arXiv subjects

Eric Ouma Jobunga

Publications and source records attributed to Eric Ouma Jobunga.

3 recordsLinked to original sources

arXiv2017

Pseudopotential for Many-Electron Atoms

Electron-electron correlation forms the basis of difficulties encountered in multi-electron systems. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in this correlation. In an effort to tackle this multi-electron problem, two complementary parameter-free pseudopotentials for $n$-electron atoms are suggested in this study. Using one of the pseudopotentials, near-exact values of the groundstate ionization potentials of helium, lithium, and berrylium atoms have been calculated. The other pseudopotential also proves to be capable of yielding reasonable and reliable ionization potentials within the non-relativistic quantum mechanics framework.

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arXiv2017

Partitioning of the Electron Correlation Energy

Electron-electron correlation forms the basis of difficulties encountered in many-body problems. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in this correlation. In an effort to tackle this many-body problem, an exact partition function for the correlation energy between two interacting states is proposed in this study. Using this partition function, a model potential for a two-electron system is derived. The model potential can accurately reproduce the singlet states of a singly excited neutral helium atom with one of its electrons frozen in the $1s$ orbital.

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arXiv2017

Alternative Multipole Expansion of the Electron Correlation Term

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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