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(nd) for the lowest excited nd states of the alkali-metal atoms. In all cases except for lithium, and appreciable net antishielding [R(nd)<0] is found. For Li and Na, R(nd) is approximately equal to the total ionic shielding or antishielding factor γ_∞, as a result of the fact that the nd wave function v₀(nd) for these atoms is essentially hydrogenic, and hence the overlap between v₀(nd) and the core wave functions u₀(nl) and their perturbations v₁(nl→l^') is very small. For Li, γ_∞ is positive, and accordingly R0.25, whereas for Na, γ_∞ is negative (antishielding), and correspondingly R-3.9 to -4.8, in going from $3d$ to $5d$. For the heavier alkali-metal atoms, namely, K, Rb, and Cs, R(nd) is generally antishielding, but with much smaller absolute values than for Na. Thus R(nd) 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(nd) obtained are less reliable, because of the sensitivity of the valence wave functions v₀(nd) to the details of the effective one-electron potential Veff(r).