Zel’dovich effect and evolution of atomic Rydberg spectra along the periodic table

Abstract

In 1959, Zel'dovich predicted that the bound-state spectrum of the nonrelativistic Coulomb problem distorted at small distances by a short-range potential undergoes a peculiar reconstruction whenever this potential alone supports a low-energy scattering resonance. However, documented experimental evidence of this effect has been lacking. Previous theoretical studies of this phenomenon were confined to the regime where the range of the short-ranged potential is much smaller than Bohr's radius of the Coulomb field. We go beyond this limitation by restricting ourselves to highly excited $s$ states. This allows us to demonstrate that along the periodic table of elements, the Zel'dovich effect manifests itself as systematic periodic variation of the Rydberg spectra with a period proportional to the cubic root of the atomic number. This dependence, which is supported by an analysis of experimental and numerical data, has its origin in the binding properties of the ionic core of the atom.