Quasi-SU(3) Coupling Induced Oblate-Prolate Shape Phase Transition in the Casten Triangle

Area of Science:

• Nuclear Physics
• Atomic Physics
• Quantum Mechanics

Background:

• The mass-130 region, including Te, Xe, and Ba isotopes, exhibits complex nuclear behavior.
• These isotopes display regular patterns, often classified using the Casten symmetry triangle.

Purpose of the Study:

• To investigate the underlying mechanisms of shape evolution and phase transitions in the mass-130 region.
• To identify the role of specific nuclear orbits and couplings in driving these phenomena.

Main Methods:

• Employed a shell model Hamiltonian with the Hartree-Fock-Bogolyubov plus generator coordinate method.
• Calculations were performed in a large model space including specific valence orbits.
• Validated the model by reproducing experimental energy levels, spectroscopic quadrupole moments, and E2 transition probabilities.

Main Results:

• Identified quasi-SU(3) couplings across the N=50 and 82 shell gaps.
• Demonstrated that proton orbit couplings (1g_{9/2}, 2d_{5/2}) lead to increased gamma softness.
• Showed that neutron orbit couplings (1h_{11/2}, 2f_{7/2}) are responsible for the oblate-to-prolate shape phase transition.

Conclusions:

• Quasi-SU(3) couplings provide a microscopic explanation for shape evolution and phase transitions in the mass-130 region.
• Spectroscopic quadrupole moments highlight hidden symmetries within shell-model configurations.
• The study offers deeper insights into the empirical symmetry triangle observed in nuclear structure.