Indirect spin-orbitKsplittings in strontium

Abstract

We use delayed field ionization to observe the microwave resonance transitions of Sr from $5snf$ to $5sng$, $5snh$, and $5sni$. The energies of the $5sn\ensuremath{\ell}$, $\ensuremath{\ell}g3$ states are split by the indirect spin-orbit coupling of the Sr core to the Rydberg electron, producing the $K$ splittings. From the $K$ splittings we extract the ionic dipole and quadrupole matrix elements, $⟨5s|r|5p⟩=3.65(25){a}_{0}$ and $⟨5s|{r}^{2}|4d⟩=12(14){a}_{0}^{2}$. From the dipole matrix element we obtain the dipole polarizability of ${\text{Sr}}^{+}$. With the dipole polarizability and the quantum defect differences of adjacent $l$ states, we can determine the ${\text{Sr}}^{+}$ quadrupole polarizability. The dipole and quadrupole polarizabilities of ${\text{Sr}}^{+}$ are ${\ensuremath{\alpha}}_{d}=86(11){a}_{0}^{3}$ and ${\ensuremath{\alpha}}_{q}=1.1\ifmmode\times\else\texttimes\fi{}{10}^{3}(10){a}_{0}^{5}$, respectively.