Multichannel Schwinger’s principle for rearrangement collisions: Positronium formation in positron-hydrogen collisions

Abstract

Post and prior forms of the multichannel Schwinger's principle for rearrangement collisions are presented using discrete basis sets. An application is made to positronium formation in positron-hydrogen collisions at low energies in the range 6.8--30.0 eV. A total number of eight terms of a type of correlated basis functions involving inverse powers of half-odd integers is required to predict accurate results in conformity with the available variational and nonvariational values in the literature. Our findings indicate that destructive interference between partial-wave contributions to the scattering amplitude is responsible for the appearance of critical angles in positronium formation. Surface plots of the differential cross section display immensely rich structure. The total positronium formation cross sections agree nicely with the observed data of Zhou et al. [Phys. Rev. A 55, 361 (1997)] in the entire energy range.