The collective vibrations of a many-fermion system

Calvin W. Johnson, Hai Ah Nam

Recent investigations have looked at the many-body spectra of random two-body interactions. In fermion systems, such as the interacting shell model, one finds pairing-like spectra, while in boson systems, such as IBM-1, one finds rotational and vibrational spectra. We discuss the search for random ensembles of fermion interactions that yield rotational and vibrational spectra, and in particular present results from a new ensemble, the ``random quadrupole-quadrupole ensemble''

Robert William Jones, Franz Mohling, Richard L. Becker

Y. M. Zhao, J. L. Ping, A. Arima

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.

Robert William Jones, Franz Mohling

Takashi Nakatsukasa, Niels R. Walet

A model Hamiltonian describing a two-level system with a crossing plus a pairing force is investigated using technique of large-amplitude collective motion. The collective path, which is determined by the decoupling conditions, is found to be almost identical to the one in the Born-Oppenheimer approximation for the case of a strong pairing force. For the weak pairing case, the obtained path describes a diabatic dynamics of the system. PACS number(s): 21.60.-n, 36.40.Sx Nuclei and metallic clusters are finite fermionic many-body systems which support many kinds of collective motion. While properties of high-frequency vibrations (giant resonances) may be well reproduced by the random-phase approximation (RPA), some low-frequency vibrations exhibit an anharmonic nature that the RPA cannot describe. Shape coexistence and fission phenomena in nuclei and clusters also have such a large amplitude nature. In order to investigate these kinds of large amplitude collective motion, one would like to reduce the number of degrees of freedom to a few judiciously chosen collective coordinates. In order to determine the collective coordinates self-consistently, we use the theory of adiabatic

Viktor Mikhaĭlovich Galit︠s︡kiĭ