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We have employed the relativistic coupled-cluster theory to calculate theelectric dipole matrix elements in the singly ionized barium (Ba$^+$) andradium (Ra$^+$). Matrix elements of Ba$^+$ are used to determine thelight-shift ratios for two different wavelengths on which recent experimentsare carried out. By combining the measured light-shift ratios and ourcalculations, we are able to estimate possible errors associate with the usedmatrix elements in Ba$^+$. Static polarizabilities of the low-lying states andlifetimes of the first excited P-states are also determined using these matrixelements in Ba$^+$. A similar approach has been followed to estimate thelifetimes and light-shift ratios in Ra$^+$.

Accurate determination of the electric dipole matrix elements, lifetimes, polarizabilities and light-shift ratios in Ba+ and Ra+