Quadrupole shielding and antishielding factors for the excitedndstates of the alkali-metal atoms

Extensive calculations have been carried out to obtain the quadrupole shielding or antishielding factors $R\left(\mathrm{nd}\right)\mathrm{}$ for the lowest excited $\mathrm{nd}$ states of the alkali-metal atoms. In all cases except for lithium, and appreciable net antishielding [$R\left(\mathrm{nd}\right)<0\mathrm{}$] is found. For Li and Na, $R\left(\mathrm{nd}\right)\mathrm{}$ is approximately equal to the total ionic shielding or antishielding factor ${\gamma }_{\infty }$, as a result of the fact that the $\mathrm{nd}$ wave function $v_0\mathrm{}\left(\mathrm{nd}\right)\mathrm{}$ for these atoms is essentially hydrogenic, and hence the overlap between $v_0\mathrm{}\left(\mathrm{nd}\right)\mathrm{}$ and the core wave functions $u_0\mathrm{}\left(\mathrm{nl}\right)\mathrm{}$ and their perturbations $v_1(nl\to l^{\prime })$ is very small. For Li, ${\gamma }_{\infty }$ is positive, and accordingly $R\cong 0.25$, whereas for Na, ${\gamma }_{\infty }$ is negative (antishielding), and correspondingly $R\cong -3.9\mathrm{} \mathrm{to} -4.8\mathrm{}$, in going from $3d$ to $5d$. For the heavier alkali-metal atoms, namely, K, Rb, and Cs, $R\left(\mathrm{nd}\right)\mathrm{}$ is generally antishielding, but with much smaller absolute values than for Na. Thus $R\left(\mathrm{nd}\right)\mathrm{}$ lies generally in the range from -0.2 to -0.5. The values obtained for Rb are the most reliable, and range from -0.48 for Rb $4d$ to -0.20 for Rb $6d$. For K and Cs, the values of $R\left(\mathrm{nd}\right)\mathrm{}$ obtained are less reliable, because of the sensitivity of the valence wave functions $v_0\mathrm{}\left(\mathrm{nd}\right)\mathrm{}$ to the details of the effective one-electron potential $V_{\mathrm{eff}}\mathrm{}\left(r\right)\mathrm{}$.