtracting the signal of the γ-flash, the corresponding baseline undershoot, and the EMP-induced noise (green trace, details in “Methods”). Still, a minimum time-of-flight threshold of 20 ns remains necessary in the analysis, rejecting all signals with shorter arrival times because they overlap with the residual dominant γ-flash structure (indicated by the shaded gray area in Fig. 4a). This corresponds to a maximum detectable neutron energy of 30 MeV, consistent with the expectations from the Monte Carlo simulations shown in Fig. 2b. The remaining EMP-related fluctuations were still comparable to the amplitude of the neutron signals, necessitating the development of a dedicated Pulse Shape Analysis (PSA) algorithm. This algorithm identifies and analyzes neutron-induced reaction signals in the diamond, considering as candidates positive signals with an amplitude larger than two times the noise standard deviation, equivalent to 4 mV amplitude. These were analyzed and characterized by (see inset) amplitude, integral, width (FWHM), and timestamp (time corresponding to 30% of the amplitude in the rising slope), i.e., the time-of-flight, which is then converted into the corresponding kinetic neutron energy. Care was taken upon the occurrence of multiple-peak structures, which were statistically examined to discard noise peaks superimposed on actual signals that would then exceed the threshold.

To determine the neutron spectrum generated at DRACO PW, signals from individual neutron interactions were measured using the diamond detector and accumulated over hundreds of laser shots for two catcher materials: LiF (160 laser shots, with ~2.3 signals/shot after background subtraction) and Cu (193 laser shots, with ~1.2 signals/shot after background subtraction). Lithium was the natural choice, as it is commonly used in accelerator-based facilities operating in similar energy ranges56–58. Copper, on the other hand, was selected as an alternative configuration to support the validation of the simulation results.

The corresponding time-of-flight spectrum from each catcher was converted into neutron energy distributions after background subtraction and correction for the neutron detection efficiency. For background estimation in the detector due to the indirect neutrons discussed before, a shadow-bar (10 cm wide and 40 cm long block of borated polyethylene) was inserted in the line of sight between the neutron source and the detector. This shadow-bar, although limited in size because of the lack of space, acted as an efficient neutron shield59: A Geant4 Monte Carlo simulations showed that it absorbed or scattered 99,9% of the incident neutrons, and as much as 99,0% if only the more penetrating high energies (>10 MeV) are considered. Ideally, an additional measurement without a catcher would help in understanding the nature of the background not related to neutrons. This was attempted using a thick polyethylene catcher as a dummy, but with proton beam energies exceeding 20 MeV, even the 12C(p,n) reaction channel (Q=−18 MeV) was open, and the measurement produced a measurable neutron field (see shot ~30 in Fig. 3). In Fig. 4b, the neutron energy histograms accumulated over 67 laser shots with (background) and 193 laser shots without (raw) the shadow-bar are compared for the Cu-catcher configuration. According to the shadow-bar method, neutron scattering accounts for 40% to 50% of the signal. This is consistent with expectations, considering the limited laboratory space and shielding constraints. The measured contribution matches the prediction of the simulation presented in Fig. 2c within a 10% (see the section on “Scattered (indirect) neutrons”). The neutron detection efficiency (green line in Fig. 4b) depends on the neutron energy and the signal amplitude threshold, in which the structures visible around 5 MeV correspond to the resonances in the cross-sections for all possible 12,13C(n,*) reactions50. The efficiency curve is obtained based on Geant4 simulations60 of the detector, considering mono-energetic neutrons in the range of 0 MeV to 50 MeV and counting the events with deposited energy above the detection threshold of 400 keV. This value was selected as a compromise: sufficiently low to maximize the limited statistics, yet high enough to remain above the noise level.

Given the limited statistics, a Bayesian framework was employed for the data analysis. The direct neutron energy distribution was estimated using an ON/OFF measurement approach61,62, where the ON data represent the combined source and background signals, and the OFF data correspond to background measurements taken with the shadow-bar in place. For each energy bin, a Poisson likelihood was used to construct the posterior probability distribution of the neutron signals.

After background subtraction and detection efficiency correction, the neutron energy distributions are then converted into neutron yield in the conventional units of n/sr/MeV/shot by considering the number of laser shots delivered, the solid angle covered by the diamond, and the bin size of the histograms. The neutron yields for the Cu and LiF catchers are shown in Fig. 4c,d. In both cases, the neutron spectrum exhibits nearly exponential behavior, consistent with the TNSA shape of the laser-driven proton spectrum63.

For neutrons with energies above 100 keV, yields of ~2×108 n/shot were measured for both Cu and LiF catchers. Above 1 MeV, the yields decrease to 9×107 n/shot and 1×108 n/shot, respectively. This nearly 30% difference between catchers is consistent with simulation predictions and can be attributed to the higher threshold of the Cu(p,n) reaction. The maximum neutron energy measured in both cases is ~30 MeV, limited by the shortest time-of-flight accessible after the γ-flash and by reduced statistics at higher energies. Nonetheless, neutron production up to 50 MeV is expected for the proton energy range of the primary beam (cf. Fig. 1b).

The neutron yields per shot measured by the diamond detector are consistent with results obtained using conventional methods, such as bubble detector measurements, matching their order of magnitude and falling within a factor of 4 (see Ref. 64).

Furthermore, these experimental results for both catcher materials (LiF and Cu) were subjected to a validation against Monte Carlo (MC) simulation predictions from Geant4 and PHITS using nuclear data from the TENDL-201965 and JENDL-466 evaluated libraries, respectively. The uncertainty band between the codes arises from differences in the particle transport, nuclear interactions methods and cross-section data employed by Geant4 and PHITS. These discrepancies between different codes in modeling high-energy particle-induced reactions and subsequent neutron transport are well-known in the nuclear physics community, and observed in other neutron production calculations, for instance at the n_TOF spallation facility67. Therefore, the band shown in Fig. 4c,d can be considered only an estimate (with its range defining a lower limit for the associated uncertainty) of the neutron spectrum, against which the experiment is compared.

This cross-validation, which included matching the total neutron flux, the spectral shape, and the relative contribution of the neutron scattering background (measured via the shadow-bar technique), demonstrated a strong level of agreement, falling within 20% to 50%. This degree of fidelity is noteworthy considering that the limited accuracy of the simulations, that each data set was obtained from fewer than 200 laser shots—limiting the available statistics—and that daily fluctuations in proton yield were already of comparable magnitude.

Overall, although no explicit nuclear reaction was investigated in this experiment, the registration and processing of single neutron-induced signals generated within the diamond detector already correspond to 12,13C(n,*) reactions produced within the detector material itself. In addition, the ability to identify individual signals and extract well-defined observables—such as time, amplitude, and FWHM (related to the incident energy, deposited energy, and signal shape, respectively)—opens the door to pulse-shape discrimination analysis and enables the exploration of correlations between these observables for deeper insight into the reaction processes of interest. These findings demonstrate the feasibility of studying neutron-induced nuclear reactions via time-of-flight using a PW laser-driven neutron source.

