Many-body theory of the Sternheimer antishielding factor for theNa+ion

The Sternheimer antishielding factor (${\gamma }_{\infty }$) for the ion ${\mathrm{Na}}^{+}$ including electron-electron interaction effects has been calculated by the linked-cluster many-body perturbation theory. The diagrams involving only the perturbation due to the external field gradient lead to radial and angular contributions of -5.02 and 0.61, respectively, adding up to a net ${\gamma }_{\infty }$ of -4.41. The diagrams involving one order in the electron-electron interaction, representing consistency effects, lead to an additional contribution of 0.87 while correlation diagrams make a smaller but significant net contribution of -0.27. The total ${\gamma }_{\infty }$ is found to be -3.81±0.10. The physical significance of various contributions to consistency and correlation effects is analyzed and comparisons are made with the results for ${\gamma }_{\infty }$ in ${\mathrm{Na}}^{+}$ by other methods. The larger importance of consistency contributions to ${\gamma }_{\infty }$ in ${\mathrm{Na}}^{+}$, as compared to that in other positive-ion systems, ${\mathrm{Mn}}^{+2\mathrm{}}$, ${\mathrm{Fe}}^{+3\mathrm{}}$, ${\mathrm{Rb}}^{+}$, ${\mathrm{Cs}}^{+}$, is discussed.