Semiempirical model of positron scattering and annihilation

Abstract

A two-parameter semiempirical theory of positron scattering and annihilation is developed and used to investigate the behavior of positrons interacting with the rare gases and metal vapors. The two-parameter theory is able to do a reasonable job of reproducing existing cross section and annihilation data for the rare gases. A model-potential calculation that correctly predicts the behavior of the phase shifts will also predict the energy dependence of ${Z}_{\mathrm{eff}}(k)$ even if the magnitude is incorrect. Analysis of the ${Z}_{\mathrm{eff}}$ versus temperature data of Kurz et al. [Phys. Rev. Lett. 77, 2929 (1996)] suggests scattering lengths of $\ensuremath{-}5.6\ifmmode\pm\else\textpm\fi{}{1.0a}_{0},$ $\ensuremath{-}10.3\ifmmode\pm\else\textpm\fi{}{2.0a}_{0},$ and $\ensuremath{-}56\ifmmode\pm\else\textpm\fi{}{15a}_{0}$ for Ar, Kr, and Xe, respectively. Existing bound-state calculations can be used to fix the values of the semi-empirical parameters for a number of metal vapors, resulting in predicted ${Z}_{\mathrm{eff}}$ of 119, 36, and 94 for Be, Mg, and Cu at threshold. In addition to the calculations, expressions relating the threshold form of ${Z}_{\mathrm{eff}}(k)$ to the complex scattering length are presented.