A unified analytical formula for indoor gamma dose assessment based on surface-density scaling

Accurate estimation of indoor gamma dose rates from natural radionuclides in building materials is essential for radiation protection. In this work, a unified analytical formula is developed based on a scaling law involving the surface density ρd, defined as the product of the density and thickness of the structural building materials (walls, floor, and ceiling). The results show that the proposed formula reproduces independent Geant4 simulation data, not used in its derivation, with high accuracy across low, intermediate, and high attenuation regimes. In comparison, existing formulas exhibit noticeable differences, particularly at low surface densities. The proposed approach provides a simple, robust, and accurate analytical representation of Geant4 results, offering a practical alternative to computationally intensive Monte Carlo simulations by reproducing their results with high fidelity through a compact analytical expression.