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Coulomb repulsion, point-like nuclear charges, Dirac paradox, soft nuclear charge density and hypermultiplet nuclear repulsion

Abstract:

A discussion about the classical Coulomb repulsion via point-like nuclear charges, usually employed within Born–Oppenheimer approximation, leads to the description of Dirac paradox: an inconsistency found when describing nuclear charges by means of Dirac’s distributions and computing with them nuclear Coulomb repulsion integrals. The way of overcoming Dirac paradox is bound to the description of soft Gaussian nuclear charge density and also to adopting a nuclear hypermultiplet Coulomb repulsion formulation. Such theoretical prospect produces a quantum mechanically compliant but simple algorithm in order to compute nuclear repulsion, which also appears to be consistently related to classical Coulomb repulsion energy, while avoiding singularities when nuclei collapse.