THERMODYNAMICS OF THE THOMAS-FERMI ATOM AT LOW TEMPERATURES.
OPERATIONAL RESEARCH BRANCH AIR DEFENCE COMMAND OTTAWA (ONTARIO)
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It is shown that an expression for the Helmholtz function on the Thomas-Fermi atom model permits one, in the limit of low temperature T, to expand the total energy as an asymptotic series in T sq. Thermodynamic functions for the case of a first-order temperature perturbation are derived from the corresponding term in the asymptotic expansion of the xenergy. They depend in addition to dependence on parameters of the unperturbed atom on two parameters derived from solution of the differential perturbation equation. These parameters differ according as the differential perturbation equation is solved under a condition of fixed atomic volume or of zero initial slope which is computationally more convenient and corresponds to published solutions. The asymptotic forms of the parameters in first case are determined for the two limits of an infinitesimal and an infinite atom. The boundary and initial parameters corresponding to fixed atomic volume are expressed in terms of the parameters corresponding to a solution under zero initial slope, and are evaluated in three cases from published solutions. These values are fitted by functions of the atom radius which have the proper limiting behavior for an infinitesimal and an infinite atom. Thus, a approximate values of the first-order temperature perturbation of thermodynamic functions become directly available. Author
- Atomic and Molecular Physics and Spectroscopy