Microwave spectroscopy of High-L n$=$28 Rydberg levels of Th2$+$: Polarizabilities and Moments of Fr-like Th3$+$

Using the microwave/RESIS technique, the relative positions of twenty Rydberg levels in n$=$28 of Th$^{\mathrm{2+}}$ with L $=$ 9, 10, 11, and 12 have been determined with MHz precision. This structure pattern was analyzed to extract measurements of several important properties of the Fr-like Th$^{\mathrm{3+}}$ ion that forms the core of this Rydberg system. Among the properties so determined are the quadrupole and hexadecapole moments, the scalar and tensor dipole polarizabilities, and the scalar quadrupole polarizability. The analysis includes significant non-adiabatic corrections.