Positronium formation for positron scattering from hydrogen: Maximum positions and scaling law

Abstract

Ground- and excited-state positronium (Ps) formation from the hydrogen atom by positron impact at low and intermediate energies have been studied within the framework of two-center two-channel eikonal final state-continuum initial distorted wave model. A general method for obtaining Ps formation into arbitrary final states has been derived. The present results of Ps (1$s$), Ps $(n=2),$ and total Ps formation cross sections agree very well with previous close-coupling calculations and experimental measurements. The maximum positions of Ps($n$) formation cross sections are found to be in good agreement with the prediction of wave vector matching model introduced by Charlton [J. Phys. B: At. Mol. Opt. Phys. 39, 4575 (2006)]. We also present a scaling law for Ps ($n$) formation cross sections that is valid for all $n$ in the entire energy range.