Quadrupole Shielding and Antishielding Factors for Several Atomic Ground States

Abstract

The atomic shielding or antishielding factor $R$ for the quadrupole hyperfine structure has been obtained for seven atomic ground states ranging from F $2{p}^{5}$ to Br $4{p}^{5}$. The values of $R$ were determined by means of the perturbed wave functions ${v}_{1}^{\ensuremath{'}}(nl\ensuremath{\rightarrow}{l}^{\ensuremath{'}})$, as obtained by solving the inhomogeneous Schr\"odinger equation for each type of excitation of the core electrons by the nuclear quadrupole moment $Q$. The resulting values of $R$ have been listed, together with those for four atomic states which had been previously investigated. For the atomic ground states in this region of the Periodic Table, $R$ is generally positive (shielding), and of the order of +0.1, except for Al $3p$ and Ga $4p$, for which $R$ is negative, because of the antishielding provided by the $2p\ensuremath{\rightarrow}p$ and $3p\ensuremath{\rightarrow}p$ perturbations, respectively. The resulting correction factors $C=\frac{1}{(1\ensuremath{-}R)}$ have been applied to the quadrupole moments of 11 nuclear isotopes. We have also obtained the ionic antishielding factor ${\ensuremath{\gamma}}_{\ensuremath{\infty}}$ for the ${\mathrm{Sc}}^{3+}$ ion, ${\ensuremath{\gamma}}_{\ensuremath{\infty}}({\mathrm{Sc}}^{3+})\ensuremath{\cong}\ensuremath{-}11.2$.