Alternative Multipole Expansion of the Electron Correlation Term
Abstract
An alternative multipole expansion of the correlation term is derived. Modified spherical Bessel type functions which simplify as a summation of multiple orders of basic trigonometric functions are generated from this new method. We use this new expansion to obtain useful insights into the electron-electron interaction. An analytic expression for the electronic correlation term is suggested. Also, a pseudopotential for helium-like system is derived from this alternative expansion, and some reasonable eigenvalues for the ground state and two autoionizing levels of helium atom, is provided as a test of efficiency of this solution approach. With some additional corrections beyond the non-relativistic limit, a helium atom groundstate energy of -2.9036 is obtained using the analytical form derived from this method and the Slater determinant expansion of the wavefunction.
Cite
@article{arxiv.1704.02009,
title = {Alternative Multipole Expansion of the Electron Correlation Term},
author = {Eric Ouma Jobunga},
journal= {arXiv preprint arXiv:1704.02009},
year = {2017}
}
Comments
6 pages