Indirect spin-orbit K splittings in strontium

We use delayed field ionization to observe the resonance transitions of Sr from $5snf$ to $5sng$, $5snh$ and $5sni$. Each resonance transition is split by the indirect spin-orbit coupling, K splitting, of the Sr core. From the K splitting we extract the ionic dipole and quadrupole matrix, $\langle5s\vert r\vert 5p\rangle=3.65(25)$a$_0$ and $\langle5s\vert r^2\vert4d\rangle =12(8)$a$_0^2$, respectively. We use the dipole matrix element to obtain the dipole polarizability of Sr$^+$. We determine the quadrupole polarizability of Sr $^+$ by the use of dipole polarizability and the quantum defect differences of the adjacent $\ell$ states. This work has been supported by the U.S. Department of Energy, Office of Basic Energy Sciences.