Ordering of atomic energy levels in excited states

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