Abstract
In this article we study the behavior of collectivity under random two-body interactions in the framework of the fermion dynamical symmetry model (FDSM). We found that a Hamiltonian with the SO(8) symmetry of the FDSM does not give vibrational and rotational modes under random interactions while a Hamiltonian with the SP(6) symmetry does. It is suggested that collective motions such as vibration and rotation are closely related not only to the quadruple-quadruple correlation in the Hamiltonian but also to the dynamical symmetries of the Hamiltonian.
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