Deformation versus Sphericity in the Ground States of the Lightest Gold Isotopes

The changes in mean-squared charge radii of neutron-deficient gold nuclei have been determined using the in-source, resonance-ionization laser spectroscopy technique, at the ISOLDE facility (CERN). From these new data, nuclear deformations are inferred, revealing a competition between deformed and spherical configurations. The isotopes ${}^{180,181,182}\mathrm{Au}$ are observed to possess well-deformed ground states and, when moving to lighter masses, a sudden transition to near-spherical shapes is seen in the extremely neutron-deficient nuclides, ${}^{176,177,179}\mathrm{Au}$. A case of shape coexistence and shape staggering is identified in ${}^{178}\mathrm{Au}$ which has a ground and isomeric state with different deformations. These new data reveal a pattern in ground-state deformation unique to the gold isotopes, whereby, when moving from the heavy to light masses, a plateau of well-deformed isotopes exists around the neutron midshell, flanked by near-spherical shapes in the heavier and lighter isotopes—a trend hitherto unseen elsewhere in the nuclear chart. The experimental charge radii are compared to those from Hartree-Fock-Bogoliubov calculations using the D1M Gogny interaction and configuration mixing between states of different deformation. The calculations are constrained by the known spins, parities, and magnetic moments of the ground states in gold nuclei and show a good agreement with the experimental results.

Figure 1

(a) Examples of hfs spectra collected during the experiment (black data points) fitted with Voigt profiles (solid lines), along with the transition centroid frequencies (vertical dashed lines) and the measuring device used. The red and blue colors represent the fits and centroids for ground and isomeric states and the low- and high-spin states in ${}^{176}\mathrm{Au}$, respectively. The $y$ axis is the number of $\alpha$ decays, or the number of ions detected per laser step, in the WM and MR TOF MS, respectively. (b) The $\delta ⟨r^2{⟩}_{A,197}$ values for gold ground (solid symbols) and isomeric (hollow symbols) states deduced from the IS extracted from the data in (a) (experimental error bars are smaller than the data points). The red and black data points are the results from the present work and literature, respectively [7, 8, 9, 10, 11, 12, 13]. The diagonal dotted lines indicate $\delta ⟨r^2{⟩}_{A,197}$ for fixed deformations predicted by the droplet model ($⟨{\beta }_2^2{⟩}_{\mathrm{DM}}^{1/2}$) [14], using the second parametrization in Ref. [15] and assuming ${\beta }_2({}^{197}\mathrm{Au})=0.11$ [9]. The dotted lines are labeled with their corresponding $⟨{\beta }_2^2{⟩}_{\mathrm{DM}}^{1/2}$ values. (c) Comparison of ground-state $\delta ⟨r^2⟩$ values near $N=104$, for iridium (purple diamond) [16, 17], platinum (teal right-pointing triangle) [17, 18, 19, 20], gold (red square), mercury (green up-pointing triangle) [21, 22, 23, 24], lead (black circle) [25, 26], and bismuth (blue down-pointing triangle) [27] isotopes—the chains are arbitrarily offset for the comparison. Error bars are omitted for clarity but are typically smaller than or the same size as the data points.

Figure 2

Comparison between experimental $\delta ⟨r^2{⟩}_{A,197}$ values (black circle) for gold isotopes with HFB calculations without (red square) and with (blue up-pointing triangle) CM included. The filled symbols connected by lines indicate ground states, while the hollow symbols represent the isomers in ${}^{178,187}\mathrm{Au}$ and the high-spin state in ${}^{176}\mathrm{Au}$. The $11/2^{-}$ isomers have been excluded for clarity.

Figure 3

Comparison between experimental (black circle) and theoretical (red square) results for ground-state $\delta ⟨r^2⟩$ values along isotopic chains. The isotopic chains are arbitrarily offset from each other for clarity and are labeled with their chemical symbol and proton number.