An Extension of the Statistical Model of the Atom

Citation

Erma, Victor A. (1961) An Extension of the Statistical Model of the Atom. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/HXPV-FH45. https://resolver.caltech.edu/CaltechETD:etd-03232006-110604

Abstract

The statisical model of the atom is extended within the semi-classical framework to inlude the correlation energy of the electron gas, obtained by an interpolation formula which reproduces the known high and low density limits exactly. The basic equations of the model are derived, and general theoretical results valid for all free atoms and ions are obtained. These include the determination of the electron density at the edge of the atom, a virial theorem for the atom, an estimate for the correlation energy as a function of Z, and a treatment of the Fermi-Amaldi correction. The theory of the compressed atom is also treated, and an equation of state as well as a virial theorem for atoms under pressure is derived. The equations of the model are solved in terms of a Thoinas-Fermi-Dirac - like approximation, in terms of a semi-convergent expansion for the potential near the nucleus, and numerically for the atoms Argon, Chromium, Krypton, Xenon and Uranium on the Burroughs Computer. Complete tables of the solutions obtained are given. The solutions of the model are illustrated in detail for the case of Argon, including a calculation of the energy terms of the Argon atom. Finally, the extended model is applied to the calculation of equations of state, the cross-section for small-angle scattering of medium-energy electrons from atoms, and atomic polarizabilities and diamagnetic susceptibilities. It is found that the extended model leads to improved agreement with experimental values.

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