Many-body theory and Gaussian-basis implementation of positron annihilation $\gamma$-ray spectra on polyatomic molecules

TL;DR

This paper develops a Gaussian-basis many-body theory approach to compute Doppler-broadened gamma-ray spectra from positron annihilation in molecules, incorporating electron-positron correlations and molecular symmetry effects.

Contribution

It introduces a new Gaussian-basis implementation for positron annihilation spectra calculations, including electron-positron correlations and symmetry considerations, in an open-source code.

Findings

Calculated spectra for furan and acetonitrile show the influence of molecular orbitals.

Partial contributions depend on orbital energies and molecular symmetry.

Electron-positron correlations significantly affect the gamma-ray spectra.

Abstract

Doppler-broadened $\gamma$-ray spectra for positron annihilation on molecules are calculated using many-body theory. By employing Gaussian bases for the electron and positron wavefunctions, a computable expression that involves a four-centre integral over the two-annihilation-photon momenta is derived for the $\gamma$ spectra in the independent particle model approximation to the annihilation vertex, and implemented in the open-source {\tt EXCITON+} code. The influence of electron-positron correlations on the $\gamma$ spectra is examined through \textit{ab initio} treatment of the positron wavefunction, whilst corrections to the annihilation vertex are treated approximately via enhancement factors previously calculated [D. G. Green and G. F. Gribakin, Phys.~Rev.~Lett.~{\bf 114}, 093201 (2015)] exactly for atoms. Calculated $\gamma$ spectra for furan and acetonitrile are presented for annihilation from the positron bound state with electrons of individual molecular orbitals. For such annihilation from the positron-molecule bound state, it is found that the magnitude of the partial contribution to the $\gamma$ spectra from individual molecular orbitals depends not just on the orbital energies, but also on the molecular symmetry, more precisely the relative localisation of the positron and electron densities.