Ionic dipole and quadrupole matrix elements from nonadiabatic core polarization

Abstract

The radial matrix elements connecting the ionic ${\mathrm{Ba}}^{+}6s$ ground state to low-lying excited $6p$ and $5d$ states can be extracted from the $K$ splittings of the bound $6sn\ensuremath{\ell}$ states in much the same way that ionic polarizabilities are extracted from the separations between $\ensuremath{\ell}$ states. We develop an expression for the $K$ splitting by a pair of expansions which allows us to compare the contributions of different ionic states. This comparison confirms that all but the lowest two may be safely ignored. Finally, we extract the radial ${\mathrm{Ba}}^{+}$ matrix elements $⟨6s\ensuremath{\mid}r\ensuremath{\mid}6p⟩=4.03(12)$ and $⟨6s\ensuremath{\mid}{r}^{2}\ensuremath{\mid}5d⟩=9.76(29)$ from the experimentally obtained $K$ splittings.