Neutron Scattered Spectra Tool (NeSST)

• NeSST is an open-source Python package that rapidly constructs primary and singly scattered neutron spectra, alongside synthetic nToF detector signals for ICF implosions.
• It integrates primary-source modeling with ENDF-based elastic and inelastic scattering methods and configurable detector response functions.
• The tool supports inverse problem analysis and sensitivity studies by unifying source formation, scattering transport, and diagnostic signal synthesis.

Searching arXiv for the cited NeSST and related neutron-spectrum papers to ground the article in the published record. Neutron Scattered Spectra Tool (NeSST) is an open-source Python package for rapidly constructing primary neutron spectra, singly scattered neutron spectra, and synthetic neutron time-of-flight (nToF) detector signals for inertial confinement fusion (ICF) implosions. It is designed as a lightweight, fast, physics-based forward model for the regime in which single scattering dominates, while also incorporating extensions for higher areal density and detector-response modeling. Its scope includes deuterium-tritium (DT), deuterium-deuterium (DD), and tritium-tritium (TT) primary reactions; elastic and inelastic scattering based on Evaluated Nuclear Data File (ENDF) libraries; Legendre-mode representations of neutron-averaged projected areal density; ion-velocity-dependent backscatter-edge kernels; and full nToF signal synthesis with configurable instrument response functions, scintillator sensitivity, and beamline attenuation (Crilly, 19 May 2026).

1. Definition and diagnostic scope

NeSST was developed to model the neutron spectral observables used to infer core ICF quantities, including ion temperature, areal density, bulk flow velocity, fuel composition, implosion asymmetries, and fusion yield. In this framework, the code is not limited to source-spectrum generation: it links source formation, single-scatter transport, geometric asymmetry, and detector response into one forward model that can be used for synthetic diagnostics, fitting, uncertainty quantification, and parameter scans (Crilly, 19 May 2026).

A concise summary of the package structure is given below.

Component	Role	Typical output
Primary-source module	DT, DD, TT source spectra and yield ratios	Source energy spectrum
Scattering module	Elastic and inelastic single-scatter spectra from fuel and materials	Scattered energy spectrum
nToF module	Detector forward model with IRF, sensitivity, and attenuation	Synthetic detector waveform

The package deliberately does not aim to replace full transport codes such as MCNP, OpenMC, IRIS3D, or Minotaur. Its stated niche is a fast analytical or semi-analytical model that is useful when rapid evaluation is more important than full transport fidelity. This places it between simple moment-based diagnostic formulas and computationally expensive neutron transport calculations. A plausible implication is that NeSST is intended for inverse problems and sensitivity studies in which many forward evaluations are required (Crilly, 19 May 2026).

2. Primary-source construction

NeSST computes primary spectra for the three thermonuclear reactions identified as most relevant to DT ICF: $$\mathrm{D} + \mathrm{T} \rightarrow \alpha + n \qquad (E_n \approx 14.03\ \mathrm{MeV})$$

$$\mathrm{D} + \mathrm{D} \rightarrow {}^3\mathrm{He} + n \qquad (E_n \approx 2.45\ \mathrm{MeV})$$

$\mathrm{T} + \mathrm{T} \rightarrow \alpha + 2n$

For DT and DD, the tool treats the reactions as two-body processes that produce nearly Gaussian peaks broadened by ion thermal motion and flow. The implemented source models include Ballabio moment fits for the mean and variance of the DT and DD spectra, Brysk-like Gaussian approximations, the Ballabio modified Gaussian, and a wrapper to pyDRESS for Monte Carlo reference calculations (Crilly, 19 May 2026).

TT is treated separately because it is a three-body reaction with a continuous spectrum extending from roughly $0$ to $10$ MeV. NeSST supports several TT models based on Brune et al. $R$-matrix calculations, experimental fits from Gatu-Johnson, and the magnetic-confinement fit from Eriksson et al. The center-of-mass TT spectrum is transformed into the laboratory frame using a Doppler broadening kernel. This is important because NeSST does not reduce TT to a single approximate spectral form; it exposes multiple physically motivated parameterizations for applications in which TT contributes materially to the source term (Crilly, 19 May 2026).

