Optimized Kohn method for scattering. I. Single-channel scattering

Abstract

An algebraic variational procedure has been developed for the calculation of the phase shift $\ensuremath{\rho}$ of the radial wave function for a particle undergoing single-channel scattering. The method is essentially an optimization of Kohn's theory with respect to the phase parameter $\ensuremath{\theta}$ as involved in Kato's wave function. Specifically, the basis set has been transformed linearly so as to permit distinction between avoidable (spurious) and unavoidable (innate) singularities. On this basis, two new optimization procedures, which are termed the minimum-basis-dependence (MBD) and minimum-error (ME) methods, have been proposed. Various standard variational theories have also been reformulated in a unified manner. Sample basis-set calculations of $\ensuremath{\rho}$ have been carried out for the Hazi-Taylor model potential in order to demonstrate the relative merits of the MBD and ME methods.