Electron and positron elastic scattering by non‐central potentials: Matrix elements and symmetry properties in the first Born approximation

Abstract

The Fourier transform of Cartesian Gaussian functions product is presented in the light of positron and electron elastic 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∞h point group optimizing the computational effort.