Laser Resonance Chromatography of ${}^{229}$Th${}^{3+}$ in He: an ab initio investigation

We propose a laser resonance chromatography (LRC) experiment on ${}^{229}$Th${}^{3+}$, with the goal of detecting the ion’s electronic ground $5f$ ${}^2$F${}_{5\mathrm{/}2}$ state and metastable $7s$ ${}^2$S${}_{1\mathrm{/}2}$ state by means of their ion mobilities. To this end, we first model the ion-neutral interaction potentials for the two electronic states with a relativistic Fock space coupled cluster method and complete basis-set extrapolation scheme. The interaction potentials are used to simulate the state-specific reduced ion mobilities in terms of the operating temperature and the external electric field. The ion mobilities differ by more than 7% at 300 K and moderate field strengths; thus, separation of the ${}^{229}$Th${}^{3+}$ metastable state lies within the reach of LRC experiments targeting optical probing and monitoring of the nuclear clock transition in this isotope.