One-photon annihilation of the electron-positron pair at heavy atomic nuclei

TL;DR

This paper derives an explicit formula for the one-photon annihilation rate of electron-positron pairs in the field of heavy atomic nuclei, applicable to various bound states in positronium-related systems.

Contribution

The authors provide a new explicit formula for the one-photon annihilation rate in the presence of heavy nuclei, enabling direct application to multiple positronium and positron-atom systems.

Findings

Derived an explicit formula for the annihilation rate.

Applicable to ground states of positronium hydrides and related systems.

Facilitates understanding of annihilation processes in heavy atomic fields.

Abstract

We investigate one-photon annihilation of the electron-positron pair in the field of a central, very heavy and positively charged atomic nucleus. The explicit formula for the annihilation rate of this process $\Gamma^{(b)}_{1 \gamma}$ is derived. Our formula for this rate can directly be used to describe the actual one-photon annihilation in the ground (bound) states of all positronium hydrides HPs, quasi-stable triplet states of the positron-helium atoms $e^{+}[$ He($2^{3}S_e$)] ions and other systems.