Calculation of Fine-Structure Splittings and Quadrupole Antishielding Factors for Atomic States

Abstract

As a test of accurate valence wave functions which have been previously obtained for the excited $\mathrm{np}$ states of the alkali atoms, we have calculated the fine-structure splittings $\Delta \nu$ using these wave functions. The resulting values of ${\Delta \nu }_{\mathrm{theor}}$ are generally in good agreement with the corresponding experimental values ${\Delta \nu }_{\mathrm{expt}}$. Calculations have also been carried out for the atomic quadrupole shielding factor $R$ for the ground states of boron ($\mathrm{B} 2p$) and aluminum ($\mathrm{Al} 3p$), and the ionic antishielding factor ${\gamma }_{\infty }$ for the ions ${\mathrm{B}}^{+}$, ${\mathrm{Al}}^{+}$, and ${\mathrm{Al}}^{3+}$. The value of $R\left(\mathrm{B} 2p\right)=+0.048$ is in good agreement with the results of calculations using spin-polarization wave functions. The result for $R\left(\mathrm{Al} 3p\right)=-0.063$ leads to a corrected value of the nuclear quadrupole moment $Q\left({\mathrm{Al}}^{27}\right)=0.140\mathrm{}\pm 0.002$ b, using the atomic-beam result of Lew and Wessel. The ionic antishielding factors ${\gamma }_{\infty }$ have the following calculated values: ${\gamma }_{\infty }\left({\mathrm{B}}^{+}\right)=+0.773\mathrm{}$, ${\gamma }_{\infty }\left({\mathrm{Al}}^{+}\right)=-1.68\mathrm{}$, and ${\gamma }_{\infty }\left({\mathrm{Al}}^{3+}\right)\cong -2.4\mathrm{}$.