Ordering of atomic energy levels in excited states

Abstract

A remarkably consistent ordering of excited atomic states with the quantity $k=n+l$, for small values of the orbital angular momentum $l$, was pointed out by Sternheimer. This fact is readily interpreted in terms of the variation of the quantum defects with $l$, and simple rules for the $k$ ordering are given. The reasons for the observed variation of the quantum defects can be understood in terms of the accumulation of zero-energy scattering phase shifts with $l$ and with $Z$, as calculated by Manson from a realistic atomic potential.