Non-relativistic binding energies of heavy neutral atoms: Dependence of correlation energy on atomic number

As shown by Milne in the early days of quantum mechanics, the non-relativistic binding energy of a heavy neutral atom with nuclear charge Ze is proportional to Z7/3 in the large Z limit. Correction terms of order Z2 and Z5/3 to Milne’s limiting large Z result were first calculated by Scott. Here, the question as to the power of Z at which correlation energy first appears in such a binding energy formula is addressed. It is shown that a recent approximation proposed by one of us (ÁN) supports an earlier extrapolation from large dimensionality D to D = 3 by Herschbach and co-workers, that correlation energy enters the large Z binding energy formula for the first time at o(Z4/3).