Calculation of fine-structure splittings in high-lyingF2states of rubidium

Abstract

We present relativistic many-body calculations of the fine-structure splittings of the $n\phantom{\rule{0.16em}{0ex}}{}^{2}F$ Rydberg states of Rb $(n=4$--16) using both order-by-order relativistic many-body perturbation theory (RMBPT), up to a subset of fourth-order corrections, and relativistic equation-of-motion coupled-cluster methods, including singles, doubles, and an approximate treatment of valence triples. Good overall agreement is found with the measurements of Brandenberger et al. [Phys. Rev. A 65, 042510 (2002); Phys. Rev. A 81, 032515 (2010)] to better than the 1% level, which is our expected level of theoretical uncertainty due to omitted higher-order correlation effects. It is shown that the RMBPT of the fine-structure splittings is complex and slowly convergent, and that relativistic effects are enhanced compared with the RMBPT of the ionization energy of the $^{2}\mathrm{F}$ states. We also analyze smaller field-theoretic contributions to the fine-structure splittings from retardation and the radiative self-energy and vacuum polarization, finding them to enter at the 0.1% level.