Analytical solution of the Thomas-Fermi equation for atoms
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≤ x≤50, 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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