Analytical solution of the Thomas-Fermi equation for atoms

M. Oulne

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Analytical solution of the Thomas-Fermi equation for atoms

M. Oulne

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Abstract

An approximate analytical solution of the Thomas-Fermi equation for neutral atoms is obtained, using the Ritz variational method, which reproduces accurately the numerical solution, in the range $0\leq x\leq50$, and its derivative at $x=0$. The proposed solution is used to calculate the total ionization energies of heavy atoms. The obtained results are in good agreement with the Hartree-Fock ones and better than those obtained from previously proposed trial functions by other authors.

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M. Oulne. 2005-11-07. Analytical solution of the Thomas-Fermi equation for atoms. https://arxiv.org/abs/physics/0511017

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