Semiclassical description of chiral geometry in triaxial nuclei

Abstract

A triaxial particle-rotor Hamiltonian for three mutually perpendicular angular momentum vectors corresponding to two high-j quasiparticles and the rotation of a triaxial collective core, is treated within a time-dependent variational principle. The resulting classical energy function is used to investigate the rotational dynamics of the system. It is found that the classical energy function exhibits two minima starting from a critical angular momentum value which depends on the singleparticle configuration and the asymmetry measure γ. The emergence of the two minima is attributed to the breaking of the chiral symmetry. Quantizing the energy function for a given angular momentum, one obtains a Schrödinger equation with a coordinate dependent mass term for a symmetrical potential which changes from a single to a double well shape as the angular momentum pass the critical value. The energies of the chiral partner bands for a given angular momentum are then given by the lowest two eigenvalues. The procedure is exemplified for maximal triaxiality and two h 11/2 quasiparticles, with the results used for the description of the chiral doublet bands in 134 Pr.

The Influence of Triaxial Deformation and Quasiparticle Alignment on the Structure of Chiral Partner Bands

“…The angular momentum where degeneracy commences depends on both quasiparticle spins and the triaxial deformation. For example, in comparison to the previous j = j = 11/2 results [3,4,9], the point of degeneracy is slightly shortened for the j = 9/2 and j = 11/2 case. Moreover, due to j = j , the prolate and oblate results are no longer equal.…”

“…The relevant part of the particle-rotor Hamiltonian with only the total angular momentum components as acting operators is dequantized through a variational principle with a coherent state for angular momentum operators [3,4,[6][7][8][9] with axis 3 chosen as a quantization axis. The later is parametrized within a stereographic representation of the total angular momentum vector, which provides a pair of canonical coordinates -the azimuth angle ϕ and the third axis projection x = I cos θ of the total spin vector.…”

“…Using the semiclassical description of Refs. [3,4,9], one showed that deviations from maximal triaxiality of the core as well as from the principal axes alignments of the quasiparticle spins are responsible for the loss of energy degeneracy at high spin states. On one hand, lower triaxiality maintains the chiral vibration regime up to very high spins.…”

Coexistence, mixing and fluctuation of nuclear shapes

“…At some point, both 0 + states exhibit a two-peak probability distribution with almost mirrored shapes. A similar situation arises in symmetric double-minimum tunneling used in molecular physics [10] or in the recent description [11,12] of the transition from chiral vibration to static chirality in nuclei. Although in both cases, the peaks are symmetrical due to the symmetry of the potential.…”

Measurements of dihadron correlations relative to the event plane in Au+Au collisions at GeV *

“…The hydrodynamic evolutions translate the initial configuration space anisotropy (and fluctuations) into final-state momentum anisotropy. The triangular anisotropy has been measured at RHIC [80,81,[122][123][124][125] with the event-plane as well as the two-particle cumulant method. Event-by-event hydrodynamic calculations are able to reproduce the measurements qualitatively, and in some cases even quantitatively [82].…”