Nuclear moments and charge radii of neutron-deficient francium isotopes and isomers

Collinear laser fluorescence spectroscopy has been performed on the ground and isomeric states of ${}^{204,206}\mathrm{Fr}$ in order to determine their spins, nuclear moments, and changes in mean-squared charge radii. A new experimental technique has been developed as part of this work which much enhances the data collection rate while maintaining the high resolution. This has permitted the extension of this study to the two isomeric states in each nucleus. The investigation of nuclear $g$ factors and mean-squared charge radii indicates that the neutron-deficient Fr isotopes lie in a transitional region from spherical towards more collective structures.

Figure 1

Effect of the different AOM radio frequencies (${\nu }_{\text{RF1}}=110,{\nu }_{\text{RF2}}=100,$ and ${\nu }_{\text{RF3}}=90$ MHz) illustrated on the cycling transition of ${}^{208}\mathrm{Fr}$. The spectra for the three different RFs are presented individually. The difference in resonance centroids as indicated by the dashed vertical lines corresponds to the RF offset. As an example, the blue dotted lines correspond to the centroid for ${\nu }_{\text{RF1}}$.

Figure 2

Observed optical fluorescence spectra for ${}^{208,206,205,204}\mathrm{Fr}$, respectively. Where appropriate, contributions of the nuclear ground and isomeric states have been marked with a $g$ and $m1,m2$, respectively. As discussed in [1], the high-frequency (low-spin) hyperfine multiplets for both ${}^{206g,m1}\mathrm{Fr}$ and ${}^{204g,m1}\mathrm{Fr}$ are doublet structures.

Figure 3

(a) Changes in mean-squared charge radii for the neutron-deficient Fr isotopes in comparison to those of Pb [15, 27]. Statistical errors are within the data points. Systematic errors for Fr are included as the shaded area for the nuclear ground states and error bars for the isomers. Isodeformation lines according to the droplet model [5, 6] are shown as the dashed lines using ${\beta }_2{(}^{213}\mathrm{Fr})=+0.008$ from [26]. The shaded area enclosed by the dotted lines corresponds to the systematic uncertainty from the atomic factors. (b) Relative change in $\delta \langle r^2\rangle$ for the Fr and Pb ground states; $\Delta =\delta {\langle r^2\rangle }_{\text{Fr}}^{N,126}-\delta {\langle r^2\rangle }_{\text{Pb}}^{N,126}$.

Figure 4

Nuclear $g$ factors for ${}^{204m2,206m2}\mathrm{Fr}$ compared to the empirical coupling for a ${[\left(\pi 1h_{9/2}\right)\otimes \left(\nu 1i_{13/2}\right)]}_{10}$ configuration (horizontal line). The filled circles for $N=119$ indicate the $g$ factor derived from the fits of hyperfine function to the data for various spins.

Figure 5

Nuclear $g$ factors for the neutron-deficient Fr isotopes and isomers. The $g$ factors for the relevant valence particle couplings have been determined empirically (see text for details). The data are color-coded with respect to the suggested proton/neutron state occupancy. The values for ${}^{207,209-213}\mathrm{Fr}$ were taken from [12] (squares) whereas ${}^{204-206,208}\mathrm{Fr}$ are from the present work (circles).