Positron-helium collisions: Positronium formation into an arbitrary excited<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>state

Abstract

The scattering amplitude for positronium formation into arbitrary excited $S$ states in positron-helium collisions in which the residual helium ion is left in the ground state, is obtained in a closed form using the first Born approximation and the first-order exchange approximation. Retaining both the post and the prior forms of the interaction potential, cross sections are computed for several incident positron energies in the range 20-2000 eV. For these energies the asymptotic limit of ${n}^{3}$ times the cross section as $n\ensuremath{\rightarrow}\ensuremath{\infty}$ is attained roughly within 0.1% beyond the excited state $16S$.