Applicability of first and second order WKB approximation to elastic scattering of two particles interacting by long-range forces

The accuracy of the first and second order WKB approximation in describing sub-Coulomb elastic scattering of ions is investigated. Thereby the scattering of non-identical as well as of identical particles is taken into consideration. It is shown that in cases where the behaviour of the scattered ions is not quasi-classical and therefore the first order WKB approximation fails, the second order WKB will be in most cases still a quite good approximation.