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 [sup 91]Zr II. Hyperfine structures in 11 levels arising from the 4[ital d][sup 3] and 4[ital d][sup 2]5[ital s] configurations were measured using the laser-rf double-resonance method in a collinear laser--ion-beam geometry. The hfs [ital A] and [ital 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[ital d][sup 2]5[ital p] configuration were derived from optical spectra. Theoretically, the [ital A] and [ital B] constants for the metastable levels having [ital 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 [ital J]=0.5 levels which differ from experiment by an average of 0.050 eV, whereas the corresponding value for the ten [ital J]=1.5 levels is 0.087 eV. For the two [ital J]=0.5 levels measured and calculated, the average error in [ital A] is 31.8%. For the three [ital J]=1.5 levels, the situation is better, with the average error in [ital A] being 9.2%. For comparison, the average errors in [ital A] using independent-particle Dirac-Fock (DF) wave functions were 88% and 136% for [ital J]=0.5 and 1.5, respectively. In all cases, the many-body (RCI) result represents a [ital vast] improvement from the DF result for the [ital A] values. The value for the electric-quadrupole moment of [sup 91]Zr obtained from a comparison of the experimental [ital 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 cm[sup [minus]1] reported in Moore's [ital Atomic] [ital Energy] [ital Levels], [ital Vol]. [ital II] (U.S. Government Printing Office, Washington, D.C., 1971) is spurious.