  Using perturbed relativistic coupled-cluster (PRCC) theory we compute the
ground state electric dipole polarizability, $\alpha$, of doubly ionized
alkaline earth metal ions $\rm{Mg}^{2+}$, $\rm{Ca}^{2+}$, $\rm{Sr}^{2+}$,
$\rm{Ba}^{2+}$ and $\rm{Ra}^{2+}$. In the present work we use the
Dirac-Coulomb-Breit atomic Hamiltonian and we also include the Uehling
potential, which is the leading order term in the vacuum polarization
corrections. We examine the correction to the orbital energies arising from the
Uehling potential in the self-consistent field calculations as well as
perturbatively. Our results of $\alpha$ are in very good agreement with the
experimental data, and we observe a change in the nature of the orbital energy
corrections arising from the vacuum polarization as we go from $\rm{Mg}^{2+}$
to Ra$^{2+}$.

Atomic Physics