The package also computes normalized yield ratios using Bosch-Hale reactivity fits for DT and DD and ENDF-based numerical integration for TT. That capability allows the construction of a composite primary source spectrum from mixed reaction channels in a DT plasma. In diagnostic usage, this matters because the inferred spectrum can depend not only on broadening and flow but also on the relative contribution of different fusion branches (Crilly, 19 May 2026).

3. Single-scatter transport and nuclear-data framework

The core scattering calculation in NeSST is a single-scatter spectral model. It forms the singly scattered spectrum by convolving the primary source with double differential scattering cross sections and weighting the result by the neutron-averaged projected areal density along the scattering path. The projected areal density is expanded in Legendre polynomials,

$$(\rho L)(\mu_s) = (\rho L)_0 \sum_{\ell} P_\ell \, P_\ell(\mu_s),$$

where $(\rho L)_0$ is the spherical average and higher coefficients encode asymmetries (Crilly, 19 May 2026).

A central design choice is that differential and total nuclear cross sections are read directly from ENDF libraries. This allows elastic and inelastic processes to be handled within a common framework. In DT fuel, the implemented channels include elastic $n$D and $n$T scattering and the inelastic breakup reactions D$$\mathrm{D} + \mathrm{D} \rightarrow {}^3\mathrm{He} + n \qquad (E_n \approx 2.45\ \mathrm{MeV})$$0 and T$$\mathrm{D} + \mathrm{D} \rightarrow {}^3\mathrm{He} + n \qquad (E_n \approx 2.45\ \mathrm{MeV})$$1. For the inelastic channels, the paper describes two ENDF-based handling modes: LAW 6 phase-space law for T$$\mathrm{D} + \mathrm{D} \rightarrow {}^3\mathrm{He} + n \qquad (E_n \approx 2.45\ \mathrm{MeV})$$2 and LAW 7 tabulated double-differential data for D$$\mathrm{D} + \mathrm{D} \rightarrow {}^3\mathrm{He} + n \qquad (E_n \approx 2.45\ \mathrm{MeV})$$3 (Crilly, 19 May 2026).

The same machinery is extended to additional bundled materials such as $$\mathrm{D} + \mathrm{D} \rightarrow {}^3\mathrm{He} + n \qquad (E_n \approx 2.45\ \mathrm{MeV})$$4C, $$\mathrm{D} + \mathrm{D} \rightarrow {}^3\mathrm{He} + n \qquad (E_n \approx 2.45\ \mathrm{MeV})$$5Be, H, D, and T, together with other ENDF-accessible materials. For these species, NeSST treats elastic scattering, discrete-level inelastic scattering, and $$\mathrm{D} + \mathrm{D} \rightarrow {}^3\mathrm{He} + n \qquad (E_n \approx 2.45\ \mathrm{MeV})$$6 processes where available. This is diagnostically relevant because ablator and structural materials can contribute appreciably to the measured spectrum, especially in down-scattered regions (Crilly, 19 May 2026).

NeSST also includes relativistic corrections to elastic scattering kinematics by default. The paper states that this matters because the neutron energies of interest are in the MeV range, making purely non-relativistic formulas slightly inaccurate. The implementation therefore uses a Lorentz-invariant four-momentum formulation when converting between center-of-mass angle and lab-frame outgoing energy. In practical terms, this is most visible in features such as the classic $$\mathrm{D} + \mathrm{D} \rightarrow {}^3\mathrm{He} + n \qquad (E_n \approx 2.45\ \mathrm{MeV})$$7T and $$\mathrm{D} + \mathrm{D} \rightarrow {}^3\mathrm{He} + n \qquad (E_n \approx 2.45\ \mathrm{MeV})$$8D backscatter edges near $$\mathrm{D} + \mathrm{D} \rightarrow {}^3\mathrm{He} + n \qquad (E_n \approx 2.45\ \mathrm{MeV})$$9 MeV and $\mathrm{T} + \mathrm{T} \rightarrow \alpha + 2n$0 MeV, respectively (Crilly, 19 May 2026).

