Symmetry-dependent analytical all-electron potential for helium atom

Abstract

Electron–electron interaction is the origin of the many-body problems usually encountered in physics and chemistry. Helium atom and other two-electron systems are the simplest many-body systems in nature. The Schrödinger equation even for such simple systems cannot be solved exactly without resorting to approximate methods. In this study, we have suggested a symmetry-dependent analytical all-electron potential for helium atom derived using an alternative multipole expansion, a variational technique, and a mean-field approximation. We have calculated the non-relativistic groundstate energy for helium atom to be −2.90422284. The suggested all-electron potential has a local Coulomb potential with embedded nuclear charge screening effect in the leading term of the multipole potential. A non-local component of the potential emanates from the higher-order angular momentum terms of the multipole series expansion. The higher-order multipole interactions are fully included through the exchange correlation processes where the interacting electrons exchange their angular momenta via the operator. With the derived potential, the effects of the local longrange and non-local short-range components, and the finite nuclear mass corrections are tested. Our results are in reasonable agreement with literature values. Indeed with the finite nuclear mass correction, we obtain the groundstate energy of helium atom to be −2.90382769.