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

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 (1s), 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. We also present a scaling law for Ps (n) formation cross sections that is valid for all n in the entire energy range.