Studies of inelastic molecular collisions using impact parameter methods. II. Exact and high-energy approximate calculations

Abstract

Exact quantum mechanical impact parameter methods have recently been extended to include inelastic collisions through the use of an effective Hamiltonian. In this paper the nature of the impact parameter formulation will be explored through specific examples. First we consider the case of a calculation for He–para-He2 where the exact impact parameter amplitudes have been computed as a Neumann series of transition matrix elements obtained from an effective Hamiltonian close coupling calculation. The purpose of this calculation is to provide a standard of functional behavior for comparison with amplitudes computed by approximate methods. Such approximate calculations were performed for Ar–TlF scattering using both exponential and fractional high-energy forms for the amplitudes. The two approximations are compared in detail, and it is found that the cross sections resulting from the exponential approximation show reasonable agreement with other calculations for the system using conventional (noneffective) close coupling and various sudden approximations. Ranges of validity for the approximations are discussed and general characteristics of the impact parameter amplitudes and the related cross section integrands are summarized. Comparison is also made with model system calculations discussed in a previous publication. A general procedure is presented for smoothing the highly oscillatory cross section integrands that commonly arise in exponential impact parameter treatments.