Properties of Fr-like Th$^{3+}$ from microwave spectroscopy of high-L Rydberg states of Th$^{2+}$

Spectroscopy of high-L n= 28 Rydberg levels of Th$^{2+}$ was recently reported using the optical RESIS method [1]. Because the ground state of Fr-like Th$^{3+}$ is a $^{2}$F$_{5/2}$ level, each (n,L) Rydberg level of Th$^{2+}$ is split into six eigenstates whose relative positions are determined by long-range e-Th$^{3+}$ interactions. Measurements of those positions can be used to determine the Th$^{3+}$ properties that control those interactions, such as polarizabilities and permanent moments. We report a much improved study of n=28 levels with 9 $\le $ L $\le $ 12, obtained with the microwave/RESIS method. The higher precision measurements allow improved determinations of a wider range of Th$^{3+}$ properties and a better test of theoretical calculations [2].\\[4pt] [1] Julie A. Keele, M.E. Hanni, Shannon L. Woods, S.R. Lundeen, and C.W. Fehrenbach, Phys. Rev. A \underline {83}, 062501 (2011)\\[0pt] [2] U.I. Safronova, W.R. Johnson, and M.S. Safronova, Phys. Rev. A \underline {74}, 042511 (2006)