Semiempirical model of positron scattering and annihilation

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 Zeff(k) even if the magnitude is incorrect. Analysis of the Zeff versus temperature data of Kurz et al. @Phys. Rev. Lett. 77, 2929 ~1996!# suggests scattering lengths of 25.661.0a0 , 210.362.0a0, and 256615a0 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 Zeff of 119, 36, and 94 for Be, Mg, and Cu at threshold. In addition to the calculations, expressions relating the threshold form of Zeff(k) to the complex scattering length are presented.