Spin squeezed states and wobbling motion in a collective Hamiltonian

A semiclassical approach combined with adiabatic approximation is applied to the particle+triaxial rotor (PTR) model in order to derive the collective potential and mass parameters of a collective Hamiltonian (CH) that depends only on the total angular momentum for the wobbling motion. The CH approximates very well the energies and $E2$ transition probabilities associated with the lowest wobbling states in both even-even and odd-mass systems. The spin squeezed state (SSS) representation with the character of a wave function in orientation angle of the total angular momentum is introduced to illustrate on the structure of the states. The probability distribution for the lowest states of the PTR and the CH agree well. This demonstrates that the method can be used to incorporate collective wobbling into the microscopic tilted axis cranking approach. A classification scheme for the wobbling mode based on the SSS states is discussed.