Enhanced sensitivity of nuclear transition frequency shift in the highly-charged ²²⁹Th⁸⁷⁺ and ²²⁹Th⁸⁶⁺ ions

The nuclear transition frequency of ²²⁹Th is highly dependent on the ionic charge state. We investigate the field shift and hyperfine interaction (HFI) shift in highly-charged ions (HCIs) ²²⁹Th⁸⁶⁺ and ²²⁹Th⁸⁷⁺. Our results demonstrate that these shifts are at least three orders of magnitude larger in HCIs than in low-charged ions (LCIs). This high sensitivity makes HCIs as potential candidates for studying electron-nucleus interactions and determining nuclear parameters. Additionally, in the stretched hyperfine states of the ²²⁹Th⁸⁷⁺ ground level, the HFI shift becomes comparable to the field shift and is enhanced by four orders of magnitude relative to that in LCIs. Consequently, if highly-charged Th ions are used for clock applications, the HFI shift must be properly accounted for.