Ultra precise determination of Cs$nS_1/2$ and Cs$nD_J$ quantum defects for sensing and computing: Evaluation of core contributions

We make absolute frequency measurements of Cs Rydberg transitions, vert 6S_1/2, F=3 rangle → vert nS_1/2 \(n=23rm{-}90\)rangle and vert nD_3/2,5/2 \(n=21rm{-}90\)rangle, with an accuracy of less than 72 rm kHz. The quantum defect parameters for the measured Rydberg series are the most precise obtained to date. The quantum defect series is terminated at δ₄, showing that prior fits requiring higher order quantum defects reflect uncertainties in the observations. The precision of the measured quantum defects allow for the calculation of Rydberg electric-dipole transitions and fine-structure intervals extrapolated from high principal quantum numbers, to rival that of sophisticated many-body relativistic calculations carried out at low Rydberg principal quantum numbers. We quantitatively predict the contributions to the quantum defect parameters from core polarization and core penetration of Cs inner shell electrons. A new value for the ionization energy, consistent across the nS_1/2 and nD_3/2,5/2 Rydberg series, is reported at 31406.467 751 48 (14) rm{cm}^-1.