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

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 |Li, right-handed |Ri, and planar |Pi configurations. The presence and the impact of the planar component is investigated as a function of the total spin for mass A≈130 nuclei with the valence h₁₁/₂ proton particle, valence h₁₁/₂ 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 |Li and |Ri and is free of the |Pi component, indicating that it is of pure chiral geometry. For the lower-energy member of the doublet, the contribution of the |Pi 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 (|Pi) and non-planar (|Li and |Ri) subspaces of the full Hilbert space.