The Thomas-Fermi-Scott-Schwinger expansion and the Schrödinger ground state energy of complex neutral atoms

Abstract

The large Z Thomas-Fermi-Scott-Schwinger expansion for the total nonrelativistic binding energy of a neutral atom is used, together with the Bohr energy formula valid at Z = 1, to construct various Padé approximants among which the two-point [3//3] approximant gives an overall improved representation for the energy for Z from 1 to 290, and very especially for the closed shell values Z = 10, 18, 36, 54, 86, 118, 168, and 290. The presence of oscillatory terms for open shells in the large Z expansion is also confirmed. © 1982 American Institute of Physics.