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    Alternative Multipole Expansion of the Electron Correlati on Term

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    1704.02009.pdf (134.7Kb)
    Date
    2017
    Author
    Jobunga, Erick Ouma
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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 ord ers 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 formderived from this method and the Slater determinant expansion of the wavefunction.
    URI
    http://hdl.handle.net/123456789/7917
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