Theoretical studies of inelastic atomic collisions in a two-state model problem

A two-state scattering problem in which two non-crossing Morse curves are coupled by an exponential potential is discussed theoretically in both the diabatic and adiabatic approximations. Inelastic cross sections are estimated by various approximate analytical formulas, which are expressed in terms of the distorted wave matrix elements. The Landau (steepest descent) method is applied to estimate the distorted wave matrix element. The previously proposed separable potential approximation in the adiabatic method is found to be best among others by comparing with the exact numerical results. Transition probability as a function of l (angular momentum of relative motion) is well reproduced by this approximation. A glory effect in the velocity dependence of the cross section is found in the low energy region, and the adiabatic approximation reproduces this undulation phenomenon well.