Symmetrydependent analytical allelectron potential for helium atom
Abstract
Electron–electron interaction is the origin of the manybody problems usually encountered in physics and
chemistry. Helium atom and other twoelectron systems are the simplest manybody 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 symmetrydependent analytical allelectron potential
for helium atom derived using an alternative multipole expansion, a variational technique, and a meanfield
approximation. We have calculated the nonrelativistic groundstate energy for helium atom to be −2.90422284.
The suggested allelectron potential has a local Coulomb potential with embedded nuclear charge screening
effect in the leading term of the multipole potential. A nonlocal component of the potential emanates from
the higherorder angular momentum terms of the multipole series expansion. The higherorder 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 nonlocal shortrange 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.
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