4. Asymmetry, ion motion, and backscatter-edge structure

A distinguishing feature of NeSST is its explicit treatment of implosion non-uniformity through the Legendre expansion of projected areal density. In the formulation described in the paper, the zeroth-order term controls the overall scattered amplitude, while higher modes distort the spectrum in angle-dependent ways. Because the relevant cross sections are azimuthally symmetric, the expansion is performed in Legendre polynomials of $\mathrm{T} + \mathrm{T} \rightarrow \alpha + 2n$1, which is sufficient for line-of-sight spectral predictions. The same discussion also states that a single line of sight is insensitive to $\mathrm{T} + \mathrm{T} \rightarrow \alpha + 2n$2 spherical-harmonic structure, so multiple detectors are needed for full reconstruction (Crilly, 19 May 2026).

The physical interpretation of the asymmetry coupling is stated directly. Forward-scattered neutrons lose less energy and therefore populate the high-energy shoulder, whereas backward-scattered neutrons lose more energy and contribute more strongly to down-scattered components. The paper gives a concrete example: a positive $\mathrm{T} + \mathrm{T} \rightarrow \alpha + 2n$3 asymmetry in the line-of-sight areal density can raise the high-energy side of the scatter continuum, while a negative $\mathrm{T} + \mathrm{T} \rightarrow \alpha + 2n$4 lowers it. This makes the spectral continuum sensitive to low-mode areal-density variation rather than only to the spherical average (Crilly, 19 May 2026).

NeSST further incorporates the effect of scattering-ion motion on the neutron backscatter edge shape by using precomputed ion-velocity-dependent scattering kernels. In the paper’s description, the backscatter edge encodes bulk flow through an edge-centroid shift and ion temperature or velocity spread through edge broadening. The implementation uses a three-dimensional kernel in $\mathrm{T} + \mathrm{T} \rightarrow \alpha + 2n$5 space, which accelerates evaluation across many temperatures and flows. This capability is especially directed at diagnosing dense-shell hydrodynamics in ICF implosions (Crilly, 19 May 2026).

5. Synthetic neutron time-of-flight diagnostics

NeSST includes a synthetic nToF forward model that converts an energy spectrum into a detector signal. The paper writes the basic detector model as

$\mathrm{T} + \mathrm{T} \rightarrow \alpha + 2n$6

where $\mathrm{T} + \mathrm{T} \rightarrow \alpha + 2n$7 is the neutron energy spectrum, $\mathrm{T} + \mathrm{T} \rightarrow \alpha + 2n$8 is the scintillator sensitivity, $\mathrm{T} + \mathrm{T} \rightarrow \alpha + 2n$9 is the line-of-sight attenuation, $0$0 is the instrument response function, and $0$1 is the neutron arrival time. The Jacobian $0$2 is included for energy-to-time conversion (Crilly, 19 May 2026).

The instrument response is decomposed into two parts: a neutron transit-time response through the scintillator and an X-ray or electronic response. The paper notes that the neutron IRF can be represented by a top-hat transit-time response or by a more physical inverse-Gaussian model for interaction times in thick scintillators. The X-ray or electronic response is modeled by analytic forms including gated Gaussian, decaying Gaussian, and logistic turn-on variants, with parameters fit to experimental calibration data (Crilly, 19 May 2026).

