Relativistic theory of binding energies of heavy positive ions

The self-consistent relativistic Thomas–Fermi theory of heavy positive ions with N electrons and nuclear charge Ze is shown to lead to a chemical potential μ which has the scaling property with ? = α²Z², α being the fine structure constant. Combining this with the Layzer–Bahcall expansion for the total energy E(Z, N), namely, it is proved that the coefficients E_nm (N) at large N have the asymptotic behavior N^n–2m/3#1/3. The corresponding result for the scaling of the relativistic Thomas–Fermi energy is Scaling properties of the higher order terms in E_nm (N) and E(Z, N) are also proposed.