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The thorium nucleus with mass number $A=229$ has attracted much interestbecause its extremely low lying first excited isomeric state at about $8$eVopens the possibility for the development of a nuclear clock. However, neitherthe exact energy of this nuclear isomer nor properties, such as nuclearmagnetic dipole and electric quadrupole moment are known to a high precision sofar. The latter can be determined by investigating the hyperfine structure ofthorium atoms or ions. Due to its electronic structure and the long lifetime ofthe nuclear isomeric state, Th$^{2+}$ is especially suitable for such kind ofstudies. In this letter we present a combined experimental and theoreticalinvestigation of the hyperfine structure of the $^{229}$Th$^{2+}$ ion in thenuclear ground and isomeric state. A very good agreement between theory andexperiment is found for the nuclear ground state. Moreover, we use ourcalculations to confirm the recently presented experimental value for thenuclear magnetic dipole moment of the thorium nuclear isomer, which was incontradiction to previous theoretical studies.

Hyperfine interaction with the $^{229}$Th nucleus and its low lying isomeric state