Analytical calculations of light ion reflection for the inverse-square interaction potential

The linear Boltzmann transport equation for diffusion and slowing down of low-energy light ions in solids is Laplace transformed in relative path-length and solved by applying the DP0 technique. The ion-target atom interaction potential is assumed to have a form of the inverse-square law and furthermore, the collision integral of the transport equation is replaced by the P3 approximation in angular variable. The Laplace transformed solution for the reflection function is found and inverted analytically leading to the distribution of backscattered particles in the relative path-length. We have shown that this analytic procedure is in good agreement with the results of numerical Laplace inversion. Simple analytic expressions for the particle and energy reflection coefficients were derived. Our results are compared with computer simulation data and experimental results of different authors. (author)