Hyperfine splittings of hydrogenlike ions and the dynamic-correlation model for one-hole nuclei

The dynamic-correlation model (DCM) has been used to calculate the ground-state hyperfine splitting in hydrogenlike ions characterized by core nuclei with one valence neutron or proton hole. For such nuclei the DCM nonperturbatively couples the single hole to the collective states of the reference closed-shell core. Within this nuclear model the magnetic moments, the nuclear radii, and the quadrupole moments of the ground states are well reproduced. The hyperfine splittings of ${}^{165}{\mathrm{Ho}}^{66+},$ ${}^{185}{\mathrm{Re}}^{74+},$ ${}^{187}{\mathrm{Re}}^{74+},$ and ${}^{207}{\mathrm{Pb}}^{81+}$ are calculated from the derived configuration-mixing amplitudes. In all cases a very good agreement with measured values is obtained.