Shells and Electron Groups in the Thomas-Fermi Atom

Abstract

Two prescriptions are given for the decomposition of the electron cloud of the Thomas-Fermi atom into charge domains that correspond to the shells and subshells of the wave-mechanical atom. Prescription 1 utilizes a rigorous analytical development of the Thomas-Fermi density function over three sets of indices identifiable with the quantum numbers: $n$, $l$, and $m$. Prescription 2 is based on a semiempirical partitioning to fit the Bohr-Stoner table of electron configurations. Agreement with wave mechanics is moderate.