An improved phase shift approach to the energy correction of the infinite order sudden approximation

A ′new method is presented for obtaining energy corrections to the infinite order sudden (IOS) approximation by incorporating the effect of the internal molecular Hamiltonian into the IOS wave function. This is done by utilizing the JWKB approximation to transform the Schrödinger equation into a differential equation for the phase. It is found that the internal Hamiltonian generates an effective potential from which a new improved phase shift is obtained. This phase shift is then used in place of the IOS phase shift to generate new transition probabilities. As an illustration the resulting improved phase shift (IPS) method is applied to the Secrest-Johnson model for the collinear collision of an atom and diatom. In the vicinity of the sudden limit, the IPS method gives results for transition probabilities, P _n→n+Δn, in significantly better agreement with the ′exact′ close coupling calculations than the IOS method, particularly for large Δn. However, when the IOS results are not even qualitatively correct, the IPS method is unable to satisfactorily provide improvements.