Some simple analytical models related to positron annihilation at a vacancy in metals are presented. The shape of the two-photon annihilation-momentum density ${\rho }_{2\gamma }$(p) is calculated at several levels of approximation. Two versions of a local Thomas-Fermi model introduced by Brandt and a more realistic mixed-density approximation of Arponen et al. are calculated analytically using Gaussian charge densities. A square-well (barrier) potential model is evaluated exactly in terms of exponential integrals. A model of the electronic screening of a vacancy-trapped positron is developed.

• Received 29 December 1986

DOI:https://doi.org/10.1103/PhysRevB.35.7392