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

• URL: http://arxiv.org/abs/2502.12364v1
• Date: Mon, 17 Feb 2025 22:58:31 GMT
• Title: Many-body theory and Gaussian-basis implementation of positron annihilation $γ$-ray spectra on polyatomic molecules
• Authors: S. K. Gregg, J. P. Cassidy, A. R. Swann, J. Hofierka, B. Cunningham, D. G. Green,
• Abstract summary: Doppler-broadened $gamma$-ray spectra for positron annihilation on molecules are calculated using many-body theory. For 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.
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• 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.

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