$\gamma$-ray spectra and enhancement factors for positron annihilation spectra with core-electrons

TL;DR

This paper develops a many-body theoretical framework to accurately calculate gamma-ray spectra and enhancement factors for positron annihilation with core and valence electrons in noble gases, aligning with experimental data.

Contribution

It introduces a new model that includes correlation effects and core electron annihilation, providing a scalable formula for enhancement factors based on orbital ionization energy.

Findings

Enhancement factors scale with orbital ionization energy.

Theoretical spectra agree with experimental measurements.

Derived formula for enhancement factors with specific parameters.

Abstract

Many-body theory is developed to calculate the $\gamma$-spectra for positron annihilation with valence and core electrons in the noble gas atoms. A proper inclusion of correlation effects and core annihilation provides for an accurate description of the measured spectra [Iwata \textit{et al.}, Phys. Rev. Lett. {\bf 79}, 39 (1997)]. The theory enables us to calculate the enhancement factors $\gamma_{nl}$, which describe the effect of electron-positron correlations for annihilation on individual electron orbitals $nl$. We find that the enhancement factors scale with the orbital ionization energy $I_{nl}$ (in electron-volt), as $\gamma_{nl}=1+\sqrt{A/I_{nl}}+(B/I_{nl})^{\beta}$, where $A\approx 40$~eV, $B\approx 24$~eV and $\beta\approx 2.3$.