Effect of the oblique incidence of radiation beams on emerging radiation behind lead and concrete shields: a multilayer method for dose transmission calculations

<i>Objective</i>. For calculating shielding in x-ray rooms, it is often assumed that the beams impinge perpendicularly on the protective barriers. This is not always true, but this premise simplifies the calculations and enhances protection by being a conservative calculation. In this work, a method for calculating radiation transmission through planar shielding that considers the obliquity of the incident beam is presented.<i>Approach</i>. The output of the method produces energy spectra according to the direction of radiation impinging on the shielding. Four angles of incidence on the barrier are considered, along with monoenergetic pencil beams with energies ranging from 10 to 150 keV and two materials: lead and concrete. The direction of emerging photons is discretized into 49 different direction vectors. Monte Carlo calculations are performed for thicknesses of 0.1, 0.5, and 1.0 mm of lead, and 1, 5, 10, and 15 cm of concrete. Additionally, a multilayer iterative method is implemented for calculating attenuation of other thicknesses.<i>Main results</i>. The distribution of radiant energy according to the coordinates of its directional vector illustrates the effect of the obliquity of the incidence and the significance of the shielding material employed. In the case of concrete, the dispersion of radiation away from the original direction of incidence is much more pronounced than in the case of lead at energies below its K-edge. The multilayer iterative method provides highly accurate values of transmitted radiant energy in both monoenergetic and polyenergetic beams, for both lead and concrete, across the various studied incidence directions.<i>Significance</i>. Considering the direction of the photons reaching a shield and the direction of the photons passing through it allows multilayer composite shielding calculations to closely approximate the calculation made for the composite shielding.