Theory of Slow Atomic Collisions. I. H2+

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'' ($\text{≳0.25}$ 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.