Simulation of the neutron reflection method using geant4

Abstract

Reactor physics, radiation shielding, non-destructive testing, and material characterization are just a few of the scientific and engineering disciplines that are supported by neutron interactions with matter. Because hydrogen has excellent neutron scattering and moderation capabilities, thermal neutrons are particularly effective in hydrogen-containing material. Because of this, thermal-neutron-based methods show a high degree of sensitivity to variables like the amount of moisture and the location of hydrogen in bulk materials. The thermal-neutron reflection (albedo) approach is one useful method in this field. In the framework defined by Csikai and Buczko, measurements are performed in a fixed source--moderator--detector arrangement. The detector response is compared in two cases: (1) without a sample and (2) with a sample placed near the detector. The reflection signal is expressed as the relative change in the thermal-neutron count rate and is commonly written as R = (I − I₀) / I₀, where I₀ is the reference count rate without the sample and I is the count rate with the sample. From this response, the literature reports a reflection-related cross-section quantity (denoted here as σβ). Csikai and Buczko describe σβ as a "semi-exact concept": although it is given in cross-section units, it is not a purely microscopic material constant. Instead, it depends on the experimental setup, including the geometry, the moderation conditions, and how the detector response is defined. Therefore, a meaningful reproduction requires detailed modelling of both neutron transport and the measurement geometry. This thesis reproduces the reference neutron-reflection setup using the Geant4 Monte Carlo toolkit in a fully computational manner; no physical experiment is performed. Rebuilding the literature geometry in a contemporary transport code, comparing simulation results with published values for specific materials, and examining the sensitivity of low-energy neutron results to modeling decisions are the key objectives. A fixed geometry model was constructed to represent the reference setup. The world volume was defined as vacuum. A polyethylene (CH2) moderator was modelled with an internal cavity. A cadmium (Cd) shell was placed around the detector region. Because cadmium strongly absorbs thermal neutrons, this shell reduces unwanted direct thermal-neutron contribution and increases sensitivity to the intended reflection mechanism. The detector was represented by a simplified BF3 sensitive volume.In relation to the moderator and detector, the sample was modeled as a disk-shaped target positioned at a fixed point. Only the sample material was altered during the simulation campaign, keeping the geometry constant so that variations in response could be ascribed to the material under the same measurement circumstances. Primary neutrons were generated with a single-particle source producing neutron per event. To avoid directional bias, neutrons were emitted isotropically into 4π. The source was placed inside the moderator so that thermalization is driven by the geometry and the probability of direct streaming toward the detector is reduced. The initial neutron energy was sampled from an experimentally measured Pu–Be energy spectrum. The spectrum was discretized into energy nodes between 0 and 10.75 MeV, and the tabulated weights were normalized and used for random sampling. This approach aims to ensure that the implemented primary generator reproduces the intended input spectrum. In this work, the detector response was defined without modelling electronics or pulse-height spectra. Instead, a simple and reproducible scoring definition directly linked to particle transport was used. Thermal-neutron counting was obtained with Geant4 command-based scoring using a scoring mesh defined independently of the mass geometry. A single-voxel mesh, "ThermalMesh," was placed between the moderator and the sample. The scored quantity was the number of neutron track entries into this voxel. An energy filter selected thermal neutrons with kinetic energy up to 0.5 eV. For each material, two runs were performed: a "sample-out" run to obtain I₀ and a "sample-in" run to obtain I. The reflection signal was then computed and σβ values were calculated using the same procedure for all materials. Simulation outputs (σβ,sim) were compared with published experimental values (σβ,exp) for 43 materials. The dataset was grouped into three classes: elements (n = 13), inorganic compounds (n = 14), and organic compounds (n = 16). Agreement was evaluated using three complementary metrics: relative deviation, standardized residuals (z-scores) computed with the combined uncertainty, and a reduced chi-square statistic to summarize class-level consistency. This allowed differences to be assessed both at the material level (via Δ% and z-scores) and at the class level (via χ²). The results show two clear patterns throughout the material groups. Only a small number of materials (large |z|) stand out in the simulation, which typically matches the experiment well for elements and inorganic compounds and follows an almost 1:1 trend. For organic compounds, the picture is different: the simulated values are lower than the experimental ones for almost all organics. However, while the simulations capture the general trend and ranking within the organic group, they remain at a lower scale. This is also reflected in the reduced chi-square values, which stay above 1 (especially for organics), meaning the raw simulation results do not fully agree with the experimental values within the combined uncertainties. Overall, this study highlights that the extracted "reflection cross section" is an effective observable that depends on the setup. It is obtained from a scoring definition positioned between the moderator and the sample in Geant4. It depends on the moderated neutron spectrum, transport through surrounding volumes, multiple scattering inside the sample, and the probability that scattered neutrons enter the scoring region. Therefore, even small differences in spectrum/geometry weighting, finite-size effects, or sample-state assumptions can give noticeable residuals. Based on the results, it is recommended to (i) increase Monte Carlo statistics for the remaining outliers, (ii) test sensitivity to low-energy neutron physics of physics list options, (iii) re-check material definitions (composition, density, physical state), and (iv) verify stability against small changes in the scoring-mesh definition and key geometric parameters. These steps will improve the consistency of the Geant4 model with experimental reflection observations by separating class-wide scale deviations from material-specific deviations.