Penning-trap mass measurements of exotic rubidium and gold isotopes for a mean-field study of pairing and quadrupole correlations

The most complex nuclei are situated between the magic and the mid-shell ones, in regions known for sudden changes of the trends of nuclear observables. These are the so-called shape-transition regions, where the nuclear paradigm changes from the vibrational liquid drop to the static rotor. With few exceptions, nuclei in these regions are radioactive, with half-lives dropping into the millisecond range. Complementing the information obtained from the low-lying excitation spectrum, nuclear binding energies and mean-square charge radii are among the observables most sensitive to these changes of nuclear structure. In the present work, a study of the shape- transition phenomenon is performed by measurements of radioactive nuclides produced by the ISOLDE facility at CERN. The masses of the neutron-rich rubidium isotopes $^{98-100}$Rb and of the neutron-deficient gold isotopes $^{180, 185, 188, 190, 191}$Au are determined using the Penning-trap mass spectrometer ISOLTRAP. The mass of $^{100}$Rb is determined for the first time. Significant deviations from the literature values are found for the isotopes $^{188, 190}$Au. A new experimental method is presented, using a recently developed multi-reflection time-of-flight mass spectrometer as a beam-analysis tool for resonance- ionization laser spectroscopy. The new method opens the path to measurements of atomic hyperfine spectra with ISOLTRAP, from which charge radii and electromagnetic moments of radioactive nuclides can be extracted. The properties of the studied nuclides map the borders of two prominent regions of quadrupole deformation, which constrain the fine balance between pairing and quadrupole correlations in the nuclear ground states. This balance is studied by the Hartree-Fock- Bogoliubov (HFB) approach. The sensitivity of the shape-transition phenomenon to the strength of pairing correlations is demonstrated. In particular, the strong odd-even staggering of charge radii in the mercury isotopic chain is shown to result in the HFB approach from the fine interplay between pairing, quadrupole correlations and quasi-particle blocking.