Analytical solution of the Thomas-Fermi equation for atoms

Details Analytical solution of the Thomas-Fermi equation for atoms Analytical solution of the Thomas-Fermi equation for atoms

2005-11-02

arxiv.org/abs/physics/0511017v2

Int. Rev. Phys., Vol.4, No 6 (2010) 349-352

Physics

Atomic Physics

Revtex, 4 pages, 2 figures

Scientific paper

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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