Enhancement of positron annihilation with core electrons

Abstract

A theoretical treatment is presented of the enhancement of positron annihilation with core electrons in a solid. A first estimate is obtained from the simple result for Coulomb scattering of a single positron-electron pair. For relative velocity $v$ large compared to the Bohr velocity ${v}_{0}=\frac{{e}^{2}}{\ensuremath{\hbar}}$ the enhancement is small, being given approximately by $\ensuremath{\chi}\ensuremath{-}1=\frac{\ensuremath{\pi}{v}_{0}}{v}$, where $\ensuremath{\chi}$ is the enhancement factor. Since core electrons typically have velocities much larger than ${v}_{0}$, the enhancement for core annihilation is expected to be small. Modifications due to the fact that the electron is embedded in a system of interacting electrons bound to an atomic nucleus are estimated from calculations partly for an electron gas of high density, and partly for a single electron closely bound to a nucleus. The enhancement is found to be similar to the result for a single, free electron but somewhat reduced in magnitude mainly due to the Pauli exclusion principle. Quantitative estimates of the small enhancement are derived for the core contribution to both the total and the momentum-dependent annihilation rates. The enhancements are much smaller than obtained in earlier treatments, and they lead to corrections for core annihilation which are significantly smaller than those derived from semiempirical estimates.