Atomic Energy Levels for the Thomas-Fermi and Thomas-Fermi-Dirac Potential

Richard Latter

Phys. Rev. 99, 510 – Published 15 July 1955

ABSTRACT

The eigenvalues of the Schrödinger equation have been obtained for the Thomas-Fermi and Thomas-Fermi-Dirac atomic potentials. Electron self-interactions were taken into account by modifying the potentials to give asymptotically the field of a unit charge. All levels were treated from $1s$ to $7d$ for a range of $Z$-values sufficient to permit easy interpolation. It was found that the energies, for either the Thomas-Fermi or Thomas-Fermi-Dirac potentials, agree in general as well with experimental ionization energies as the Hartree or Hartree-Fock approximations. Applications of the statistical potential to other atomic problems are indicated.

• Received 24 January 1955

DOI:https://doi.org/10.1103/PhysRev.99.510

©1955 American Physical Society

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