On Molière and Fermi–Eyges scattering theories in hadrontherapy

We consider the evaluation of lateral spread distributions of charged particle beams at therapeutic energies, due to an absorber in the form of a homogeneous slab or of a stack. We show that the Molière theory has the same degree of flexibility as the Fermi-Eyges, but is much more accurate and does not present particular computing difficulties with the energy loss formula we have employed. It is also shown that the non-Gaussian shape of the projected one dimensional (1D) distributions is not a complication for passing from the projected to the spatial two-dimensional (2D) distribution, if one assumes circular symmetry. All the calculations are compared with the results of the FLUKA code. The nuclear interaction is not considered here, because it is outside of the scope of this work.