Methods
Laser-driven neutron source
Experiments were performed at the DRACO PW laser at the Helmholtz-Zentrum Dresden-Rossendorf. DRACO PW is a double-CPA Ti:Sa laser system, providing 30 fs (FWHM) laser pulses with a central wavelength of 810 nm (50 nm bandwidth FWHM). The pulses carried an energy of ~18 J and were focused onto thin (~250 nm) Formvar plastic foils (C5H8O2, ne=230nc when fully ionized) by an f/2.3 off-axis parabolic mirror to a FWHM spot size of 2.6 μm, yielding peak intensities of 5.4×1021 W/cm2. Plasma mirror (PM) cleaning was applied to improve the temporal contrast by almost four orders of magnitude, essentially removing all remaining prepulses and limiting the ionization and plasma dynamics to the last ps before the peak of the laser20,80–82. PM operation limited the shot rate to about one shot every 20 s and the total number of shots to about 200 shots per day. The work presented herein corresponds to neutrons generated using two different catcher options (10 mm thick LiF and 3 mm thick Cu) on two separated days. The complete experimental campaign took place over several days, which were devoted to the optimization of the LPA and detection systems.

Particle diagnostics
The spatial proton intensity distribution was measured using calibrated radiochromic film (RCF) stacks in several reference shots. A Thomson Parabola spectrometer (TPS) placed at 45° was used to measure ion spectra for every laser shot. A small fraction of the ion beam emitted from the target was delivered by passing through the 4 mm diameter hole in the catcher and a pair of small pinholes towards the TPS. This resulted in a set of two parabolic traces, one recorded with a microchannel plate in imaging configuration to assess the cut-off energy with high spatial resolution and high dynamic range, and the other used a calibrated Gd2O2S:Tb (GOS) scintillating screen44 for absolute proton number determination in the proton energy range of 5 MeV to 25 MeV. The TPS and RCF data, with remarkable agreement, indicate that a total of 5×1012 protons/sr/shot to 6×1012 protons/sr/shot are produced by each laser pulse. Considering the beam divergence of around ~20°, this corresponds to a proton beam intensity of 5.6×1011 particles/shot (spectrally integrated for >2 MeV). The predominant heavy ion species was C6+. In the text, these are labeled as carbon ions for simplicity. On-shot spatially resolved particle detection was conducted with a proton beam profiler. Another calibrated GOS scintillator screen was attached to the rear of the catcher to measure the beam profile of protons with an energy larger than 40 MeV. A bandpass-filtered (540(2) nm) CMOS camera captured the emitted luminescence light.

Electron spectra were recorded shot-to-shot using a magnetic spectrometer positioned in the laser-forward direction, 640 mm from the source. Electrons entered through a 10 mm diameter aperture and were magnetically dispersed and deflected onto a GOS scintillating screen imaged by a CMOS camera. Spectral information was retrieved using a custom code incorporating a General Particle Tracer simulation of the spectrometer response. The system was optimized for electrons with kinetic energies of 1 MeV to 60 MeV and allowed evaluation of electron temperatures in the range of 0.5 MeV to 40 MeV.

All neutron detectors were placed outside the vacuum chamber.

Integral neutron production was measured using PND-type Bubble detectors and a Bubble Reader from Bubble Technology Industries, positioned at various locations around the target area. To achieve reasonable bubble counts (~100, to reduce statistical and read-out errors), approximately 10 laser shots were accumulated. The bubble count was then converted into a neutron yield according to the protocol in64, which considered the detector response from the manufacturer and applied temperature and energy corrections based on the MC-simulated neutron energy spectrum at the bubble detectors’ positions.

Traces of the diamond detector (4×4 mm2 surface and 500 μm thickness), mounted at 1.5 m from the target, were amplified using a 2 GHz C2-HV Broadband Amplifier by CIVIDEC Instrumentation and recorded with a Tektronix MSO64B oscilloscope (6 GHz bandwidth, 12 bits, 10 GS/s). The main challenge was the prompt detector saturation due to the X-ray photon flash (γ-flash in the following) and the pile-up resulting from harsh radiation and high instantaneous flux, which prevented the measurement of individual fast neutron signals at low time-of-flight. These factors, the high signal originating from the γ-flash and the high interaction rate at the detector caused by the high instantaneous flux, generate the signal undershoot due to the coupling of the amplifier. To minimize these issues, 50 mm of lead filter was added in front of the detector.

Following the X-ray photon flash, the trace exhibited high-frequency noise for approximately 250 ns due to the electromagnetic pulse (EMP) from the laser-plasma interaction. Initially, the EMP noise reached amplitudes up to 200 mV, but it was reduced to a few mV by using EM shielding around the detector and electronics and by using passive low-pass filters in the bias voltage supply cable. The detector was also electrically isolated to decouple its ground from the common ground of the whole accelerator installation. For this purpose, the detector was connected to an independent power supply, and plastic foils were used to prevent metallic contact with other surrounding materials. The oscilloscope was placed outside the laser bunker to prevent ground loops and extra EMP coupling in the acquisition system itself. The saturation due to the γ-flash and the EMP ringing were relatively consistent between shots of a single day; thus, the corresponding exponentially decaying tail and the constant oscillating component were averaged across all recorded traces and subtracted from each trace, resulting in a significantly cleaner baseline that allowed for better signal identification. Signal undershoot and associated baseline shifts were corrected by locally averaging the values immediately before and after the signal.

The detector was energy-calibrated to establish the detection threshold applied in the signal analysis. According to the manufacturer, the energy deposited in the detector for a signal depends directly on the area of the signal and the carbon ionization energy (13 eV), and inversely on the detector impedance (50 Ω), the gain of the amplifier (150), and the electron charge. To avoid integrating residual noise into the signals, the area is calculated assuming the step-function shape of the signals50, i.e., multiplying the signal’s width (FWHM) by its amplitude, since these variables are less affected by noise. To assess the effect of the uncertainties in the signal area and possible gain variation, ±30% fluctuations in the calibration were tolerated, which are within the statistical uncertainties.

