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∞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 .

Interference patterns in the scattering of positrons and electrons by diatomic homonuclear molecules are ab initio calculated. Our results are compared to model potential calculations with incident particles in twisted and plane wave states. All calculations are obtained in the first Born approximation framework. The comparison of the elastic differential cross sections shows how an ab initio description of the electronic molecular structure influence the interference minima structure. The origin of such patterns are also discussed.