Positronium formation in s-wave positron-hydrogen scattering

Abstract

Detailed investigations are made of the convergence of the K-matrix elements and the cross sections for elastic scattering and positronium formation in the s-wave scattering of positrons by atomic hydrogen in the energy range 6.8-10.2 eV. The Kohn and inverse Kohn variational methods are used with trial functions containing many linear variational parameters and associated short-range correlation terms, and results are obtained for a set of systematically improved trial functions. The diagonal elements of the K matrix and the eigenphase shifts obtained with these trial functions can be fitted very accurately to a convergence formula which permits extrapolation to the essentially exact results corresponding to an infinite number of short-range correlation functions. No such convergence formula applies to the off-diagonal matrix element K12, nor to the cross sections, but the very slight changes in the results as the trial functions undergo their final improvements strongly suggest that the most accurate values obtained here for K12 and the cross sections for positronium formation and elastic scattering are in error by no more than 5%, 10% and 5% respectively.