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

• DOI: 10.48550/arxiv.2502.12364
• Publication Date: 2025-01-01
• Authors: Gregg, S. K.; Cassidy, J. P.; Swann, A. R.; Hofierka, J.; Cunningham, B.; Green, D. G.
• Keywords: Chemical Physics (physics.chem-ph); Quantum Physics; Atomic Physics (physics.atom-ph); Physics - Chemical Physics; FOS: Physical sciences; Physics - Atomic and Molecular Clusters; Computational Physics (physics.comp-ph); Atomic and Molecular Clusters (physics.atm-clus); Quantum Physics (quant-ph); Physics - Computational Physics; Physics - Atomic Physics

Doppler-broadened $γ$-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 $γ$ 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 $γ$ 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 $γ$ 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 $γ$ 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.