Analytical approach to study the scattering of protons at the boundary of stack of inhomogeneous slabs in proton therapy

In proton therapy, as a prominent method for treating tumors, investigation of transport of the protons in the matter, which is a result of three main interactions of stopping, scattering, and nonelastic nuclear interactions, is highly important. In addition to the experimental method Monte Carlo simulations and the analytical process. There are sufficiently accurate physical beam models in the analytical approach to approximate the depth-dose distribution. However, this study involves challenges in the presence of localized inhomogeneities, which are unavoidable in body tissues. Investigating the behavior of protons in such a medium is vital to investigate three factors, including scattering, energy distribution, and fluence reduction in the boundaries. The present study deals with the scattering of protons in the slabs of different lengths and materials using the Fermi-Eyges theory. The results showed that the material composition also has a key effect on the scattering of protons in addition to the depth of penetration. The studies on the arrangement of layers and the effect of energy on the scattering showed that the arrangement of materials in the beam path has no significant effect on the final result. The scattering decreases with increasing the energy of the incident beam. It was found that the results are confirmed with the expected physics of the solved problems. To validate the results, the maximum scattering angle of the analytical method was compared with those of to the simulation using the MCNPX Monte Carlo code.