Monte Carlo (MC) simulations
To evaluate the influence of the different secondary particles and to inform the design of the experimental setup, simulations were performed with the MC code PHITS (version 3.31)83,84, applying input parameters as presented in Fig. 1. The geometry was adapted to the real laboratory infrastructure consisting of concrete walls and floor, vacuum vessel (stainless steel and aluminum assembly) with inner components (such as glass parabola, breadboard, and magnet yokes), and detector system (bubbles, scintillators, and diamond), including applied lead shielding. Both catcher options, LiF and Cu, used in the experiment were evaluated. Within the simulation framework, the following settings were applied: (1) JENDL-4.066,85 nuclear data library was used for neutron transport and to model proton-induced nuclear reactions, e.g., (p,n) reactions. (2) TENDL-201965 was used for photonuclear reactions, and (3) EGS5 (Electron-Gamma Shower, version 5) code86 for photon and electron transport. (4) The Kurotama87 and Intra-Nuclear Cascade of Liège (INCL)88 models were implemented as part of the simulation settings. Simulations of the neutron efficiency of the diamond detector were performed for a simplified geometry with the GEANT4 toolkit60,89,90 using the QGSP_BIC_AllHP physics list, the JEFF-3.3 nuclear data library91 and the NRESP model92 for neutron transport and proton-induced reactions.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript reports the development of a laser-driven neutron source (LDNS) and fast neutron energy spectrometer based on a single-event analysis technique. The authors succeeded in generating MeV-energy neutrons over continuous 200 laser shots on the DRACO laser facility. The neutrons ranging from 1 to 30 MeV are analyzed by the single-event spectrometer, capable of resolving individual neutron-induced reactions. The authors also discussed the possibility of laser-driven fast neutron spectroscopy compared with conventional accelerator-based neutron sources. In general, the study of LDNS and its applications is growing rapidly these days. However, in order to attract the interest of many readers from a wide range of fields, the manuscript should be revised, where descriptions that are difficult to understand for researchers outside the field and several inaccurate descriptions need to be changed.\nAs to the title “Single-event neutron time-of-flight spectroscopy with a petawatt-laser-driven neutron source,” the “single event” mode, as the antonym of current mode, is a technical term used in nuclear physics and high-energy physics,and is unfamiliar to researchers in other fields. The authors should reconsider using it in the title. In addition, “Spectroscopy” is generally defined as a fundamental tool to explore the characteristics of matter, including the composition, physical structure, electronic structure and so on. This manuscript only demonstrated the neutron detector system, not showing the result of spectroscopy. In my opinion, “spectroscopy” should be changed into “spectrometer” or “energy analyzer”.\nIn the abstract, the authors described “However, their use in single-event fast neutron spectroscopy remains unproven.” This statement is misunderstanding because the demonstration of the single-event spectroscopy by epi-thermal neutrons from LDNS has already been reported in a journal of Nature Springer group [Koizumi et al., Scientific Reports14, 21916 (2024)], where the areal density of two kinds of metal plates (Ag and In) were successfully analyzed. The authors should refer to the manuscript above and explain the novel point of this manuscript including the difference between fast and epi-thermal neutrons.\nOn page 3, the authors raised three key capabilities that must be established for the research of neutron-induced nuclear reactions. However, they contain some statements that are not in line with reality. In the item (1), the authors claim that bubble detectors and activation methods are not suitable in the harsh environment of the laser plasma acceleration (LPA). This statement isn't fair. These detection methods provide meaningful results of neutron counting when they're used correctly. Many researchers know from experience that when the bubble detectors are located near the chamber wall (as shown in Fig. 1 of this manuscript), the number of neutrons generated from the LDNS is always overestimated. This is because the neutrons from the chamber wall are directly injected into the bubble detectors. To avoid this, bubble detectors are often placed near the LDNS, where the effect of backgrounds, including neutrons from the chamber wall, is expected to be small. Also in the use of activation method [33], the activation sample was collated directly on the LDNS because of the reason above. The statement by the authors may give an impression that these detectors are always unsuitable in the LPA experiments, but that's not what the authors intended.\nIn the same item, the authors claim that the current mode operation of neutron scintillator detectors is not suitable for the LDNS experiments. This is misunderstanding, because the current mode operation can serve as a reliable spectrometer when the backgrounds are appropriately subtracted. The current mode detector is historically established by the researchers of nuclear physics [Bowman et al., Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 297, 183(1990)], not only by the researchers of LPA, and regarded as a reliable method. In the field of LPA and LDNS studies, the neutron resonance spectroscopy was successfully obtained by the current mode detector system [21], where the gamma-ray flash was suppressed by the high-speed voltage switch system and the background level was determined from the resonance signal of 100% absorption. (Note the reference 21 is explained as a study of radiographic imaging on Page 2. This is not correct. The radiographic imaging was shown by Yogo et al., Applied Physics Express 14, 106001 (2021)). Recently, the temperature of the samples were analyzed [Lan et al., Nature Communications 15, 5365 (2024)] by the Doppler broadening of the resonance signal obtained in the current mode spectroscopy driven by LDNS. These results should be considered in the manuscript. In addition, the statement on page 5, “In previous LDNS experiments, detection systems have mostly operated in current or integral mode,or relied on passive detectors such as activation foils or bubble dosimeters. While these approaches are suitable for estimating total neutron yields or monitoring source stability, they do not provide the time-resolved and event-specific information required for neutron spectroscopy or reaction studies.” should be reconsidered.\nIn the item (2), the authors claim that “To achieve sufficient statistics, single-event signals need to be accumulated over many laser shots.” What is the lower limit of shot number required for the spectroscopy the authors try to demonstrate? 200 shots are sufficient for it? Is the requirement of many laser shots (“many” is not a scientific term) attributed to the neutron number per shot or the limit coming from the pile-up effect of the single-event detector in high neutron flux condition?\nOn page 5, the authors described “Contrary to conventional accelerator-based sources, particles other than protons are also produced in the laser-pitcher interaction and are emitted in different directions. The impact of these is strongly dependent on the specifics of the experimental setup and has been neglected in all previous studies.” Please show the evidence that all previous studies neglected the effect.\nFig. 4 (b) shows the comparison between the raw data and the background, where the background value is higher than the raw data for the energy higher than 10 MeV. This result indicates that the statistics is not sufficient in the single laser shot measurement. Is it possible to integrate the data over several laser shots to ensure the statistics? The low statistics results in the large error bars shown in the frame (c) and (d).\nFig. 4(c,d) show the results of MC simulations by Geant 4 as lower limit and PHITS as upper limit. Why does the Geant4/PHITS result show lower/upper limit of the neutron spectrum? Please explain the deference of physics and processes assumed in the two codes.\nFigures 4(c) and (d) show that only two or three data points are obtained for each 5-MeV energy range. This indicates that the energy bin is too discrete to analyze the nuclear reactions assumed in this work. Enhancing the statistics will resolve this problem. Why don't the authors integrate the neutron spectra over several laser shots? How many shots are useful for analysis out of 200 laser shots?\nOn page 9, the authors discuss the energy resolution of their LDNS in the TOF method (see Fig. 5) and compare it with the results of conventional accelerator-based neutron sources.\nThe DRACO results appear to be simulation-based values (or calculations based on the laser pulse width), not experimental values. If so, the authors should clarify that they are based on simulations to avoid any misunderstanding. In general, comparisons with results from other research fields should be made with caution. If the neutron pulse width in LDNS has not been obtained experimentally, then careful consideration should be given to claiming the superiority of LDNS compared to accelerators. Note that the neutron pulse duration can be evaluated experimentally from the width of the neutron resonance absorption, as described in the manuscripts by Lan and Bowman mentioned above.