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 $Z_{\mathrm{eff}}\mathrm{}\left(k\right)\mathrm{}$ 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 $-5.6\pm {1.0a}_0,$ $-10.3\pm {2.0a}_0,$ and $-56\pm {15a}_0$ 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 $Z_{\mathrm{eff}}\mathrm{}\left(k\right)\mathrm{}$ to the complex scattering length are presented.

• Received 16 October 2001

DOI:https://doi.org/10.1103/PhysRevA.65.042705