Optimizing the paths for including the correction term to the hyperspherical hidden crossing method: Application to Ps formation in e(+)-Li collisions

摘要

A correction term to the hyperspherical hidden crossing method (HHCM) was previously derived for large hyperradius R using the one-Sturmian theory. With the correction term, the HHCM potentials agree asymptotically with close-coupling channel potentials through order 1/R-2. Here, we present an optimal pair of paths in the complex R plane for the inclusion of the correction term. With this new pair of paths, the correction term can be treated in a consistent way for the two levels associated with a transition. Using the new paths, we apply the HHCM with the correction term to calculate s-, p-, d-, and f- partial wave cross sections for Ps formation in e(+)-Li collisions in the energy range 0 - 1.8 eV. The comparison of the total Ps formation cross section, with both an accurate hyperspherical close-coupling calculation and experimental measurements, shows that the HHCM with the correction term is a reliable method to describe collisions involving three charged particles. A systematic study of the Stuckelberg phase with respect to orbital angular momentum and momentum of the incident positron provides interesting insights into the scattering process.