\nIn the conclusion, the authors described “An interesting choice of samples and reactions could be fission on 235U and 239Pu in the spirit of the very recent experiment of the NIFFTE Collaboration [65] at LANL for measuring the 239Pu/235U fission cross section ratio with an unprecedented accuracy of just 1%.” However, even after reading the abstract and Introduction of [65], the reviewer cannot understand the importance. The importance may not clear to many readers. Please explain the importance in detail or give another example.\nMinor points\nRef [2] is a paper on nuclear fission, not an appropriate example of a paper on neutron application to nuclear physics. The following paper is recommended instead.\n\"The neutron. its properties and basic interactions\" Hartmut Abele\nProgress in Particle and Nuclear Physics, 60, 1-81 (2008).\nThis has over 300 citations.\nRef [1] and [11] are identical.\nOne of the two can be changed into\n\"Neutron reactions in astrophysics\" R Reifarth, C Lederer and F Käppeler\nJournal of Physics G: Nuclear and Particle Physics, 41, 053101 (2014).", "reviewer_2": "This work by Millan-Callado et. al. presents a significant advance in single event time of flight measurements for laser driven neutron sources. The data presented is convincing that neutron induced reactions are a potential avenue for study at LDNS with diamond detectors and significant attention to characterizing the difficult radiation environment. I am impressed by the work and recommend it for publication. The raw data, analysis, and text present a strong argument, however I would suggest a few additional details could be added, at the discretion of the authors and editors, to benefit the reader.\n1. To measure and distinguish single neutron events from the background is a difficult task. The authors diamond detectors are sensitive to neutrons, charged particles, and high energy photons which are all created in the laser interaction. Experiments with Cu and LiF catchers are fully described with and without the shadow bar. The shadow bar is designed to shield the diamond radiation detector from the direct neutrons and only measure the scattered background, but could itself affect the scattered signal in unanticipated ways. No experiments are described without a catcher target that could assist in determining the neutron background from \"other components of the experimental setup and the laser interaction chamber.\" If these experiments were performed their inclusion would strengthen the result. I understand that beam time is limited.\n2.In the same theme, additional information and testing on the shadow bar configuration would be greatly appreciated. The background determination is important enough in the single neutron results presented, 40-50% of the signal, that I believe the shadow bar deserves more attention in the body of the work.\n3.Much of the paper describes the Monte Carlo simulations.These simulations take as inputs the interpolated proton, electron and x-ray spectra shown in figure 1 and output the expected contribution to the neutron signal shown in figure 3. Including a few spectra in figure 1 from different shots alongside the interpolations could further convince the reader that these measurements were performed correctly.\n4. In it unclear in the figure caption and text if the reported RSD values are for all 204 plotted shots or for only the \"unshaded region [which] represents shots with optimized neutron performance (stability within 26 % standard deviation).\" I would prefer to have RSD for only the optimized shots and also include the RSD of the optimized shots between different days.\n5. In figure 4, the key representation of the single event neutron data, I believe a few extra details would help the reader. In the inset in part a, I suggest that the energy of that single neutron event be included. Where does that single neutron signal fall on the plots in part b and c? And what are the energies of the other two neutron signals at 40 and 90 ns?\n6. Finally it is implied that this type of data at DRACO can be collected with ~200 shots per day and that the beam time this paper is based on occurred over several days. Understanding the total number of shots for the entire campaign, the number of shots to produce figure 4 c,d, and a comparison of the background and performance over multiple days would benefit the reader."}, "author_response": "Response to Reviewers\nReviewer comment #1: The manuscript reports the development of a laser-driven neutron source (LDNS) and fast neutron energy spectrometer based on a single-event analysis technique. The authors succeeded in generating MeV-energy neutrons over continuous 200 laser shots on the DRACO laser facility. The neutrons ranging from 1 to 30 MeV are analyzed by the single-event spectrometer, capable of resolving individual neutron-induced reactions. The authors also discussed the possibility of laser-driven fast neutron spectroscopy compared with conventional accelerator-based neutron sources. In general, the study of LDNS and its applications is growing rapidly these days. However, in order to attract the interest of many readers from a wide range of fields, the manuscript should be revised, where descriptions that are difficult to understand for researchers outside the field and several inaccurate descriptions need to be changed.\nResponse: We would like to thank the appreciations of the reviewer regarding the interest of this work for a wide range of fields, and the specific comments that have helped us revising the text to make it more precise, and accessible and understandable for the interdisciplinary audience of Nature Communications.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #2: As to the title “Single-event neutron time-of-flight spectroscopy with a petawatt-laser-driven neutron source,” the “single event” mode, as the antonym of current mode, is a technical term used in nuclear physics and high-energy physics, and is unfamiliar to researchers in other fields. The authors should reconsider using it in the title. In addition, “Spectroscopy” is generally defined as a fundamental tool to explore the characteristics of matter, including the composition, physical structure, electronic structure and so on. This manuscript only demonstrated the neutron detector system, not showing the result of spectroscopy. In my opinion, “spectroscopy” should be changed into “spectrometer” or “energy analyzer”.\nResponse: We appreciate the reviewer's feedback regarding the accessibility of the title and its precision, particularly for readers outside the nuclear and high-energy physics community. We have considered both suggestions carefully.\nWe agree that the term \"Spectroscopy\", despite being technically precise for the measurement technique used in nuclear and particle physics where signals from individual radiation or particle interaction events are recorded and analyzed, rather than averaged over many events; can be widely associated with the application of analyzing matter properties (composition, structure, etc.). While our technique is indeed a foundational step towards such applications, the manuscript primarily focuses on the demonstration and characterization of the measurement methodology itself: the successful detection and analysis of individual neutron events in the challenging petawatt laser environment.\nTo reflect the scope of the work more accurately, which is the development of the measurement system and method, we have adopted the reviewer's suggestion to use the term \"Spectrometry\" instead of \"Spectroscopy\" in the title. We believe this choice reduces ambiguity and aligns better with the technical content of the paper, which establishes a new metrology.\nNevertheless, we respectfully request to retain the term \"Single-Event\" in the title and text.\nIn nuclear physics and high-energy physics, \"Single-Event\" is the precise technical term required to distinguish our method from current-mode or charge-integrated detection methods. Single-Event detection for fast neutrons is the core innovation of our work: moving LDNS measurements from bulk-averaged data to the ability to analyze individual neutron interactions with high fidelity. This mode of operation is critical for studying time-of-flight (TOF) and reaction kinetics under the ultrashort pulse duration characteristic of LDNSs. The term \"single-event\" directly conveys this fundamental change in measurement capability.\nTo mitigate the risk of misunderstanding by researchers from other fields, we have ensured that the text provides a clear definition of the concepts \"single-event\", \"single-shot\" or \"single-particle”, with the emphasis in “Single-Event Spectrometry” as a measurement technique where the signals from individual radiation or particle interaction events are recorded and analyzed.\nThe revised title is now:\nSingle-event fast neutron time-of-flight spectrometry with a petawatt-laser-driven neutron source\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #3: In the abstract, the authors described “However, their use in single-event fast neutron spectroscopy remains unproven.” This statement is misunderstanding because the demonstration of the single-event spectroscopy by epi-thermal neutrons from LDNS has already been reported in a journal of Nature Springer group [Koizumi et al., Scientific Reports14, 21916 (2024)], where the areal density of two kinds of metal plates (Ag and In) were successfully analyzed. The authors should refer to the manuscript above and explain the novel point of this manuscript including the difference between fast and epi-thermal neutrons.