Detection of barium 6sng to 6snh, 6sni and 6snk microwave transitions using selective excitation to autoionizing states

We use selective laser excitation to an autoionizing state to observe the microwave transitions of Ba from the $6sng$ Rydberg states to the $6snh$, $6sni$, and $6snk$ states for $15\ensuremath{\le}n\ensuremath{\le}18$. We extract the dipole and quadrupole polarizabilities of Ba${}^{+}$ from the measured $\ensuremath{\Delta}\ensuremath{\ell}$ intervals of the Ba $6sn\ensuremath{\ell}$ states of $\ensuremath{\ell}\ensuremath{\ge}5$ using a nonadiabatic core polarization model. The values we determine for the dipole and quadrupole polarizabilities are ${\ensuremath{\alpha}}_{d}=124.81(25){a}_{0}^{3}$ and ${\ensuremath{\alpha}}_{q}=2478(50){a}_{0}^{5}$, respectively.