Identifying Neutron Sources using Recoil and Time-of-Flight Spectroscopy

TL;DR

The work tackles identifying neutron sources directly from measured energy spectra, addressing ill-conditioning from spectral similarity and environmental modulation. It introduces a Bayesian framework that models the observed spectrum as a weighted sum of spectral templates and computes the marginal likelihood $\mathcal{Z}=\int \mathcal{L}(\boldsymbol{\uptheta};\mathcal{D},\mathcal{M}) p(\boldsymbol{\uptheta}|\mathcal{M}) d\boldsymbol{\uptheta}$ using nested sampling $\text{dynesty}$ with a negative-binomial likelihood to capture overdispersion. By comparing competing source-ensemble models via Bayes factors or posterior odds $\mathcal{O}_{ij}$, the method achieves decisive discrimination ($>4\sigma$) between single- and multi-source configurations in recoil and TOF data from Cf-252 and PuBe at around $10^3$ events. The study shows recoil spectroscopy provides higher information gain per event than TOF due to lower dispersion, and outlines a path to physics-informed template banks for extending the framework to more realistic environments and applications in planetary science, nuclear forensics, and emergency response.

Abstract

Neutron-source identification is central to nuclear physics and its applications, from planetary science to nuclear security, yet direct discrimination from neutron spectra remains fundamentally elusive. Here, we introduce a Bayesian protocol that directly infers source ensembles from measured neutron spectra by combining full-spectrum template matching with probabilistic evidence evaluation. Applying this protocol to recoil and time-of-flight spectroscopy, we recover single- and two-source configurations with strong statistical significance ($>\!\!4σ$) at event counts as low as $\sim\!\!10^{3}$. These results demonstrate that neutron spectral signatures can be leveraged for robust source identification, opening a new observational window for both fundamental research and operationally driven applications.

Figures (4)

• Figure 1: Bayesian evidence results for three experiments using recoil spectroscopy. (a--b) Single-source Cf-252 experiment. (c--d) Single-source PuBe experiment. (e--f) Two-source Cf-252 & PuBe experiment. Panels (a,c,e) show log evidences $\log\mathcal{Z}_i$ for each model $\mathcal{M}_i$ (diagonal), log Bayes factors $\Updelta\log\mathcal{Z}_{10}=\log\mathcal{Z}_1-\log\mathcal{Z}_0$ (above-diagonal entries), and log posterior odds ratios $\log\mathcal{O}_{10}=\Updelta\log\mathcal{Z}_{10}+\log p(\mathcal{M}_1)-\log p(\mathcal{M}_0)$ (below-diagonal entries) with $p(\mathcal{M}) \propto 4^{-\operatorname{dim}(\mathcal{M})}$. Uncertainties are indicated using least-significant-figure notation, with lower statistical-significance bounds in square brackets trotta2008a. Panels (b,d,f) show the measured energy spectra (coverage factor $k=1$) alongside maximum-a-posteriori predictions and 95 central posterior predictive intervals (shaded area) for the retrieved (true) source set.
• Figure 2: Same as \ref{['fig:ResultRecoil']} but using TOF instead of recoil spectroscopy.
• Figure 3: Posterior model probability $p(\mathcal{M}_\mathrm{true}\mid\mathcal{D})$ of retrieving the true source model $\mathcal{M}_\mathrm{true}$ as a function of the total number of detected events, for varying prior exponents $\lambda$ in the model prior $p(\mathcal{M}) \propto 2^{\lambda\operatorname{dim}(\mathcal{M})}$ with $\lambda\in[-3,+3]$. Panels (a,b) show the single-source Cf-252 experiment, (c,d) the single-source PuBe experiment, and (e,f) the two-source Cf-252 & PuBe experiment. Panels (a,c,e) display posteriors conditioned on recoil spectroscopy data, while (b,d,f) show posteriors conditioned on TOF spectroscopy data. In addition to the number of detected events, the corresponding measurement times for each spectroscopy modality are indicated.
• Figure 4: Information gain $\mathcal{IG}\left(\mathcal{M}_\mathrm{true};\mathcal{D}\right)$ about the true source model $\mathcal{M}_\mathrm{true}$ from observing data $\mathcal{D}$ as a function of the total number of detected events, for varying prior exponents $\lambda$ in the model prior $p(\mathcal{M}) \propto 2^{\lambda\operatorname{dim}(\mathcal{M})}$ with $\lambda\in[-3,+3]$. Panels (a,b) show the single-source Cf-252 experiment, (c,d) the single-source PuBe experiment, and (e,f) the two-source Cf-252 & PuBe experiment. Panels (a,c,e) display $\mathcal{IG}$ for recoil spectroscopy data, while (b,d,f) show $\mathcal{IG}$ for TOF spectroscopy data. In addition to the number of detected events, the corresponding measurement times for each spectroscopy modality are indicated.