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Electron and Positron Scattering by Non-Central Potentials: Matrix Elements and Symmetry Properties in the First Born Approximation
• Marcos Barp,
• Felipe Arretche
Marcos Barp
Federal University of Santa Catarina
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Felipe Arretche
Federal University of Santa Catarina
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## Abstract

The Fourier transform of Cartesian Gaussian functions product is presented in the light of positron scattering. The calculation of this class of integrals is crucial in order to obtain the scattering amplitude in the first Born approximation framework for an ab initio method recently proposed. A general solution to the scattering amplitude is given to a molecular target with no restriction due to symmetry. Moreover, symmetry relations are presented with the purpose of identifying terms that do not contribute to the calculation for the molecules in the $$D_{\infty h}$$ point group optimizing the computational effort.

Keywords — Positron and electron scattering, Fourier transform of the Gaussian product theorem, McMurchie-Davidson procedure, Obara-Saika procedure, linear molecules .

#### Peer review status:UNDER REVIEW

09 Nov 2021Submitted to International Journal of Quantum Chemistry
10 Nov 2021Submission Checks Completed
10 Nov 2021Assigned to Editor
15 Nov 2021Reviewer(s) Assigned
11 Dec 2021Review(s) Completed, Editorial Evaluation Pending
04 Jan 2022Editorial Decision: Revise Major
15 Jan 20221st Revision Received
20 Jan 2022Submission Checks Completed
20 Jan 2022Assigned to Editor
20 Jan 2022Reviewer(s) Assigned