Isotope shift in hafnium I: Parametric analysis,ab initio calculation, and changes in nuclear charge radii

Abstract

The isotope shift in the arc spectrum of hafnium was studied in 10 lines for the isotopes176Hf,178Hf, and180Hf by means of a photoelectric recording Fabry-Perot spectrometer with digital data processing. The observed shifts together with results from an earlier study were analyzed by means of the parametric method. The field shift difference between the terms 5d3(4F) 6s5F and3F resulted in 17(2) mK for the isotope pair178,180Hf. This reflects the influence of a second-order effect which is described by the parameterg2=−4.4(6) mK. The parameterz5d, displaying the magnitude of spin-dependent effects in the isotope shift of 5d36s, was found to be 0.8(2) mK for the same isotope pair. The experimental data are compared with results obtained from the non-relativistic Hartree-Fock method. The calculated electron densities describe the experimental field shifts with good accuracy. Hartree-Fock screening ratios for various types of transitions were used to evaluate changes in mean-square nuclear charge radii. The mean value ofλ178,180≈δ〈r2〉178,180 equals 0.069(10) fm2.