Experimental and theoretical Ritz–Rydberg analysis of the electronic structure of highly charged ions of lead and bismuth by optical spectroscopy

Intra-configuration fine-structure transitions in highly charged ions (HCIs) result in most cases from changes in the coupling of equivalent electrons. They are multipole forbidden to varying degrees and often occur within the optical range. In HCI with semi-filled <?CDATA nd^?> n d and <?CDATA nf^?> n f subshells, electrons can in principle couple to states which are energetically close but with very different total angular momenta, e.g. <?CDATA 0x2A7D J x2A7D 10?> 0 ⩽ J ⩽ 10 . This gives rise to metastable states with very long lifetimes that exhibit particularly interesting clock transitions or, as in the case of orbital level crossings, acquire a considerable sensitivity to a possible variation of the fine-structure constant α . We investigate both experimentally and theoretically connecting the ground state and adjacent states of Pb XXII to Pb XXXIV and Bi X to Bi XV, respectively, covering complex couplings of electrons in the <?CDATA 4f^?> 4 f and <?CDATA 5d^?> 5 d shells. These and others such as <?CDATA nd^?> n d and <?CDATA nf^?> n f , which also contain equivalent electrons, are of interest for frequency metrology using quantum logic spectroscopy, for atomic structure and QED theory tests, and for the search for Dark Matter candidates. We infer their level structure, benchmark calculations from two different electronic structure codes, and lay the groundwork for inferring the wavelengths of forbidden transitions of higher multipolarity in the optical and VUV region.