Analytic approximations to distorted wave integrals, for inelastic molecular collision cross sections

Abstract

Several methods-for approximating distorted wave integrals using analytic formulae are presented and compared. The various methods are applied to the calculation of rotationally and vibrationally inelastic HeH 2 collisions and the resulting integrals compared with their exact counterparts. Some of the methods involve the use of the modified wave number approximation. This approximation is shown to break down seriously at large values of the orbital angular momentum. A further important point which is demonstrated is the importance of the region around the outer classical turning point of the two channels involved in the calculation. Among all the methods examined, a recently proposed one based on a generalisation of the well-known Mies formula is found to be the most reliable. A slightly improved version of this method is also developed and tested. Comparison of this improved method with exact calculations establishes its reliability over a large range of energies and total angular momentum quantum numbers.