Penning-trap mass spectrometry and mean-field study of nuclear shape coexistence in the neutron-deficient lead region

We present a study of nuclear shape coexistence in the region of neutron-deficient lead isotopes. The midshell gold isotopes ${}^{180,185,188,190}\mathrm{Au}$ $\left(Z=79\right)$, the two long-lived nuclear states in ${}^{197}\mathrm{At}$ $\left(Z=85\right)$, and the neutron-rich nuclide ${}^{219}\mathrm{At}$ were produced by the ISOLDE facility at CERN and their masses were determined with the high-precision Penning-trap mass spectrometer ISOLTRAP. The studied gold isotopes address the trend of binding energies in a region of the nuclear chart where the nuclear charge radii show pronounced discontinuities. Significant deviations from the atomic-mass evaluation were found for ${}^{188,190}\mathrm{Au}$. The new trend of two-neutron separation energies is smoother, although it does reveal the onset of deformation. The origin of this effect is interpreted in connection to the odd-even staggering of binding energies, as well as theoretically by Hartree-Fock-Bogoliubov calculations including quasiparticle blocking. The role of blocking for reproducing the large odd-even staggering of charge radii in the mercury isotopic chain is illustrated.

Figure 1

Schematic view of the ISOLTRAP experiment. For details, see text.

Figure 2

Time-of-flight spectrum of $A=190$ isobars after 1000 laps in the MR-ToF MS, with the RILIS optimized for maximum Au ionization efficiency.

Figure 3

Time-of-flight ion-cyclotron resonances of ${}^{197}\mathrm{At}^{+}$, using a Ramsey-type excitation scheme [39, 40]. The full blue symbols correspond to a weight of the $9/2^{-}$ state in the measured beam of approximately 74.4%, the rest being the $1/2^{+}$ state. The open red symbols correspond to a weight of the $9/2^{-}$ state of approximately 27.4%. The fits by the theoretical line shapes are also shown. The dashed lines mark the centers of the two resonances.

Figure 4

Upper panel: experimental two-neutron separation energies for the gold and mercury isotopes compared to the mean-square charge radii of the gold isotopes. Lower panel: three-point empirical pairing gap for the mercury and gold isotopes in the region of interest. The experimental masses are from the atomic-mass evaluation [27] (empty symbols), this work (full symbols), and Ref. [29]. The mean-square charge radii are given as displacement to the $N=115$ value and taken from the Fricke evaluation [66].

Figure 5

Experimental two-neutron separation energies (upper panel) and mean-square charge radii (lower panel) for the gold and mercury isotopes, compared to the results of HFB calculations without quasiparticle blocking. The experimental masses are from the atomic-mass evaluation [27] (empty symbols), this work (full symbols), and Ref. [29]. The mean-square charge radii are given as displacement to the $N=110$ value and taken from the Fricke evaluation [66, 76]. The calculations are presented separately for the lowest-energy oblate (blue squares) and prolate (green diamonds) solution, as well as for the ground state (empty red circles), assigned to the solution of lowest energy. The trends of the computed observables in a spherical HFB calculation are given with dashed lines. The two-neutron separation energies and charge radii of mercury isotopes are offset in order to better separate the two isotopic chains.

Figure 6

Difference in binding energy between the prolate and the oblate mean-field configuration for a calculation without quasiparticle blocking (black squares) and with quasiparticle blocking (red circles) for mercury isotopes. Negative values correspond to nuclei for which the prolate configuration is more bound.

Figure 7

Same as Fig. 5, but the calculations include proton quasiparticle blocking for the gold isotopes of even neutron number and neutron quasiparticle blocking for the odd mercury isotopes.