Extension of the Statistical Model of the Atom

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Abstract
The statistical model of the atom is extended within the semiclassical framework to include 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, and a treatment of the Fermi-Amaldi correction. The equations of the model are solved in terms of a Thomas-Fermi-Dirac-like approximation, in terms of a semiconvergent expansion for the potential near the nucleus, and numerically on a computer for the atoms argon, chromium, krypton, xenon, and uranium. 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 application of the extended model is illustrated by a calculation of atomic polarizabilities and diamagnetic susceptibilities and the results are compared with experiment.

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