\nResponse: It is indeed crucial to make the distinction between epithermal and fast neutrons. Furthermore, the work by Koizumi et al. (2024) is very relevant, and in this context is an excellent demonstration of LDNS-based single-event neutron spectroscopy for epithermal neutrons.\nOur previous wording, \"remains unproven,\" was indeed too broad and we apologize for the lack of specificity. Although the abstract (and the full manuscript) it was always contextualize in the regime of high-energy neutrons, which is not directly applicable in Koizumi et al. (2024), we have amended the abstract to clearly acknowledge the precedents in other energy regimes and to precisely define the scope and novelty of our work, which lies in the higher energy regime (fast neutrons, E > 1 MeV) and the associated technical challenges.\nThe statement in the Abstract has been modified from:\n“However, their use in single-event fast neutron spectroscopy remains unproven...”\nto:\n\"While single-event neutron spectroscopy has been demonstrated with epithermal and low-energy neutrons, its application to fast neutron spectrometry is more challenging and remains unproven.\"\nClarification of novelty and energy regimes\nThe critical difference between epithermal (or low-energy) and fast neutrons defines the novelty of our study:\n• Epithermal/Low-Energy Neutrons (~ 0.5 eV 1 MeV): These neutrons primarily interact via absorption or scattering at relatively low recoil energies. The work by Koizumi et al. focuses on this regime, which is ideal for material analysis through resonance phenomena and is technically less demanding on the detector's time resolution, signal-to-noise ratio within a harsh environment and fast recovery from the gamma-flash.\n• Fast Neutrons (E > 1 MeV): This regime is dominated by inelastic scattering and fast-neutron-induced reactions. Accurate spectroscopy in this regime requires detectors capable of resolving fast recoil protons or alpha particles (e.g., in our diamond detector) operating in the extreme high-energy particle and gamma-ray background generated by the petawatt laser-plasma interaction, which is a significant challenge when the detector must be placed close to the source.\nOur main novelty is the successful demonstration of single-event counting spectroscopy for fast neutrons (at only tens of ns after the laser shot) while operating under the full, unmitigated electromagnetic and radiation background of the petawatt laser interaction and demonstrating stable multi-shot performance (over 200 shots), which is a key requirement for any future experimental campaign.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #4: On page 3, the authors raised three key capabilities that must be established for the research of neutron-induced nuclear reactions. However, they contain some statements that are not in line with reality. In the item (1), the authors claim that bubble detectors and activation methods are not suitable in the harsh environment of the laser plasma acceleration (LPA). This statement isn't fair. These detection methods provide meaningful results of neutron counting when they're used correctly. Many researchers know from experience that when the bubble detectors are located near the chamber wall (as shown in Fig. 1 of this manuscript), the number of neutrons generated from the LDNS is always overestimated. This is because the neutrons from the chamber wall are directly injected into the bubble detectors. To avoid this, bubble detectors are often placed near the LDNS, where the effect of backgrounds, including neutrons from the chamber wall, is expected to be small. Also in the use of activation method [33], the activation sample was collated directly on the LDNS because of the reason above. The statement by the authors may give an impression that these detectors are always unsuitable in the LPA experiments, but that's not what the authors intended.\nResponse: The reviewer is raising a fair point and a potential source of misunderstanding regarding the role and suitability of established detection techniques in the LDNS community. It was not our intention to give the impression that these methods are generally unsuitable in the LPA environment, we fully acknowledge that techniques such as bubble detectors and activation analysis are successfully and routinely employed in LDNS experiments for reliable neutron counting and bulk spectrometry.\nThe ambiguity stems from the term \"single-event\" itself. In this context, we are referring to the need of record and analyze each individual particle interaction within the detector to obtain complete information about individual reactions, which is essential for advanced Time-of-Flight (TOF) analysis and specific nuclear reaction cross-section measurements that constitute our proposed future research program. This resolution is not achievable with methods that integrate signals, such as bubble detectors, activation analysis, or current-mode operation.\nWe have revised item (1) in the text to:\n1. Explicitly define the requirement as \"single-event resolution\".\n2. Acknowledge and validate the successful use of passive and current-mode detectors in LDNS experiments for their intended purpose (counting and bulk spectrometry).\n3. Refocus the critique by stating that these bulk-integrating methods \"are insufficient for this specific requirement\" of individual reaction fidelity.\nWe believe this revision clarifies that our argument is one of functional necessity for a specific advanced measurement technique rather than a general critique of established detectors.\nThe text is now re-written as follows:\n1) It is necessary to obtain as complete information as possible about individual reactions and interaction events (i.e., single-event detection). This high degree of fidelity necessitates a measurement technique that can resolve each individual particle interaction, which is a key requirement for time-of-flight (TOF) analysis and reaction cross-section studies. Consequently, detection methods that integrate over all interactions within their active volume, such as passive neutron detectors (e.g., bubble detectors \\cite{Ing1997}), retrospective activation methods \\cite{Mori:2021}, or the typical current-mode operation of scintillator detectors \\cite{mirfayzi2015calibration} that are commonly and successfully employed in LDNS experiments for neutron counting and bulk spectrometry, are incompatible with this specific requirement. Thus, a single-event fast neutron detection system must be established that is capable of operating in the harsh environment of an LPA and, what is more difficult, very shortly after the laser shot.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #5: In the same item, the authors claim that the current mode operation of neutron scintillator detectors is not suitable for the LDNS experiments. This is misunderstanding, because the current mode operation can serve as a reliable spectrometer when the backgrounds are appropriately subtracted. The current mode detector is historically established by the researchers of nuclear physics [Bowman et al., Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 297, 183(1990)], not only by the researchers of LPA, and regarded as a reliable method. In the field of LPA and LDNS studies, the neutron resonance spectroscopy was successfully obtained by the current mode detector system [21], where the gamma-ray flash was suppressed by the high-speed voltage switch system and the background level was determined from the resonance signal of 100% absorption. (Note the reference 21 is explained as a study of radiographic imaging on Page 2. This is not correct. The radiographic imaging was shown by Yogo et al., Applied Physics Express 14, 106001 (2021)). Recently, the temperature of the samples were analyzed [Lan et al., Nature Communications 15, 5365 (2024)] by the Doppler broadening of the resonance signal obtained in the current mode spectroscopy driven by LDNS. These results should be considered in the manuscript. In addition, the statement on page 5, “In previous LDNS experiments, detection systems have mostly operated in current or integral mode or relied on passive detectors such as activation foils or bubble dosimeters. While these approaches are suitable for estimating total neutron yields or monitoring source stability, they do not provide the time-resolved and event-specific information required for neutron spectroscopy or reaction studies.” should be reconsidered.\nResponse: We appreciate the reviewer pointing out the incorrect description of Reference [21] on Page 2. We have corrected it in the text and we have checked the neighboring references for accuracy.