The atomic antishielding factor $R$ for the quadrupole hyperfine structure has been evaluated for the lowest three excited $\mathrm{np}$ states for each of the alkali atoms, i.e., for a total of fifteen atomic states. The values of $R$ were determined by means of the perturbed wave functions $v_1^{\prime }(nl\to l^{\prime })$, as obtained by solving the inhomogeneous Schrödinger equation for each type of excitation of the core electrons by the nuclear quadrupole moment $Q$. In order to obtain reliable values of $R$, we have obtained accurate valence wave functions $v\left(\mathrm{np}\right)\mathrm{}$ for the $\mathrm{np}$ excited states from the requirement that the calculated energy eigenvalues $E_0\mathrm{}\left(\mathrm{np}\right)\mathrm{}$ should reproduce the observed energy levels. The wave function $v\left(n_{0}p\right)$ for the lowest valence $\mathrm{np}$ state ($n=n_0$, e.g., $n_0=3\mathrm{}$ for Na) was checked for each alkali atom by calculating the oscillator strength $f_{n_{0}s\to n_{0}p}$ for the lowest $n_{0}s\to \mathrm{np}$ transition. The calculated values of $f_{n_{0}s\to n_{0}p}$ were found to be in good agreement with experiment. As an example of the values of $R\left(\mathrm{np}\right)\mathrm{}$ obtained, we have found for Rb: $R\left(5p\right)=-0.257\mathrm{}$; $R\left(6p\right)=-0.207\mathrm{}$; and $R\left(7p\right)=-0.190\mathrm{}$. The resulting correction factors $\mathcal{C}=\frac{1}{\mathrm{}(1-R)\mathrm{}}$ are $\mathcal{C}\mathrm{}\left(5p\right)=0.796\mathrm{}$, $\mathcal{C}\mathrm{}\left(6p\right)=0.829\mathrm{}$, and $\mathcal{C}\mathrm{}\left(7p\right)=0.840\mathrm{}$. At the end of the paper we give the corrected values of $Q$ for twelve alkali isotopes, for which experimental data are available, namely, for the following nuclei: ${\mathrm{Na}}^{23}$, ${\mathrm{K}}^{39}$, ${\mathrm{K}}^{40}$, ${\mathrm{K}}^{41}$, ${\mathrm{Rb}}^{85}$, ${\mathrm{Rb}}^{87}$, ${\mathrm{Cs}}^{131}$, ${\mathrm{Cs}}^{132}$, ${\mathrm{Cs}}^{133}$, ${\mathrm{Cs}}^{134}$, ${\mathrm{Cs}}^{135}$, and ${\mathrm{Cs}}^{137}$. We have also given a brief summary of the present experimental evidence supporting the existence of the quadrupole shielding and antishielding effects for atomic states.

• Received 2 October 1970

DOI:https://doi.org/10.1103/PhysRevA.3.837