Thomas-Fermi revisited: The outer regions of the atom

The consequences of exchange and the first quantum kinetic-energy correction are extrapolated outward in the statistical atom, up to a sharp boundary. Possible locations of that boundary are considered, and two are tested in the context of the diamagnetic susceptibility of neutral and ionized atoms with closed-shell configurations. The comparisons with experimental values and with Hartree-Fock (HF) calculations are reasonably successful, favoring one of the boundary options. An appendix presents, for neutral-atom energies, the detailed comparison between the HF calculations at integer $Z$ values and the continuous curve of the statistical theory, with its known coefficients of $Z^{\frac{7}{3}}$, $Z^{\frac{6}{3}}$, and $Z^{\frac{5}{3}}$. The deviation between the two oscillates smoothly, with decreasing amplitude and lengthening period as $Z$ increases; there is no striking evidence of shell structure. An asymmetry between positive and negative deviations suggests an additional, small multiple of $Z$. It produces agreement between the statistical and HF calculations to better than 0.1%, for $Z\ge 32$.