Partial dynamical symmetry and anharmonicity in γ-soft nuclei

The concept of dynamical symmetry (DS) is now widely accepted to be of central importance in our understanding of many-body systems, such as nuclei. Its hallmarks are the solvability of the complete spectrum, and the existence of exact quantum numbers for all eigenstates. However, in most applications to realistic systems, the predictions of an exact DS are rarely fulfilled and one is compelled to break it. More often one finds that the assumed symmetry is not obeyed uniformly, i.e., is fulfilled by only some states but not by others. The need to address such situations has led to the introduction of partial dynamical symmetries (PDSs). The essential idea is to relax the stringent conditions of complete solvability, so that the DS is broken, but part of the eigen spectrum remains solvable with good symmetry. Various types of bosonic and fermionic PDS, have been shown to be relevant to nuclear spectroscopy [1-7] and to quantum phase transitions [8]. In the present contribution we extend the notion of PDS to encompass Hamiltonians with higher-order terms. We present a systematic procedure for constructing such PDS Hamiltonians and demonstrate their relevance to the anharmonicity of excited bands in the -soft nucleus 196Pt. The work, to be reported, was done in collaboration with J.E. Garcfa-Ramos (Huelva) and P. Van backer (GANIL) [9]. The SO(6)-DS limit of the interacting boson model (IBM) [10], provides a good description of the rotational spectrum and E2 rates for states in the ground band of 196Pt [11]. However, the resulting fit to energies of excited bands is quite poor. The empirical anharmonicity of excited vibrational bands is large and negative. On the other hand, in the SO(6)-DS limit, the calculated anharmonicity is fixed by the number of valence nucleons, and is found to be in marked disagreement with the empirical value. A detailed study of double-phonon excitations within the IBM, has concluded that large anharmonicities can be incorporated only by the inclusion of at least cubic terms in the Hamiltonian [12]. In the IBM there are 17 possible three-body interactions. One is thus confronted with the need to select suitable higher-order terms that can break the DS in excited bands but preserve it in the ground band. As will be shown, this can be accomplished by the PDS construction mentioned above. The advantage of using higher-order interactions with PDS is that they can be introduced without destroying results previously obtained with a DS for a segment of the spectrum. These virtues generate an efficient tool which can greatly enhance the scope of algebraic modeling of quantum many-body systems.(author)