Three-level mixing model for nuclear chiral rotation: Role of planar component

Abstract

Three- and two-level mixing models are proposed to understand the doubling of states at the same spin and parity in triaxially-deformed atomic nuclei with odd numbers of protons and neutrons. The Particle-Rotor Model for such nuclei is solved using the newly proposed basis which couples angular momenta of two valence nucleons and the rotating triaxial mean-field into left-handed $|\mathcal{L}⟩$, right-handed $|\mathcal{R}⟩$, and planar $|\mathcal{P}⟩$ configurations. The presence and the impact of the planar component is investigated as a function of the total spin for mass A$\approx$130 nuclei with the valence h${}_{11/2}$ proton particle, valence h${}_{11/2}$ neutron hole and the maximum difference between principle axes allowed by the quadrupole deformation of the mean field. It is concluded that at each spin value the higher-energy member of a doublet of states is built on the anti-symmetric combination of $|\mathcal{L}⟩$ and $|\mathcal{R}⟩$ and is free of the $|\mathcal{P}⟩$ component, indicating that it is of pure chiral geometry. For the lower-energy member of the doublet, the contribution of the $|\mathcal{P}⟩$ component to the eigenfunction first decreases and then increases as a function of the total spin. This trend as well as the energy splitting between the doublet states are both determined by the Hamiltonian matrix elements between the planar ($|\mathcal{P}⟩$) and non-planar ($|\mathcal{L}⟩$ and $|\mathcal{R}⟩$) subspaces of the full Hilbert space.

12 pages, 5 figures, accepted as a Rapid Communication in Physical Review C