Comparison of theR-matrix and Hulthén-Kohn methods for a model multichannel scattering problem

Abstract

Exact asymptotic wave functions are included in the basis set for variational calculations of the $K$ matrix in a multichannel model problem. Rapid convergence to exact results is demonstrated for both the variational $R$-matrix method and for the restricted-interpolated-anomaly-free (RIAF) variant of the Hulth\'en-Kohn method. If "irregular" asymptotic functions are omitted, convergence of the $R$-matrix calculations is much less satisfactory. By a particular choice of the form of discrete basis functions, vanishing at a fixed radius ${r}_{1}$ in the model problem, the main computational steps of both methods are made to be identical.