Isotope-shift measurements and King-fit analysis in nickel isotopes

The isotope shifts of the $3d^{9}4s{}^{3}D_3\to 3d^{9}4p{}^{3}P_2$ transition in the stable even-even nickel isotopes were measured. An improved accuracy was achieved by transforming the systematic contribution of the wavelength-meter-based laser-frequency measurement into a statistical-acting contribution by measuring the same observables at different frequency sets. A detailed King-fit analysis was performed to extract the mass-shift and field-shift parameters, which are crucial for the determination of the charge radii of short-lived isotopes from recently measured isotope shifts. A critical dependence of the achievable charge-radius accuracy on the choice of the reference isotope in the King-fit analysis was observed and is discussed.

Figure 1

Schematic of the BECOLA beamline. A ${\mathrm{Ni}}^{+}$ ion beam was produced in a Penning-ionization-gauge (PIG) source. In the radio-frequency-quadrupole trap (RFQ) the beam was cooled and bunched. Laser and ion beams were superimposed and aligned through two 3-mm apertures at 2.1-m distance. The beam was neutralized through charge-exchange reactions with Na vapor. Fluorescence light was collected by three mirror-based detection units. Further ion optics for beam deflection and collimation are not shown.

Figure 2

Typical resonance spectra of ${}^{58,60,62,64}\mathrm{Ni}$. Due to inelastic collisions during the charge exchange process [31], the line shape is slightly asymmetric, which was considered in the fit function [35]. The abscissa is relative to ${}^{58}\mathrm{Ni}$.

Figure 3

King plots based on (a) the isotope shifts $\delta {\nu }^{A,58}$ of the present work (red) and of Ref. [24] (blue), (b) the isotope shifts $\delta {\nu }^{A,60}$ of the present work (red) and of Ref. [20] (blue), and the differential mean-square charge radii of Table 4. The straight solid red line was obtained by the linear regression applied to our data (blue for literature data) and the dashed lines show the $1\sigma$ confidence interval. The dominant contribution to the fit uncertainty is the uncertainty of the modified differential mean-squared charge radii.

Figure 4

Uncertainty of the differential mean-square charge-radius $\mathrm{\Delta }\delta {\langle r^2\rangle }^{54,A^{\prime }}$ extracted from an isotope-shift measurement $\delta {\nu }^{54,A^{\prime }}$. The reference isotope dependence originates in the different uncertainties of $K_{\alpha }$ and $F$ and the distance to the reference isotopes in the King-plot diagram. The minimum is located at the center of the reference isotopes. To disentangle the impact of the uncertainties of the atomic factors and the isotope-shift measurement, the resulting uncertainty is plotted for $\mathrm{\Delta }\delta {\nu }^{54,A^{\prime }}=0\mathrm{MHz}$ and $\mathrm{\Delta }\delta {\nu }^{54,A^{\prime }}=10\mathrm{MHz}$. See text for more details.