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

Abstract

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 Nn+13/ 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)/Z73/ 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 Z125/ is also discussed.