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arXiv · 1704.02009

Alternative Multipole Expansion of the Electron Correlation Term

Eric Ouma Jobunga
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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.

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Eric Ouma Jobunga. 2017-04-06. Alternative Multipole Expansion of the Electron Correlation Term. https://arxiv.org/abs/1704.02009

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