\nWe also acknowledge the reviewer's detailed point regarding the current-mode operation of scintillator detectors. We agree that current-mode detectors, when properly managed (e.g., background subtraction, gamma flash suppression), have been historically established in nuclear physics and have been successfully employed in LDNS experiments for neutron resonance spectroscopy, but only because this does not require a precise counting of individual neutrons but only the sample-in/sample-out ratio in which the background and efficiency corrections are cancelled, which is not the case for spectrometry or neutron time-of-flight in general, and that is indeed their limitation. However, as it was addressed in the previous comment, our use of the term \"unsuitable\" was strictly limited to the necessity for single-event resolution in many applications. Both passive detectors and current-mode detectors inherently operate by integrating or averaging the signal over many interactions and over a finite time window. This approach, while excellent for bulk measurements and total yield estimation, does not provide the time-resolved information necessary for the advanced nuclear reaction studies proposed in our manuscript. Our work focuses on establishing this specific single-event fast neutron time-of-flight methodology in the LPA environment.\nConsidering these discussions, the statement on Page 5 has been revised to remove any suggestion that these methods are generally unsuitable, now focusing solely on the limitation for single-event analysis:\nIn previous LDNS experiments, detection systems have mostly operated in current or integral mode (relying on a neutron scintillator signal proportional to the total instantaneous rate of interactions) or relied on passive detectors (such as activation foils or bubble dosimeters). While these bulk-integrated approaches may be valid for characterizing the source, providing good estimations of the total neutron yields and establishing the source stability, they fundamentally lack the temporal resolution and event-specific fidelity necessary for time-of-flight measurements and the analysis of individual neutron reaction kinematics as pursued in this work. Furthermore, in LDNS measurements the scintillators are normally surrounded by massive shielding, as in the experiment presented herein, that affect heavily the detector response to both neutron and photons.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #6: In the item (2), the authors claim that “To achieve sufficient statistics, single-event signals need to be accumulated over many laser shots.” What is the lower limit of shot number required for the spectroscopy the authors try to demonstrate? 200 shots are sufficient for it? Is the requirement of many laser shots (“many” is not a scientific term) attributed to the neutron number per shot or the limit coming from the pile-up effect of the single-event detector in high neutron flux condition?\nResponse: We understand the need of a more precise discussion about the requirements for shot accumulation. Indeed, the term \"many\" is unscientific and needs clarification, as it touches upon the core challenges of LDNS particle detection experiments. We have modified the text in Item (2) to replace the vague term and explicitly incorporate the inherent variability of this requirement, which is essential context for our work:\n(2) To achieve sufficient statistics for reliable neutron time-of-flight analysis in single-event experiments, individual detector signals must be accumulated over multiple laser shots. The precise number of laser shots required is highly variable and experiment-specific, depending on factors such as the detector's intrinsic efficiency, the solid angle coverage, the target nuclear cross-section, and the desired energy resolution. For instance, ~200 laser shots are sufficient for the demonstration experiment presented herein, but more than 10$^5$ proton beam pulses at the CERN n\\_TOF spallation source have been necessary recently to measure accurately the $^{12}$C(n,p/d) reactions up to 25~MeV \\cite{Zugec:2025}. This inherent requirement for accumulation dictates the need for stable, high-repetition-rate source operation and shot-to-shot monitoring of the experimental conditions to ensure data integrity.\nAs noted in the revised text, the required number of shots varies and is determined by a complex interplay of factors:\n• Necessity for accumulation (neutron yield/efficiency limit): the primary driver for accumulating hundreds or thousands of shots is the need to populate small energy bins for spectrum analysis. This requirement stems from the low intrinsic detection efficiency (a necessary design choice to mitigate pile-up) combined with the need to measure specific nuclear cross-sections, especially those that are small or in the high-energy tail.\n• Sufficient statistics for this work: the 200 shots delivered in the DRACO experiment were sufficient for the goal of this manuscript: to successfully demonstrate the feasibility of the single-event TOF metrology in the harsh PW environment and to benchmark the measured reaction rates against MC simulations. Full, high-resolution spectroscopy would indeed demand a higher number of accumulated events, highlighting the importance of the stable, multi-shot platform we have established.\nWe believe the revised statement provides the necessary context and scientific justification for the requirement of sustained, high-repetition-rate operation.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #7: On page 5, the authors described “Contrary to conventional accelerator-based sources, particles other than protons are also produced in the laser-pitcher interaction and are emitted in different directions. The impact of these is strongly dependent on the specifics of the experimental setup and has been neglected in all previous studies.” Please show the evidence that all previous studies neglected the effect.\nResponse: The use of the term \"all\" is inappropriate in scientific literature as it is difficult to prove a negative universal. However, we have not found a single reference in which such secondary neutrons sources have been considered. In order to keep our claim of being the first to study this issue in detail while avoiding claiming a complete absence of consideration, we have changed the text to:\n\"... and, to the best of the author's knowledge, has not been addressed in current LDNS literature,…\"\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #8: Fig. 4 (b) shows the comparison between the raw data and the background, where the background value is higher than the raw data for the energy higher than 10 MeV. This result indicates that the statistics is not sufficient in the single laser shot measurement. Is it possible to integrate the data over several laser shots to ensure the statistics? The low statistics results in the large error bars shown in the frame (c) and (d).\nResponse: This observation provides a valuable opportunity to clarify the nature of single-event spectrometry and the data acquisition presented in Figure 4.\nThe reviewer's premise that Figure 4 (b) is a single-laser-shot measurement is incorrect. Figure 4 (b), (c), and (d) already represent the cumulative results of ~200 laser shots. We have clarified this fact in the main text: “To determine the neutron spectrum generated at DRACO~PW, signals from individual neutron interactions were measured using the diamond detector and accumulated over hundreds of laser shots for two catcher materials: LiF (160 laser shots, with $\\sim$2.3 signals/shot) and Cu (193 laser shot, with $\\sim$1.2 signals/shot).” and have explicitly updated the caption for Figure 4 to state \"Neutron energy histograms accumulated over 67 laser shot with (background) and 193 laser shots without (raw) the shadow-bar} for p-Cu pitcher-catcher configuration showing the effect of the background \"\nWe agree that the low statistics in the high-energy region leads to large error bars in Figures 4 (c) and (d). This is an inherent limitation of this initial proof-of-concept experiment. Our primary goal was to demonstrate the feasibility of the single-event methodology in LDNS—achieving stable operation, managing the extreme background environment, and extracting any measurable reaction signal—, not to deliver high-precision time-of-flight data. The ~200 accumulated shots were sufficient to demonstrate the single-event capability and to validate the resulting reaction rates against Monte Carlo simulations.\nImproving the statistics in the high-energy tail will be the objective of future campaigns by using a LPA set-up that can deal with higher repetition rate and total number of laser shots, thus increasing the total number of shots accumulated (as suggested in our discussion), and employing detector arrays.\nTo deal with the low statistics and optimize the signal-to-background ratio in the ToF spectra, we adjusted the energy resolution (binning) to 2 MeV.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #9: Fig. 4(c,d) show the results of MC simulations by Geant 4 as lower limit and PHITS as upper limit. Why does the Geant4/PHITS result show lower/upper limit of the neutron spectrum? Please explain the deference of physics and processes assumed in the two codes.\nResponse: Comparing results from different Monte Carlo codes is a common and essential practice in nuclear and high-energy physics. This is done to establish the model-dependent uncertainty inherent in simulating complex particle interactions, such as those governing neutron production and transport in a pitcher-catcher setup. Discrepancies between codes, particularly in the prediction of differential cross-sections for hadron-nucleus interactions, are well-known. In this way, the band defined by these two established codes provides an estimate (actually, a lower limit)of the systematic uncertainty of the expected neutron yield against which the measurements is compared.