Self-Consistent Harmonic Oscillator Model and Tilted Rotation

Abstract

The three dimensional harmonic oscillator model including a cranking term is used for an energy variational calculation. Energy minima are found under variation of the three oscillator frequencies determining the shape of the system for given values of the three components of the rotational vector which determines the orientation of the angular momentum in the intrinsic frame. Tilted rotations are established by numerical means for triaxial nuclei. The onset of tilted rotations is related to an instability of the mean field as verified by the random phase approximation. Analytic expressions are derived for the critical rotational frequencies associated with the mean field instability.

16 pages, 2 figures, extended version

References in corpus (3)

• Dynamic instability of a rotating Bose-Einstein condensate
• A superfluid gyroscope with cold atomic gases
• SU(3) density matrix theory

Cited by in corpus (10)

• The physics of exceptional points
• Principal problems in Bose-Einstein condensation of dilute gases
• Effects of symmetry breaking in finite quantum systems
• Instability of nuclear wobbling motion and tilted axis rotation
• Microscopic analysis of shape-phase transitions in even-even N~90 rotating nuclei
• Arbitrary-angle rotation of the polarization of a dipolar Bose-Einstein condensate
• Backbending and $Gamma$-Vibrations
• Stationary states, dynamical stability, and vorticity of Bose-Einstein condensates in tilted rotating harmonic traps
• Quadrupole correlations and inertial properties of rotating nuclei
• Instabilities, nonhermiticity and exceptional points in the cranking model