Hyperfine structure in 229gTh3+ as a probe of the 229gTh→ 229mTh nuclear excitation energy.

We identify a potential means to extract the 229gTh→ 229mTh nuclear excitation energy from precision microwave spectroscopy of the 5F(5/2,7/2) hyperfine manifolds in the ion 229gTh3+. The hyperfine interaction mixes this ground fine structure doublet with states of the nuclear isomer, introducing small but observable shifts to the hyperfine sublevels. We demonstrate how accurate atomic structure calculations may be combined with the measurement of the hyperfine intervals to quantify the effects of this mixing. Further knowledge of the magnetic dipole decay rate of the isomer, as recently reported, allows an indirect determination of the nuclear excitation energy.