Light shifts and electric dipole matrix elements in Ba⁺ and Ra⁺

We present an analysis of the recent measurements of the light-shift ratio in Ba⁺ at two different wavelengths that enables us to reduce the uncertainty of the largest E1 dipole matrix elements of Ba⁺. These matrix elements are, for instance, of interest for the proposed parity-nonconservation (PNC) experiment in Ba⁺. We show that a new measurement of the light-shift ratio in Ba⁺ at a wavelength of 350 nm could further reduce the uncertainty of the (for PNC studies most important) ⟨5D_3/2||D||6P_1/2⟩ matrix element. Finally, as groundwork for the planned PNC experiment at KVI, we present relativistic coupled-cluster calculations of the E1 matrix elements for Ra⁺, and investigate the potential of similar light-shift ratio measurements in this ion.