Coupled channel problems with Morse potentials: A simple and fast method

Abstract

The coupled channel problem for inelastic scattering of molecules is formulated in terms of Jost functions. The resulting integral equation for Jost functions is solved by iteration (power expansion in the interaction strength). For Morse potentials the integrals for the translation part occurring in the iterative solution can be carried out analytically. The solution then is obtained as a rapidly converging series for the remaining degrees of freedom. The expansion coefficients of the series are obtained from a simple recurrence relation. The method is applied to the problem of scattering of molecules from surfaces, in particular, the transfer of translational energy into rotational, substrate vibrational and combined rotational-vibrational degrees of freedom. The results are compared with the so-called sudden approximation and some simple ways of improving the sudden approximation are discussed.