Properties of Fr-like Th3+from rf spectroscopy of high-LTh2+Rydberg ions

Relative positions of twenty $n=28$ Rydberg levels of Th${}^{2+}$ with $L=9$, 10, 11, and 12 were determined with sub-MHz precision using the rf-RESIS (resonant excitation Stark ionization spectroscopy) technique. The pattern of binding energies was analyzed with the effective potential model, modified to account for significant nonadiabatic effects. The analysis yielded measurements of several properties of the Fr-like Th${}^{3+}$ core ion, including the quadrupole moment, $Q=0.5931$(14) a.u.; hexadecapole moment, \ensuremath{\Pi} $=$ \ensuremath{-}0.69(28) a.u.; $g$ factor, ${g}_{J}=1.24$(48); scalar and tensor dipole polarizabilities, \ensuremath{\alpha}${}_{D}$${}_{,0}=15.224$(33) a.u. and \ensuremath{\alpha}${}_{D}$${}_{,2}$ $=$ \ensuremath{-}5.30(11) a.u.; scalar quadrupole polarizability, \ensuremath{\alpha}${}_{Q}$${}_{,0}=60$(15) a.u.; and the reduced dipole and octupole matrix elements connecting the ground 5$f$ ${}^{2}$${F}_{5/2}$ level with the low-lying 6$d$ ${}^{2}$${D}_{3/2}$ level, $|{\ensuremath{\langle}}^{2}{F}_{5/2}||{\mathrm{M}}^{[1]}|{|}^{2}{D}_{3/2}\ensuremath{\rangle}|=1.436(2)$ a.u. and $|{\ensuremath{\langle}}^{2}{F}_{5/2}||{\mathrm{M}}^{[3]}|{|}^{2}{D}_{3/2}\ensuremath{\rangle}|=3.3(1.1)$ a.u. The measured properties are compared with theoretical predictions.