Combined Variable-Phase-R-Matrix Approach to Scattering Problems

Abstract

A procedure which combines the methods of variable-phase and $R$-matrix theory is formulated for multichannel scattering processes. $R$-matrix theory is used to obtain the logarithmic derivative of the scattering functions at a radius $a$, beyond which all exchange potentials are negligible. Variable-phase theory is used to construct a radially dependent reaction matrix which is integrated from $a$ to infinity. The method is applied to a two-channel model which has some of the features of the low-energy electron-hydrogen problem. Essentially exact results are obtained with as few as 40 $R$-matrix states (20 per channel).