Hyperfine Anomalies in Fr: Boundaries of the Spherical Single Particle Model

We have measured the hyperfine splitting of the $7P_{1/2}$ state at the 100 ppm level in Fr isotopes (${}^{206g,206m,207,209,213,221}\mathrm{Fr}$) near the closed neutron shell ($N=126$ in ${}^{213}\mathrm{Fr}$). The measurements in five isotopes and a nuclear isomeric state of francium, combined with previous determinations of the $7S_{1/2}$ splittings, reveal the spatial distribution of the nuclear magnetization, i.e., the Bohr-Weisskopf effect. We compare our results with a simple shell model consisting of unpaired single valence nucleons orbiting a spherical nucleus, and find good agreement over a range of neutron-deficient isotopes (${}^{207–213}\mathrm{Fr}$). Also, we find near-constant proton anomalies for several even-$N$ isotopes. This identifies a set of Fr isotopes whose nuclear structure can be understood well enough for the extraction of weak interaction parameters from parity nonconservation studies.

Figure 1

Measurement scheme. (a) Atomic energy levels relevant for trapping and measuring. (b) Sideband frequency scan around 2.9 GHz (isotope dependent). (c) Time sequence for trapping and data collection.

Figure 2

Sample of experimental data. Top: Fluorescence counts as a function of sideband frequency for ${}^{213}\mathrm{Fr}$ with separate Lorentzian fits to each of the resonances. The hyperfine splitting is the difference of the frequency position of the two peaks and it gives $5739.60\pm 0.030\mathrm{MHz}$. Bottom: Normalized residuals of the fits.

Figure 3

$R_{\mathrm{HFS}}(A)$ as defined in Eq. (2), for several Fr isotopes normalized to the value for ${}^{213}\mathrm{Fr}$ (closed neutron shell $N=126$). Blue diamonds are current measurements. Red squares are from Ref. [20]. The green circles are predictions based on Ref. [27]. The ground state ${}^{206g}\mathrm{Fr}$ is shown to the left of the isomer ${}^{206m}\mathrm{Fr}$. Both are enclosed in rectangles with the respective calculations. The proton resides on the indicated $\pi h_{9/2}$ orbital.