Positronium formation in the ground and excited states(n=2levels)in a positron-negative hydrogen-ion collision

Abstract

An approach has been proposed and developed to study the positronium (Ps) formation cross sections in the ground and excited $n=2$ levels for the exothermic reaction in a positron-negative hydrogen-ion $({\mathrm{H}}^{\ensuremath{-}})$ collision in the framework of Coulomb distorted eikonal approximation. Both the differential cross sections (DCS) as well as integrated cross sections [partial total cross sections (TCS)] have been investigated for the $1s$, $2s$, and $2p$ states in a broad energy range, e.g., $1--200\phantom{\rule{0.3em}{0ex}}\text{eV}$. For lower incident energy, the Ps formation in the $2p$ state is found to dominate over the $1s$ and $2s$ states while for the higher incident energy, the formation to ground state $(1s)$ dominates the other two states. Present results have been compared with other existing theoretical results where available in the absence of any experimental data. Both the DCS and the partial TCS results are found to agree quite satisfactorily with the coupled pseudostate results of McAlinden et al. [Phys. Rev. A 65, 032715 (2002)] in the low-energy range $1--10\phantom{\rule{0.3em}{0ex}}\text{eV}$. At higher incident energies, the present results are always lower than the Coulomb Born and orthogonalized Coulomb Born results of Basu Choudhury et al. [Phys. Rev. A 33, 2358 (1986)] and Straton et al. [Phys. Rev. A 44, 7335 (1991)], respectively. The present DCS $(1s,2s)$ exhibits double peak structure at high incident energy that could be attributed to higher-order effects. The signature of the present double peak structure which is totally absent in the Coulomb Born approximation or in the orthogonalized Coulomb Born approximation becomes more prominent with increasing incident energy.