An integrated experimental-deterministic photon transport framework for radiation dosimetry: Application to naturally...

Conventional radiological assessment of building materials predominantly relies on empirical hazard indices that provide screening information but do not explicitly describe photon transport within finite material geometries. This study presents an integrated experimental and deterministic modelling framework for evaluating 17 naturally occurring radioactive building materials collected in Katsina State, Nigeria. Activity concentrations of ²²⁶Ra, ²³²Th and ⁴⁰K were measured using NaI(Tl) gamma-ray spectrometry and used as source-term inputs to a deterministic photon-transport model based on the diffusion approximation of the Linear Boltzmann Transport Equation (LBTE). The governing equation was solved numerically using the Finite Element Method (FEM) for a representative slab geometry. Conventional radiological indices were also calculated for screening purposes. The measured activity concentrations were 18.80-45.50 Bq kg^-1 for ²²⁶Ra, 14.82-93.70 Bq kg^-1 for ²³²Th and 130.80-489.70 Bq kg^-1 for ⁴⁰K. The deterministic calculations produced spatial photon-flux and surface-dose estimates for the representative geometry. Comparison with conventional dose estimates gave r = 0.990 and R² = 0.980, with RMSE = 51.95 nGy h^-1 and MAE = 49.85 nGy h^-1. Because both calculations use the same measured radionuclide concentrations, these statistics are interpreted as a numerical consistency assessment rather than independent validation. The study therefore demonstrates a proof-of-concept deterministic framework; independent experimental dose measurements and/or Monte Carlo benchmarking are required before quantitative predictive validity can be claimed.