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• W2011013669 abstract "The generalization of the Thomas-Fermi-Dirac atom model to include a temperature perturbation of first order is considered, as formulated from a variational procedure by Umeda and Tomishima. Initially, no restriction is imposed on the shape of the atom's boundary surface. It is shown that the model yields direct analogs for the case with exchange of relations given by Brachman for the Helmholtz function and the entropy in the extended Thomas-Fermi atom model for arbitrary temperature. The virial theorem is derived for an atom of general shape on the model in question, by means of which one obtains analogs of expressions for the heat capacity of the Thomas-Fermi atom. These results yield a set of theorems involving the energy which are direct analogs of ones in the Thomas-Fermi case at arbitrary temperature, and represent a generalization of Milne's theorem, which expresses the energy of an atom at zero temperature in terms of boundary and initial parameters derived from the solution of the Thomas-Fermi equation. The entropy of the temperature-perturbed atom is obtained in terms of a quadrature on the corresponding solution of the Thomas-Fermi-Dirac equation for zero temperature, in a form corresponding to a result of Mayer in the Thomas-Fermi case. The following analog of Mayer's theorem is established: every thermodynamic function of a Thomas-Fermi-Dirac atom in the first-order temperature-perturbed case can be expressed in terms of quadratures on the corresponding solution of the Thomas-Fermi-Dirac equation for zero temperature. Results obtained are specialized to a spherically symmetric atom, and explicit expressions for the temperature perturbations in thermodynamic functions for this case are given in terms of quadratures on the corresponding unperturbed solution of the Thomas-Fermi-Dirac equation. It is argued that the results obtained for the analogs of the theorems of Brachman and Milne are probably exact for arbitrary temperature, in the stricter formulation of the generalized Thomas-Fermi-Dirac atom model given by Ashkin and Cowan." @default.
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• W2011013669 date "1957-07-01" @default.
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• W2011013669 title "Thermodynamic Functions on the Generalized Thomas-Fermi-Dirac Theory" @default.
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• W2011013669 doi "https://doi.org/10.1103/physrev.107.33" @default.
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