Correlation trends in the ground state static electric dipole polarizabilities of closed-shell atoms and ions

We employ the closed-shell perturbed relativistic coupled-cluster (RCC) theory developed by us earlier [Phys. Rev. A {\bf 77}, 062516 (2008)] to evaluate the ground state static electric dipole polarizabilities (\alpha s) of several atomic systems. In this work, we have incorporated a class of higher order many-body effects in our calculations that had not been taken into account in the above paper. We highlight their importance in improving the accuracy of $\alpha$. We also calculate the ground state \alpha s of the inert gas atoms and several iso-electronic singly and doubly charged ions in order to make a comparative study of the trends of the correlation effects. Furthermore, we have developed a method to construct intermediate diagrams that are required for the computation of the unperturbed singles and doubles coupled-cluster amplitudes. Our RCC results are compared with those of many-body perturbation theory at different orders to demonstrate the importance of higher order correlation effects for the accurate determination of (\alpha s) of the systems that we have considered.