Estimation of the gamma-ray field in air from radioactive sources in the ground by numerical solution of the Boltzmann transport equation

Gamma-ray field in air from radioactive sources uniformly distributed in the ground is calculated by numerically solving the photon transport equation. The scattered flux is developed on the Legendre polynomials basis of the spherical harmonics method and a double P1 approximation is applied. The method is implemented in the Octave programming package. The calculation of the gamma-ray field is also done by Monte Carlo simulation using an optimised geometry model of the soil-air medium that is implemented in Geant4 simulation code. The results obtained by the two methods are in good agreement. The computing time for the spherical harmonics deterministic method is significantly less than the Monte Carlo simulation. Dose rate conversion factors in the air are calculated for the natural radioactive series of ²³⁸U and ²³²Th and for ⁴⁰K nuclide and for soils contaminated by various radionuclides. The results are in agreement with the published theoretical and experimental studies. (authors)