Isotope shift and hyperfine structure in the atomic spectrum of hafnium by laser spectroscopy

The isotope shift and the hyperfine structure of 14 spectral lines of Hf i were investigated using high-resolution laser spectroscopy of a well-collimated beam of Hf atoms. The hyperfine splitting constants A and B of the electronic states ${}_{}{}^5{}_{}{}^{}$${\mathit{G}}_5$,...${,}^5$${\mathit{G}}_2$${,}^5$${\mathit{F}}_3$ of the excited configuration 5${\mathit{d}}^2$6s6p and of some electronic states of 5d6${\mathit{s}}^2$6p were obtained for the two stable odd isotopes ${}_{}{}^{177}{}_{}{}^{}\mathrm{Hf}$ and ${}_{}{}^{179}{}_{}{}^{}\mathrm{Hf}$. From these data one-electron hyperfine splitting parameters could be deduced, e.g., ${\mathit{a}}_{6\mathit{s}}$=3.08(15) GHz for the magnetic dipole part in the case of ${}_{}{}^{177}{}_{}{}^{}\mathrm{Hf}$. Our accurate experimental values of the isotope shifts between the stable Hf isotopes 174, 176–180 allow a reliable separation of the effect of the specific mass shift and of the field shift for all observed spectral lines. Using the field shift of the 545.29-nm line, which corresponds to an almost pure 5${\mathit{d}}^2$6${\mathit{s}}^{2\mathrm{-}}$5${\mathit{d}}^2$6s6p transition, the change in mean-square nuclear charge radius between ${}_{}{}^{178}{}_{}{}^{}\mathrm{Hf}$ and ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}$ was determined to be δ〈${\mathit{r}}^2$〉=0.098(13) ${\mathrm{fm}}^2$. Values of δ〈${\mathit{r}}^2$〉 for the Hf isotopes 174, 176, 177, and 179 referred to ${}_{}{}^{178}{}_{}{}^{}\mathrm{Hf}$ are also available from the present work.