Quadrupole Shielding and Antishielding Factors for Atomic States

Abstract

The atomic shielding (or antishielding) factor $R$ for the quadrupole hyperfine structure has been evaluated for several excited atomic states. 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 $Q$. For the case of copper, the calculations provide a quantitative explanation of the fact that the values of $Q({\mathrm{Cu}}^{65})$ obtained from two different excited configurations ($3{d}^{9}4{s}^{2}$ and $3{d}^{10}4p$) differ considerably from each other (by \ensuremath{\gtrsim}40%), when the correction factor $\frac{1}{(1\ensuremath{-}R)}$ is not applied. The calculated values of $R$, namely ${R}_{3d}=+0.178$ (shielding) and ${R}_{4p}=\ensuremath{-}0.175$ (antishielding), bring the two corrected values of $Q$ into very good agreement. We thus obtain $Q({\mathrm{Cu}}^{65})=(\ensuremath{-}0.195\ifmmode\pm\else\textpm\fi{}0.004)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{2}$. Besides the work on Cu $3d$ and $4p$, the following calculations have also been carried out: (1) ${R}_{5d}$ for the $5d$ states of Pr and Tm; (2) ${R}_{2p}$ and ${R}_{3p}$ for the $2p$ and $3p$ states of Li; (3) ${R}_{2p}$ for the $2s2p^{3}P$ excited state of beryllium.