Positronium formation into arbitrary excited states ine+-H scattering

Abstract

The rearrangement collision problem of positronium formation into arbitrary $n$,$l$,$m$ states by positrons from hydrogen atoms in the ground state has been investigated employing the first Born approximation and the first-order exchange approximation. It is shown that for fixed $l$,$m$, ${n}^{3}$ times the asymptotic cross section, if multiplied by the factor ${\mathbf{\ensuremath{\Pi}}}_{\ensuremath{\alpha}=0}^{l}(1\ensuremath{-}{\ensuremath{\alpha}}^{2}{n}^{\ensuremath{-}2})$, gives a good estimate of the ${n}^{3}$ cross section of the corresponding $n$,$l$,$m$ state when $n$ is not too low. For $s$ state the first-order-exchange-approximation results are greater than those of the first Born approximation. The momentum-transfer cross sections in the first Born approximation overestimate the first-order-exchange-approximation results throughout the energy range considered.