A justification for the use of the Langer modification in Miller's classical analog method of non-adiabatic scattering

Abstract

The analytical behavior of the S matrix in Miller's classical analog method for electronic degrees of freedom in non-adiabatic scattering is considered. It is demonstrated that the Langer modification, which replaces the action variables n k with n k + 1 2 , results in an acceptable functional form at the singular points in the classical equations of motion governing this method. If the Langer modification is not made, or if the action variables are shifted by other than half integers, then the S matrix does not behave reasonably at these points.