Hyperfine-structure studies of Zr ii: Experimental and relativistic configuration-interaction results

We report an experimental and theoretical study of the hyperfine structure (hfs) in various metastable levels in ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$ i i. Hyperfine structures in 11 levels arising from the 4${\mathit{d}}^3$ and 4${\mathit{d}}^2$5s configurations were measured using the laser-rf double-resonance method in a collinear laser–ion-beam geometry. The hfs A and B constants were measured to a precision of 4 and 11 kHz, respectively. Less precise values for hfs constants for nine upper levels in the 4${\mathit{d}}^2$5p configuration were derived from optical spectra. Theoretically, the A and B constants for the metastable levels having J=0.5 and 1.5 were calculated using a relativistic configuration-interaction (RCI) approach. The final many-body wave function produced energy gaps between the five J=0.5 levels which differ from experiment by an average of 0.050 eV, whereas the corresponding value for the ten J=1.5 levels is 0.087 eV. For the two J=0.5 levels measured and calculated, the average error in A is 31.8%. For the three J=1.5 levels, the situation is better, with the average error in A being 9.2%. For comparison, the average errors in A using independent-particle Dirac-Fock (DF) wave functions were 88% and 136% for J=0.5 and 1.5, respectively. In all cases, the many-body (RCI) result represents a vast improvement from the DF result for the A values. The value for the electric-quadrupole moment of ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$ obtained from a comparison of the experimental B values and theoretical matrix elements is 0.257(0.013) b. In addition, the calculations confirm a previous report that the level at 17 614.00 ${\mathrm{cm}}^{\mathrm{-}1}$ reported in Moore’s Atomic Energy Levels, Vol. II (U.S. Government Printing Office, Washington, D.C., 1971) is spurious.