Theory of Slow Atomic Collisions. I. H2+

Abstract

A theory of zero-order elastic and first-order inelastic scattering for slow atomic collisions in the system H2+ is presented. The method of stationary states and partial wave analysis is used and is the first such treatment which meets the formal requirement of scattering theory that the zero-order eigenfunctions become correct eigenfunctions at R→∞; the ``perturbed-stationary-states'' method, for example, fails to meet this criterion. The method is applicable only to electronic states which are ``tightly bound'' (≳0.25 eV below the ionization limit); no treatment of scattering to ``continuum'' states of the electron is given. The use of partial wave analysis makes possible the elimination of practical difficulties which appear in the time-dependent treatments due to nonorthogonality of the electronic basis functions. The zero-order eigenfunctions may properly be termed ``adiabatic'' solutions, since they are physically the logical extension of the Born—Oppenheimer concept to unbound states, and for many problems zero-order elastic scattering is indeed just potential scattering by the Born—Oppenheimer potential. First-order inelastic scattering cross sections can be computed from electronic transition matrix elements which differ in significant respects from those of the ``perturbed stationary states'' method.