Determination of the S and P° Rydberg energy levels of rubidium-like ions by the method of interpolation of relativistic quantum defects

The method of interpolation of relativistic quantum defects is used for determining the energies of Rydberg levels of rubidium-like ions. For this purpose, the values of relativistic quantum defects calculated by the Dirac-Fock method at three points, two of which correspond to discrete levels and the third, to the ionization threshold, are approximated by a second-degree polynomial. By using the continuous function μ(E) thus obtained, one can readily determine the energy value for any discrete level. A formula for calculating the threshold value of the quantum defect μ(0) (the phase shift δ(0)) is given. The approximation coefficients corresponding to the nS _1/2, nP°_1/2, and nP°_3/2 levels are presented. For better agreement with the experimental results, an empirical correction to the quantum defect is introduced, which weakly depends on energy. The calculations were performed for 17 members of the rubidium isoelectronic sequence (from Rb to Fr⁵⁰⁺).