Atomic-binding-energy oscillations

We investigate the oscillatory supplement to the statistical nonrelativistic binding-energy formula for neutral atoms. The semiclassical approach proves capable of deriving these oscillations. It turns out that their amplitude is proportional to $Z^{4/3}$ (Z is the number of electrons), and that their period is determined by the maximum angular momentum available in Thomas-Fermi atoms, i.e., 0.928$Z^{1/3}$. Our calculation also provides an understanding of the peculiar shape of the oscillations, which show sharp minima and wide, structured maxima.