Scintillator sensitivity is modeled as energy dependent and based on proton recoil physics. The package supports multiple parameterizations, including Verbinski tabulated response, Birks-law models, Craun–Smith–Bethe variants, and stopping-power-based closures. Beamline attenuation is also included using ENDF total cross sections for line-of-sight materials such as air, windows, and structural elements. The paper presents attenuation in Beer–Lambert form,

$0$3

Together, these components make the synthetic output closer to an actual detector waveform than an idealized neutron spectrum (Crilly, 19 May 2026).

The same module can also represent time-dependent emission and finite burn duration through a more general convolution over emission time. This is relevant when the burn duration is not negligible compared with the detector flight time, especially at intermediate detector distances. In that regime, the nToF signal depends not only on energy-dependent flight time and detector response but also on the temporal source history (Crilly, 19 May 2026).

6. Related forward models, assumptions, and interpretive limits

NeSST is built around the single-scatter approximation, but the paper also describes approximate extensions for higher areal density. These include an approximate second-scatter term obtained by reapplying the single-scatter kernel to the first-scatter spectrum, together with transmission of the primary beam. The paper is explicit that the second-scatter construction is only approximate. This is one of the main interpretive limits of the framework and is part of the reason the code is positioned as complementary to full transport solvers rather than a substitute for them (Crilly, 19 May 2026).

The methodological context includes kinetic forward models for primary neutron production that do not assume Maxwellian ion distributions. One such approach computes the neutron spectrum directly from fully resolved ion distribution functions $0$4 in ion Vlasov–Fokker–Planck simulations, implemented in the spherical code iFP. In that formulation, the source spectrum is obtained by evaluating a two-body reaction kernel and integrating it over phase space, reducing the problem in spherical geometry to a five-dimensional numerical integral. The paper emphasizes that this avoids both Maxwellian closure and PIC sampling noise and that it does not approximate the distribution functions or the differential cross section beyond the chosen nuclear-data parameterization (Appelbe et al., 2023).

That kinetic comparison is diagnostically significant because the neutron spectrum is weighted toward the high-energy tail of the ion velocity distribution. In the shock-driven ICF implosions reported in the iFP study, the Maxwellian approximation broadened the spectrum artificially and made the plasma appear hotter, with apparent ion temperatures inferred from spectral variance differing substantially: DD kinetic $0$5 keV versus Maxwellian $0$6 keV, and DT kinetic $0$7 keV versus Maxwellian $0$8 keV. This suggests that a fast forward model such as NeSST is most naturally interpreted within a hierarchy of models ranging from moment-based closures to fully kinetic source calculations (Appelbe et al., 2023).

A broader caution about time-of-flight interpretation appears in work outside ICF proper. Measurements of light water on the EQ-SANS time-of-flight SANS instrument showed that scattered neutrons can emerge with energies clustered around room-temperature thermal energies, roughly $0$9 meV, regardless of the incident neutron energy, owing to thermalization within the sample. Because wavelength assignment in TOF instruments depends on arrival time, the paper concludes that inelastic processes directly affect the inferred wavelength and therefore the reduced cross section (Do et al., 2013). Although that study does not introduce NeSST by name and concerns a different experimental regime, it is described as being very much in the spirit of a NeSST-like workflow: measured TOF spectra are interpreted as neutron energy spectra, the energy redistribution is quantified through kinematics and Monte Carlo transport, and the consequences for reduction are highlighted. A plausible implication is that NeSST’s full forward treatment of detector response and spectral redistribution addresses a general diagnostic principle rather than a narrowly instrumental one (Do et al., 2013).

In aggregate, NeSST occupies a specific methodological position: it provides rapid, physics-informed modeling of ICF neutron spectra and nToF signals, with explicit treatment of primary-source physics, ENDF-based scattering, asymmetry, ion-velocity effects, and detector response, while retaining clearly stated approximations in transport and multiple scattering. Its principal significance lies in making those coupled effects tractable for fitting, synthetic diagnostics, and sensitivity analysis without the computational cost of full neutron transport simulation (Crilly, 19 May 2026).