Nuclear-spin mixing oscillations in229Th89+

The ${}^{229}\mathrm{Th}$ nucleus is known to have a ${3/2}^{+}$ level at $3.5\pm 1.0\hspace{0.5em}\mathrm{eV}$ above the ${5/2}^{+}$ ground state. In a hydrogenlike ${}^{229}{\mathrm{Th}}^{89+}$ ion these two levels are predicted to mix due to the high magnetic field produced at the nucleus by the $1s$ electron. This paper gives a theoretical analysis of the time evolution of the ${}^{229}{\mathrm{Th}}^{89+}$ hydrogenlike system after its formation in a fast collision process. In particular, nuclear-spin mixing oscillations are considered and the oscillation frequency is estimated to be about ${10}^{15}\hspace{0.5em}{\mathrm{s}}^{-1}.$ The time dependence of population of the hyperfine structure levels is determined. Considerations are extended to other ions of ${}^{229}\mathrm{Th}$ with the last electron in a higher s state. Consequences of different energy of the isomer are examined. A possible way to confront these predictions with experiment is briefly outlined.