Two-photon Annihilation of Positrons with K-shell Electrons of H-like ions

TL;DR

This paper provides a relativistic QED calculation of two-photon positron annihilation with electrons in H-like ions, revealing how the dominant annihilation process varies with nuclear charge and collision energy.

Contribution

It introduces a fully relativistic approach that nonperturbatively accounts for nuclear interactions and accurately removes infrared divergences, extending understanding of positron annihilation in heavy ions.

Findings

Two-photon annihilation dominates in low and medium-Z ions.

One-photon annihilation becomes dominant in high-Z ions.

The cross sections vary significantly with collision energy and nuclear charge.

Abstract

The two-photon annihilation of a positron with an electron bound in the 1s state of a H-like ion is calculated within the fully relativistic QED framework. The interaction with the nucleus is treated nonperturbatively, thus allowing the calculations to be carried out for the annihilation with strongly-bound inner shells of heavy ions. Infrared divergences, appearing when one of the emitted photons approaches the low-frequency limit, are accurately eliminated from final expressions. The total cross section of the two-photon and one-photon annihilation processes are compared for a wide range of collision energies and nuclear charge numbers. It is demonstrated that the two-photon annihilation channel dominates over the one-photon channel for the low and medium-Z ions, whereas for the high-Z ions the situation reverses.