Collective model of chiral and wobbling modes in nuclei

Recent progress of collective Hamiltonian for the chiral and wobbling modes in nuclei is reviewed. A brief introduction about the experimental and theoretical research statuses of the chirality and wobbling is given first. Procedures of constructing collective Hamiltonian, based on the tilted axis cranking approach, are shown in details. The newly developed collective Hamiltonian is used to investigate the chiral and wobbling modes. For the chiral modes, we study the microscopic mechanism of the energy difference between the chiral doublets with respect to the rotational frequency. It is demonstrated that the gradually increased potential barrier suppresses the tunneling probabilities between the left- and right-handed states and thus causes the decreasing of the energy difference. For the wobbling modes, the variation trends of wobbling frequencies for simple, longitudinal, and transverse wobblers are studied and found to be related to the stiffness of the collective potential.