Application of the method of split fluxes to the problem of light ion reflection

A new approach to the solution of the problem of ion reflection from a semi-infinite layer of a substance has been proposed. The approach is based on using the method of split fluxes in the equation for the reflection function (RF). The nonlinear integral equation for RF of ions was obtained directly from the transport Boltzmann equation. The system of linear integral equations for partial RF of any order was also obtained. Based on the analysis of the equation for the first partial RF, we have showed the nature of the peak of true singular reflection in the energy spectrum of reflected particles. The equations for the calculation of the angular and energy spectra of light ions reflected due to two elastic collisions with atoms of the medium have been derived.