NUMERICALLY STABLE SOLUTION OF COUPLED-CHANNEL EQUATIONS - THE WAVE-FUNCTION

In two earlier papers a numerically stable solution of the stationary Schrodinger equation for coupled channels was presented. The Schroding er function and its first derivative were expressed in terms of two ma trices: A so-called local reflection matrix (LORE) and an inverse loca l transmission matrix (INTRA). These matrices obey very simple boundar y conditions: They approach asymptotically zero (one) on one side of t he reaction path and the reflection (transmission) matrix on the other side. Hence by propagating both matrices along the reaction path one can determine directly the observable scattering matrix elements witho ut ever having to calculate wave functions. On the other hand it is of ten useful to know the wave functions, for instance in order to interp ret scattering data in terms of 'flow patterns' etc. Although the rela tion between the INTRA-LORE and the wave function is simple, a straigh t forward calculation is not possible. It would involve an inversion o f the INTRA which is numerically ill behaved. In this paper we describ e a numerically stable method of computing the wave function and illus trate by two examples of surface reactions.