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 P 3 approximation in angular variable. The approximative Laplace-transformed solution for the reflection function is found and inverted leading to the distribution of backscattered particles in the relative path-length. Analytic expressions for the particle and energy reflection coefficients were derived and our results are compared with a large number of computer simulation data.