Spin squeezed states and wobbling motion in collective Hamiltonian

Abstract

A semiclassical approach is proposed to calculate the collective potential and mass parameters to formulate a collective Hamiltonian capable of describing the wobbling motion in both even-even and odd-mass systems. By diagonalizing the resulting collective Hamiltonian (CH), one can obtain the energies and wave functions associated with the wobbling states. Furthermore, a novel technique called spin squeezed state (SSS) maps is introduced based on the derived wave functions. To validate the results obtained from the collective Hamiltonian, a comparative analysis is conducted against predictions from the triaxial rotor model (TRM) and particle triaxial rotor (PTR) model. Notably, the SSS plots determined using the TRM and PTR models exhibit a strong correlation with the probability density distributions of the wave functions obtained from the CH. This correlation highlights the consistency and coherence between the different theoretical approaches when describing the wobbling phenomenon and associated rotational dynamics.