Fermionic Foundations Of The Interacting Boson Model And The Structure Of The Rotational Nuclei

Full text: The interacting boson model (IBM) has been quite successful in describing the low-lying nuclear collective motion in nuclei. Much effort has been devoted to the understanding of the microscopic origin of the IBM, to derive the parameters of the model microscopically, namely, from nucleon's degrees of freedom [1]. The shell-model Hilbert space is very large for a many-nucleon system with a large number of nucleons, and for this reason, it is very difficult and sometimes almost impossible to treat the shell-model Hamiltonian exactly. We therefore have to truncate the Hilbert space to the SD-subspace constructed by S- and D-pairs. The truncated Fermi-model space was transformed into an ideal boson space, and the boson image of the shell-model Hamiltonian was obtained in an exact manner. After transforming the shell-model space into ideal boson space, only two kinds of bosons-one S-boson, one D-boson, which correspond to the most collective Tamm-Dancoff phonon modes with l=0, 2 - were retained as collective bosons. The S- and D-bosons are the building blocks of the IBM and microscopically they are considered as the collective S- and D-nucleon pairs. This directly implies that fermionic S- and D-pairs should play a dominant role in the low-lying collective states. This kind of work is also important for microscopic foundation of the Fermion Dynamical Symmetry Model [2], because the model is based on the collective SD-pairs. In the second part of this paper is considered a mapping method for strongly deformed nuclei. Although this mapping is for deformed nuclei, it is somewhat related to the Otsuka-Arima-Iachello (OAI) mapping. Then we have to apply the theory to the realistic case. We compare the results of full shell-model calculation, the IBM calculation with the OAI mapping and the calculation in the nucleon pair space. The results of mapping are good for deformed limit, it can describe the general features of isotopes Er and Dy. References: 1. T.Otsuka, Progr. Theor. Phys., Suppl. No 125, 1996, p.5.; 2. C.L.Wu, H.T.Chen. Nucl.Phys. A570, 1994, p.377. (authors)