Collective Hamiltonian for wobbling modes

Abstract

The simple, longitudinal, and transverse wobblers are systematically studied within the framework of collective Hamiltonian, where the collective potential and mass parameter included are obtained based on the tilted axis cranking approach. Solving the collective Hamiltonian by diagonalization, the energies and the wave functions of the wobbling states are obtained. The obtained results are compared with those by harmonic approximation formula and particle rotor model. The wobbling energies calculated by the collective Hamiltonian are closer to the exact solutions by particle rotor model than harmonic approximation formula. It is confirmed that the wobbling frequency increases with the rotational frequency in simple and longitudinal wobbling motions while decreases in transverse wobbling motion. These variation trends are related to the stiffness of the collective potential in the collective Hamiltonian.

Wobbling motion in Pr135 within a collective Hamiltonian

“…[33,34]. Choosing the azimuth angle ϕ as the collective coordinate, the collective Hamiltonian readŝ…”

“…of TAC calculations with respect to the polar angle θ for given ϕ [33,34]. For a high-j, the TAC Hamiltonian reads [3] h ′ =ĥ def − ω ·ĵ,…”

“…The quantum fluctuations along ϕ are taken into account to go beyond the mean-field approximation. Using this model, the simple, longitudinal, and transverse wobblers were systematically studied and the variation trends of their wobbling frequencies were confirmed [34].…”

“…Theoretically, the triaxial particle rotor model (PRM) [1,[15][16][17][18][19][20][21][22] and the cranking model plus random phase approximation (RPA) [23][24][25][26][27][28][29][30][31][32] have been widely used to describe the wobbling motion. Recently, based on the cranking mean field and treating the nuclear orientation as collective degree of freedom, a collective Hamiltonian was constructed and applied for the chiral [33] and wobbling modes [34]. Usually, the orientation of a nucleus in the rotating mean field is described by the polar angle θ and azimuth angle ϕ in spherical coordinates.…”

“…Usually, the orientation of a nucleus in the rotating mean field is described by the polar angle θ and azimuth angle ϕ in spherical coordinates. In the collective Hamiltonian for wobbling modes, the azimuth angle ϕ is taken as the collective coordinate since the motion along the ϕ direction is much easier than in the θ direction [34]. The quantum fluctuations along ϕ are taken into account to go beyond the mean-field approximation.…”