\nWe have modified the text near Figure 4 to briefly include this explanation, ensuring the reader understands the physical origin of the uncertainty band:\nFurthermore, these experimental results for both catcher materials (LiF and Cu) were subjected to a validation against Monte Carlo (MC) simulation predictions from Geant4 and PHITS, using in both cases nuclear data from the JENDL-4 evaluated library. The uncertainty band between the codes arises from differences in the particle transport methods, nuclear interaction models and cross-section data employed by Geant4 and PHITS. These discrepancies between different codes in modeling high-energy particle-induced reactions and subsequent neutron transport are well-known in the nuclear physics community (see for instance https://doi.org/10.1140/epja/i2016-16100-8). The band shown in Fig.\\ref{Fig_Diamond}c and d therefore serves as an estimate (with its range defining a lower-limit for the associated uncertainty) of the neutron spectrum, against which the experiment is compared.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #10: Figures 4(c) and (d) show that only two or three data points are obtained for each 5-MeV energy range. This indicates that the energy bin is too discrete to analyze the nuclear reactions assumed in this work. Enhancing the statistics will resolve this problem. Why don't the authors integrate the neutron spectra over several laser shots? How many shots are useful for analysis out of 200 laser shots?\nResponse: Indeed, the data presented in Figures 4(b), (c), and (d) already represent the cumulative results of hundreds of laser shots. This is very important and, thanks also to a previous comment, it is now addressed more clearly in the text, which now includes the precise number of laser shots (160 for LiF, 193 for Cu and 67 for shadow-cone) as well the average number of detector signals per laser-shot\nThe statistics achieved with the accumulation of ~200 shots is limited, however that was the maximum number of valid shots that could be delivered within a single day at DRACO, and it’s outstanding for this kind of facilities.\nThe available statistics sets the limit for the neutron energy bin width: if they are narrower, the error bars become too large, thus we believe a that a 2 MeV binning is reasonable for the purpose of the experiment: the feasibility of the single-event TOF method in the harsh PW environment.\nAlthough quite broad, it allows a fare comparison with the expected neutron spectrum, which is smooth and thus does not require a fine binning. Being this said, future measurements should profit from the continuous increase in shot frequencies that new developments are allowing, thus providing the means to achieve higher statistics, reducing the energy bin width, and opening the door to study narrow structures such as neutron resonances.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #11: On page 9, the authors discuss the energy resolution of their LDNS in the TOF method (see Fig. 5) and compare it with the results of conventional accelerator-based neutron sources.\nThe DRACO results appear to be simulation-based values (or calculations based on the laser pulse width), not experimental values. If so, the authors should clarify that they are based on simulations to avoid any misunderstanding. In general, comparisons with results from other research fields should be made with caution. If the neutron pulse width in LDNS has not been obtained experimentally, then careful consideration should be given to claiming the superiority of LDNS compared to accelerators. Note that the neutron pulse duration can be evaluated experimentally from the width of the neutron resonance absorption, as described in the manuscripts by Lan and Bowman mentioned above.\nResponse: The referee is right recommending caution when comparing facilities. Indeed, we believe that a few, but important, details were missing in the text so that any reader can understand and judge what is being compared. In the revised text it is explicitly mentioned that the energy resolution values considered for DRACO are based on Geant4 Monte Carlo simulations starting from a conventional “ps” proton pulse (Dromey et al., 2026), that indeed has not been measured in this experiment. Now we also mention that to fully exploit the excellent time resolution of LDNS the set-up must be combined with high performance fast detectors, of which a few examples are referenced.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #12: In the conclusion, the authors described “An interesting choice of samples and reactions could be fission on 235U and 239Pu in the spirit of the very recent experiment of the NIFFTE Collaboration [65] at LANL for measuring the 239Pu/235U fission cross section ratio with an unprecedented accuracy of just 1%.” However, even after reading the abstract and Introduction of [65], the reviewer cannot understand the importance. The importance may not clear to many readers. Please explain the importance in detail or give another example.\nResponse: After having demonstrated the feasibility of doing using LDNS for ToF experiments in nuclear physics, we believe that it is important for the reader to visualize how an actual cross section measurements could be carried out, that’s why values of pulse frequency, detector configuration and time duration are given for an experiment that could be comparable to the state of the art in the field, illustrated by the mentioned work by the NIFFTTE Collaboration. That experiment represents the stats-of-the art in neutron reaction studies in terms of accuracy, wealth of observables and impact of the results.\nWe hope that the inclusion of two sentences in this last paragraph clarifies the situation.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #13:\nMinor Points:\n- Ref [2] is a paper on nuclear fission, not an appropriate example of a paper on neutron application to nuclear physics. The following paper is recommended instead: Hartmut Abele, \"The neutron. its properties and basic interactions\" , Progress in Particle and Nuclear Physics, 60, 1-81 (2008). This has over 300 citations.\n- Ref [1] and [11] are identical. One of the two can be changed into \"Neutron reactions in astrophysics\" R Reifarth, C Lederer and F Käppeler, Journal of Physics G: Nuclear and Particle Physics, 41, 053101 (2014).\nResponse: We thank the reviewer for these precise and helpful suggestions regarding the references. All corresponding citations in the text have been updated to reflect these changes.\nReport from Reviewer 2 on Nature Communications manuscript NCOMMS-25-47297\nGeneral comment: This work by Millan-Callado et. al. presents a significant advance in single event time of flight measurements for laser driven neutron sources. The data presented is convincing that neutron induced reactions are a potential avenue for study at LDNS with diamond detectors and significant attention to characterizing the difficult radiation environment. I am impressed by the work and recommend it for publication. The raw data, analysis, and text present a strong argument, however I would suggest a few additional details could be added, at the discretion of the authors and editors, to benefit the reader.\nResponse:\nWe would like to thank the reviewer for the positive assessment of our work and the recommendation for publication. The revision based on the helpful comments has helped us to improve the manuscript.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #1: To measure and distinguish single neutron events from the background is a difficult task. The authors diamond detectors are sensitive to neutrons, charged particles, and high energy photons which are all created in the laser interaction. Experiments with Cu and LiF catchers are fully described with and without the shadow bar. The shadow bar is designed to shield the diamond radiation detector from the direct neutrons and only measure the scattered background but could itself affect the scattered signal in unanticipated ways. No experiments are described without a catcher target that could assist in determining the neutron background from \"other components of the experimental setup and the laser interaction chamber.\" If these experiments were performed their inclusion would strengthen the result. I understand that beam time is limited.\nResponse: Indeed, time at a PW laser facility is very limited, but we attempted the measurement indicated by the reviewer by means of a polyethylene catcher that could have served as dummy. However, the maximum energy of the LPA protons was very high and produced neutrons when reacting with carbon nuclei. The text now includes this information:\n“Ideally, an additional measurement without a catcher would help understanding the nature of the background unrelated to neutrons. This was attempted using a polyethylene catcher as a dummy, but with proton beam energies exceeding 20~MeV even the $^{12}$C(p,n) reaction channel (Q=-18 MeV) was open, and the measurement produced a measurable neutron field (see shot $\\sim$30 in Fig. 3.”.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #2: In the same theme, additional information and testing on the shadow bar configuration would be greatly appreciated. The background determination is important enough in the single neutron results presented, 40-50% of the signal, that I believe the shadow bar deserves more attention in the body of the work.\nResponse: The background is indeed comparable to the direct neutron components and the shadow bar measurement, as well as the simulations, was key to assess it. The technique is widely used for this purpose.