Multiple Shape Coexistence in ^{110,112}Cd

The Proxy-SU(3) Symmetry in Atomic Nuclei

The microscopic origins and the current predictions of the proxy-SU(3) symmetry model of atomic nuclei were reviewed. Beginning with experimental evidence for the special roles played by nucleon pairs with maximal spatial overlap, the proxy-SU(3) approximation scheme is introduced; its validity is demonstrated through Nilsson model calculations and its connection to the spherical shell model. The major role played by the highest weight-irreducible representations of SU(3) in shaping up the nuclear properties is pointed out, resulting in parameter-free predictions of the collective variables β and γ for even–even nuclei in the explanation of the dominance of prolate over oblate shapes in the ground states of even–even nuclei, in the prediction of a shape/phase transition from prolate to oblate shapes below closed shells, and in the prediction of specific islands on the nuclear chart in which shape coexistence is confined. Further developments within the proxy-SU(3) scheme are outlined.

Islands of Shape Coexistence: Theoretical Predictions and Experimental Evidence

Parameter-free theoretical predictions based on a dual shell mechanism within the proxy-SU(3) symmetry of atomic nuclei, as well as covariant density functional theory calculations using the DDME2 functional indicate that shape coexistence (SC) based on the particle-hole excitation mechanism cannot occur everywhere on the nuclear chart but is restricted on islands lying within regions of 7–8, 17–20, 34–40, 59–70, 96–112, 146–168 protons or neutrons. Systematics of data for even-even nuclei possessing K=0 (beta) and K=2 (gamma) bands support the existence of these islands, on which shape coexistence appears whenever the K=0 bandhead 02+ and the first excited state of the ground state band 21+ lie close in energy, with nuclei characterized by 02+ lying below the 21+ found in the center of these islands. In addition, a simple theoretical mechanism leading to multiple-shape coexistence is briefly discussed.

Emerging nuclear collectivity in 124−130Te

The emergence of nuclear collectivity near doubly-magic 132Sn was explored along the stable, eveneven 124−130Te isotopes. Preliminary measurements of the B(E2; 41+ → 21+) transition strengths are reported from Coulomb excitation experiments primarily aimed at measuring the g factors of the 41+ states. Isotopically enriched Te targets were excited by 198-205 MeV 58Ni beams. A comparison of transition strengths obtained is made to large-scale shell-model calculations with successes and limitations discussed.

Physics of Nuclei: Key Role of an Emergent Symmetry

We show through first-principles nuclear structure calculations that the special nature of the strong nuclear force determines highly regular patterns heretofore unrecognized in nuclei that can be tied to an emergent approximate symmetry. This symmetry is ubiquitous and mathematically tracks with a symplectic symmetry group. This, in turn, has important implications for understanding the physics of nuclei: we find that nuclei are made of only a few equilibrium shapes, deformed or not, with associated vibrations and rotations. It also opens the path for ab initio large-scale modeling of open-shell intermediate-mass nuclei without the need for renormalized interactions and effective charges.

Evidence for shape coexistence in 52Cr through conversion-electron and pair-conversion spectroscopy

Electric monopole (E0) transitions are a highly sensitive probe of the charge distribution of an atomic nucleus. A large E0 transition strength (ρ2(E0)) is a clear indicator of nuclear shape coexistence. In the region between doubly magic 40Ca and 56Ni, E0 transitions have never been observed in the Ti or Cr isotopes, nor in the heavier iron isotopes (56,58Fe). We have performed the first measurements of the E0 transitions in 52Cr via conversion-electron and pair-conversion spectroscopy using the Super-e spectrometer at the Australian National University Heavy Ion Accelerator Facility. We present the first spectra obtained for 52Cr, including the first observation of the E0 transition from the first-excited 0+ state in 52Cr, in both electron-positron pairs and conversion-electron spectroscopy. The preliminary values for the E0 strength in the 1531keV 2+ → 2+ transition in 52Cr is ρ2(E0) × 103 = 470(190), and for the 1728-keV 23+ → 21+ transition, it is ρ2(E0) 103 = 1800(1200). The large E0 strengths observed are consistent with shape coexistence in this region. However, despite the relatively precise observation of the conversion-electron and electron-positron pair intensities, the E0 strengths have large uncertainties. More precise determinations of relevant spectroscopic quantities, such as the state lifetimes and transition mixing ratios for mixed M1 + E2 transitions, are needed to determine the E0 strength more precisely.