Symmetry Dependent Analytical Pseudopotential 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 Schr¨odinger 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 pseudopotential for helium atom derived using the alternative multipole expansion, a variational technique, and the mean-field theory. We have calculated the non-relativistic groundstate energy for helium atom to be −2.9059. The suggested pseudopotential 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 pseudopotential emanates from the higher-order terms of the multipole series expansion. The higher-order multipole interactions are fully included via the exchange correlation processes where the operator exchanges angular momentum with the atom. With the derived potential, we can claim that an analytical solution to helium atom has been found. Our results are in reasonable agreement with literature values.