\nIn the revised text, we have added to the text our design calculations and estimates on the efficiency of the shadow bar:\n“This shadow bar, although limited in size because of the lack of space, acted as an efficient neutron shield \\cite{shadowbars}: Geant4 Monte Carlo simulation showed that it absorbed or scattered 99,9\\% of the incident neutrons, and as much as 99,0\\% if only the more penetrating high energies (>10~MeV) are considered.”\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #3: Much of the paper describes the Monte Carlo simulations. These simulations take as inputs the interpolated proton, electron and x-ray spectra shown in figure 1 and output the expected contribution to the neutron signal shown in figure 3. Including a few spectra in figure 1 from different shots alongside the interpolations could further convince the reader that these measurements were performed correctly.\nResponse: While reasonable in other contexts, the request by the reviewer to show more spectra of different shots in Fig-.1 is not applicable in this case. Talken as example the proton spectra, which is the most important input, it has a complex structure (broad spectrum and strong energy dependent divergence) that cannot be monitored without affecting the beam itself. Therefore, we have used a couple of detector systems based on different principles, each providing a different piece of information the is then combined to estimate the proton beam intensity and energy distribution. This is sketched in fig 1b and key metrics are then collected in fig3. Now overlaying e.g. TPS spectra, which would need to be scaled to full solid angle, and which are only valid (absolutely calibrated against Lanex) in certain energy ranges and are complemented below and above such angle with data from other systems and previous measurements, would be incomplete and misleading. The same applies to x-rays and electrons.\nWe believe that there is enough literature about LPA experiments at DRACO and also about the techniques to characterize the proton, x-rays and electrons fields produced, and therefore believe that it is better to not add further spectra to the manuscript.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #4: In it unclear in the figure caption and text if the reported RSD values are for all 204 plotted shots or for only the \"unshaded region [which] represents shots with optimized neutron performance (stability within 26 % standard deviation).\" I would prefer to have RSD for only the optimized shots and also include the RSD of the optimized shots between different days.\nResponse: It is indeed unclear. We have now clarified in both the figure caption and the main text that the RSDs given correspond to the consecutive 193 laser shots on the Cu target.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #5: In figure 4, the key representation of the single event neutron data, I believe a few extra details would help the reader. In the inset in part a, I suggest that the energy of that single neutron event be included. Where does that single neutron signal fall on the plots in part b and c? And what are the energies of the other two neutron signals at 40 and 90 ns?\nResponse: It is true that it is difficult to correlate the time-of-flight in 4 a) with the neutron energies displayed in b), c) and d), as the relationship is not lineal. Now Fig. 4a features a second X-axis in the top showing the neutron energy, which we think it is indeed very useful for the reader.\n------------------------------------------------------------------------------------------------------------------------\nReviewer comment #6: Finally, it is implied that this type of data at DRACO can be collected with ~200 shots per day and that the beam time this paper is based on occurred over several days. Understanding the total number of shots for the entire campaign, the number of shots to produce figure 4 c,d, and a comparison of the background and performance over multiple days would benefit the reader.\nResponse: This is partially explained in the methods section. The Plasma Mirror (PM) operation limited the shot rate to about one shot every 20 seconds and the total number of shots to about 200 shots per day, but now the description in the spirit of the reviewer’s comment:\n“PM operation limited the shot rate to about one shot every 20 seconds and the total number of shots to about 200 shots per day. The work presented herein correspond to neutrons generated using two different catcher options (\\qty{10}{mm} thick LiF and \\qty{3}{mm} thick Cu) on two separate days. The complete experimental campaign took place over several days, which were devoted to the optimization of the LPA and detection systems”"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The revisions made by the authors have addressed most of the reviewer’s concerns, and the revised manuscript represents a substantial improvement over the previous version. Overall, the reviewer is largely satisfied with the technical clarifications and the refined positioning of the present work.\nWhile the revised manuscript improves the clarity of the scope and novelty of the present work, I note an important remaining issue regarding the treatment of prior studies on laser-driven neutron resonance spectroscopy.\nIt is appreciated that, through the revision process, the authors have recognized the importance of the work by Koizumi et al., Sci. Rep. 14, 21916 (2024) and have modified the abstract to acknowledge prior demonstrations of single-event neutron spectroscopy at lower neutron energies. However, this recognition is currently reflected only by a brief addition in the abstract. Given the direct conceptual relevance of this study to the present work, it should be explicitly cited and discussed in the main text (e.g., in the Introduction and/or Discussion), and included as a formal reference.\nIn addition, other closely related prior studies on laser-driven neutron resonance absorption spectroscopy are not adequately acknowledged in the main text. In particular, A. Yogo et al., Phys. Rev. X 13, 011011 (2023), which was cited as an example of neutron generation in the order of 10^10 neutrons/shot in the present form, demonstrated single-shot neutron resonance absorption spectroscopy using a laser-driven neutron source, while Z. Lan et al., Nat. Commun. 15, 5365 (2024) reported resonance absorption analysis using LDNSs in a current-mode detection scheme. These works are highly relevant for contextualizing the spectroscopic capabilities of LDNSs and for clarifying the distinction between single-event and current-mode approaches, and should therefore be explicitly cited and discussed in the main text.\nIn its present form, the manuscript acknowledges prior resonance spectroscopy studies only implicitly or partially, which may give readers an incomplete view of the development of the field. I consider it essential that these works be explicitly cited and that their relationship to the present study—particularly in terms of neutron energy regime, detection mode (single-event vs. current-mode), and spectroscopic capability—be clearly discussed in the main text.\nI regard this point as mandatory to ensure proper attribution and to accurately position the present work within the existing literature before the manuscript can be accepted.", "reviewer_2": "I have read the revisions to the paper and am pleased with the improvements. I recommend publication of this final result."}, "author_response": "Response:\nWe would like to thank the reviewer for the positive assessment of our work and the recommendation for publication.\nWe understand that the suggestions regarding a more detailed reference to previous works on neutron resonance spectroscopy are reasonable and have thus added the necessary text and references in the main text of the paper. The new text and references are marked in red for easier revision and are also given in the following:\nLDNSs have been experimentally realized and investigated, most commonly by directing LPA protons or deuterons onto neutron converter targets in various configurations \\cite{roth2013bright, Lelievre2023, Jiao2023} (see Ref. \\cite{Mirfayzi:2025} for the most recent review). Proof-of-concept experiments have shown the use of laser-driven neutrons for radiographic imaging \\cite{Yogo2021}, material analysis \\cite{Zimmer2022, Mirani2023}, and as diagnostic tools in laser-plasma physics \\cite{Alejo2017, Alejo2022,Yao2023}. Among these, the most studied application compatible with current LDNS capabilities is neutron resonance spectroscopy. This is a non-destructive material analysis technique where the dips in a transmission measurement are unambiguously assigned to a given isotope. The technique has been achieved both in a single shot, operating a neutron detector in current mode \\cite{Lan2024}, and by averaging over a few shots, employing single-neutron detection \\cite{Yogo2023, Koizumi2024}. However, to date, experimental work has been limited to moderated sources delivering epithermal neutrons in the eV range. For unmoderated fast-neutron sources, only prospective studies on resonance spectroscopy or single-neutron detection have been reported \\cite{Mirani2023}. Consequently, more complex measurements approaching full nuclear-physics experiments remain unexplored. Even if they have been recognized as a key scientific case at upcoming world-class laser facilities like ELI-NP \\cite{ELI-NP:2016}, their feasibility has yet to be experimentally demonstrated."}]

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