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Variational principle for obtaining approximate analytical solutions of the temperature-perturbed Thomas–Fermi equation for compressed atoms

✍ Scribed by P. Csavinszky; C. E. Tarr; F. Vosman

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
365 KB
Volume
17
Category
Article
ISSN
0020-7608

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✦ Synopsis

Abstract

A temperature correction to the Thomas–Fermi (TF) model of a neutral compressed atom has been given by Marshak and Bethe. The aim of the present work is to point out that, by formulating a variational principle, one may obtain approximate analytical solutions of the temperature‐perturbed TF equation. As a test of the proposed theory, the total energy of a Ne atom, confined to a spherical container, has been calculated as a function of the container radius at T = 0°K. Comparison of the data obtained with energy values calculated by Ludeña, using a self‐consistent‐field Hartree–Fock approach, shows reasonable agreement. It is, therefore, concluded that the variational approach suggested in this paper is a sound one.

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Addendum to “variational principle for o
Addendum to “variational principle for obtaining approximate analytical solutions of the temperature-perturbed Thomas–Fermi equation for compressed atoms”
✍ P. Csavinszky; C. E. Tarr 📂 Article 📅 1981 🏛 John Wiley and Sons 🌐 English ⚖ 210 KB

## Abstract In the present work the total energy of a Ne atom at __T__ = 0 K is calculated as a function of a spherical container radius. The calculation is based on the Thomas–Fermi (TF) equation, which is solved approximately by an equivalent variational principle. The effect of an approximate ex