Many-body aspects of positron annihilation in the electron gas

TL;DR

This paper uses advanced many-body theory to analyze positron annihilation in an electron gas, showing that sophisticated models are needed to match experimental data and exploring conditions for electron-positron pair formation.

Contribution

It applies the optimized Fermi Hypernetted Chain method to positron annihilation, demonstrating the importance of detailed many-body calculations for accurate results.

Findings

Most accurate theory matches experimental annihilation rates

Electron-positron pair distribution influences annihilation behavior

Pair formation occurs at specific electron density regimes

Abstract

We investigate positron annihilation in electron liquid as a case study for many-body theory, in particular the optimized Fermi Hypernetted Chain (FHNC-EL) method. We examine several approximation schemes and show that one has to go up to the most sophisticated implementation of the theory available at the moment in order to get annihilation rates that agree reasonably well with experimental data. Even though there is basically just one number to look at, the electron-positron pair distribution function at zero distance, it is exactly this number that dictates how the full pair distribution behaves: In most cases, it falls off monotonously towards unity as the distance increases. Cases where the electron-positron pair distribution exhibits a dip are precursors to the formation of bound electron--positron pairs. The formation of electron-positron pairs is indicated by a divergence of the FHNC-EL equations, from this we can estimate the density regime where positrons must be localized. This occurs in our calculations in the range 9.4 <= r_s <=10, where r_s is the dimensionless density parameter of the electron liquid.