Exact solution of two-state non-Hermitian equations of motion in charge capture

Abstract

The non-orthogonality of many of the atomic and molecule orbital basis sets which include translation factors result in a non-Hermitian set of coupled equations of motion for the problem of charge transfer in ion-atom collisions., The adiabatic models and many of the numerical calculations that have been developed to describe this process impose Hermiticity by employing a prescription for averaging the interaction matrix element. The authors find that the non-Hermitian equations can be solved in closed form for a two-state basis with plane-wave translation factors and an exponential coupling term. The result can be compared directly with that of the corresponding adiabatic model derived from the Hermitian equations. Furthermore, the authors obtain the exact first-order perturbation result from the authors solution of the coupled equations as the velocity becomes large. Thus, the non-Hermitian formulation merges the adiabatic theory and the Born limit.