Coefficients of light-ion reflection from a solid surface

An analytical theory of the reflection of light ions from solids is presented. The theory is based on the method of solving the elastic scattering problem (the Oswald–Kasper–Gauckler method), successfully tested in the theory of electron scattering. The solution of a boundary value problem for light ion reflection from solids based on the invariant imbedding method is constructed. Particle interaction with amorphous and polycrystalline samples is considered. Analytical formulas for calculating the integral reflection coefficients of particles and energy are obtained. It is shown that an analytical solution can be obtained only within the framework of a small-angle approximation. Obtained analytical solutions are based on the path length distribution function taking into account the maximum residual range. It was shown that within the framework of an analytical theory the reflection coefficients are determined by two dimensionless parameters — the ratio of the residual range to the transport path length and the screening parameter. The results of theoretical consideration are compared with the data of computer simulation. Numerical calculations are performed for the case of reflection of protons with initial energy E0 = 1–10 keV from Be, C, Cu and W targets for different scattering geometries. The results of the calculated integral reflection coefficients of particles and energy show the satisfactory agreement between analytics and computer simulation.