Reflection coefficients of low-energy light ions for the power form of the interaction potential

In this paper, the reflection of low-energy light ions from solids is considered within an analytic transport theory. The anisotropy of the collision integral of the ion transport equation is taken into account by means of an appropriate polynomial approximation of the third order in the angular variable. The Laplace transformed transport equation over the path length is treated by the double Legendre polynomial approximation and solved in the lowest order. For power potentials V(R)∝ R−1/m, the universal path length and energy distributions, as well as the particle and energy reflection coefficients, are obtained in the form of series expansions. For the special case of the inverse-square law (m=1/2), reflection functions are derived in a closed analytic form. These results, based on the anisotropic approximation of the collision integral compared with computer simulations and experimental data, appear to be superior to previous theoretical results.