Chemical potential and total energy of heavy positive atomic ions in the weak ionization limit

The chemical potential μ (Z,N) of a heavy positive ion with nuclear charge Ze and N electrons is obtained from the Thomas–Fermi theory near the weak ionization limit specified by q = 1−(N/Z) small as where c = 1/2 (731/2−7). The corresponding form of the total energy E(Z,N) is obtained in terms of the neutral atom energy E(Z,Z) as