Atomic Quadrupole Moments of the Excited States of the Rare Gases

In connection with a recent experiment of Sandars and Stewart, the atomic quadrupole moments for the excited states $n{p}^5{n}^{\prime }s (n^{\prime }=n+1)$ of the rare gases have been calculated, in particular, the induced moment due to the $n^{\prime }s\to d$ excitation produced by the quadrupole potential due to the vacancy in the $\mathrm{np}$ shell. Sandars and Stewart have written the total quadrupole moment ${\Theta }_{\mathrm{atom}}$ as: ${\Theta }_{\mathrm{atom}}=\Theta \mathrm{}\left(\mathrm{np}\right)(1\mathrm{}-R_{\Theta })$, where $\Theta \mathrm{}\left(\mathrm{np}\right)\mathrm{}$ is the quadrupole moment due to the $\mathrm{np}$ vacancy, and $R_{\Theta }$ is a suitable shielding factor associated with $n^{\prime }s\to d$. In the present work, $R_{\Theta }$ was calculated by obtaining the perturbation $\nu _1^{}{}_{}{}^{\prime }(n^{\prime }s\to d)$ of the $n^{\prime }s$ wave function due to the quadrupole potential of the $\mathrm{np}$ vacancy. It was found that the calculated values of $R_{\Theta }$ are in very good agreement with the experimental values for all four cases (Ne, Ar, Kr, and Xe). The calculated values of $R_{\Theta }$ range from 0.82 for Ne to 1.33 for Xe, in good agreement with the experimental results.