Proof of a conjecture about atomic and molecular cores related to Scott's correction

A great deal is known about the ground states of large atoms in the framework of the non-relativistic Schrödinger equation, with fixed (i.e., infinitely massive) nuclei. The leading term, in powers of the nuclear charge Z, is given exactly by Thomas-Fermi theory, as was proved by Lieb and Simon [12]; see [11] for a review. This leading term in the energy is proportional to Z ^7/3, with the proportionahty constant depending on the ratio of N/Z, which is assumed to be held fixed as Z → ∞. Here, N is the electron number. Neutrality, i.e., N=Z is not required, even though it is the case of primary physical interest. The characteristic length scale for the electron density (in the sense that all the electrons can be found on this scale in the limit Z → ∞) is Z^1/3 The fact that the true quantummechanical electron density, Q_d, converges (after suitable scaUng) to the Thomas-Fermi density, Q^Tf, as Z → ∞ with N/Z fixed was proved in [12]. The chemical radius, which is another length altogether, is believed, but not proved, to be order Z⁰ as Z → ∞.