Non-relativistic theory of atomic and ionic binding energies for large atomic number

The Z -1 expansion of the total energy of an ion with N electrons has by now been worked out are fully for systems with from 2 to 10 electrons, up to third order. This paper is concerned with the behaviour of the energy coefficients epsilon n (N) in the Z -1 expansion. The principal results are as follows: to establish epsilon n (N) approximately N n+1 3/ for sufficiently large N, by appeal to the Thomas-Fermi theory of positive ions; to obtain the first two terms in epsilon 0 (N) exactly in such an asymptotic expansion; to give approximate forms for large N for epsilon 1 (N) and epsilon 2 (N); to point out that the total energy E(Z,N) can be plotted, as Z becomes large, in a universal form by considering E(Z,N)/Z 7 3/ against N/Z. It is emphasized that the Thomas-Fermi theory of the binding energies of neutral atoms is giving an approximate summation to all orders in Z -1 of the Z -1 expansion. The relation of the present theory to the result of Foldy that atomic binding energies in the range Z=2 to 90 are approximately proportional to Z 12 5/ is also discussed.