A novel technique for measuring the microwave transitions and the indirect spin-orbit splittings in the high angular momentum Rydberg states of barium

We use a novel detection technique, selective laser excitation to the autoionizing states, to observe the microwave transitions of Ba from $6sng$ to $6snh$, $6sni$ and $6snk$ for $n$= $15$, $16$, $17$ and $18$. We extract the dipole and quadrupole polarizabilities of Ba$^+$ from the measured intervals between the $6snh-6sni$ and $6sni-6snk$ states of Ba using the non-adiabatic core polarization model. The values we determine for the dipole and quadrupole polarizabilities are $\alpha_d=129.03(57)\;a_0^3$ and $\alpha_q=1790(76)\; a_0^5$, respectively. The energies of the $6sn\ell$, $\ell\geq5$ states are split by the indirect spin-orbit coupling of the Ba core to the Rydberg electron, producing the $K$ splittings. From the $K$ splittings we extract the ionic dipole and quadrupole matrix elements, $<6s|r|6p>=4.10(9)\;a_0$ and $<6s|r^2 |5d>=9.64(15)\;a_0^2$, respectively.