Microscopic Calculations for O(6) Nuclei by the Interacting Boson Model

Abstract

We present microscopic calculations of the Interacting Boson Model (IBM) based on the shell model interaction by using the OAI mapping approach. We determine the col­ lective pairs, which correspond to the IBM bosons, by the number conserved Hartree-Fock­ Bogoluibov (HFB) and the proton-neutron Tamm-Dancoff methods, and we take into consid­ eration couplings to the non-collective degrees of freedom. The present realistic calculations are carried out for the Te, Xe and Ba isotopes. Among them, the Xe isotopes are known by numerous phenomenological works to show the 0(6) symmetry. We present the clear 0(6) symmetry in the spectra and the wave function which are microscopically obtained. Low-lying spectra of medium and medium-heavy nuclei show simple and regular structures, although these nuclei consist of many interacting protons and neutrons and their dynamics is intrinsically very complicate. This is known to be the collec­ tive motion. Especially, in the case of even-even nuclei, there are quite simpler and common features in energy levels and electro-magnetic transitions. The understand­ ing of them has been one of the main problems in nuclear structure. Many theories have been advocated, developed and extended. Among them, the Interacting Boson Model (IBM), l)- 6 ) which was first introduced by Arima and Iachello in the 1970's, has shown to be rather successful. In the IBM, nucleon collective pairs are approximated in terms of bosons. This notion can simplify the treatment of the nucleon many-body system. Furthermore this ansatz facilitates the group theoretical treatment. Originally s and d bosons, which are counterparts of S(J = 0) and D(J = 2) nucleon pairs, are introduced as the building blocks of the IBM. Because these bosons do not distinguish the proton and neutron degrees of freedom, the nucleon pair counterparts of these bosons are ambiguous. But, the s and d bosons span a U(6) space and its group chains containing the 0(3) subgroup correspond physically to vibrational, rotational and '"'( unstable nuclei as limiting cases. These group chains are U(5), SU(3) and 0(6) limits. Unlike to other collective models, the IBM can give us a clear description of the 0(6) nuclei besides the U(5) and SU(3) nuclei. There are many nuclei, the spectra of which show the pattern of these group theoretical limits. Furthermore the intermediate situations between three limits are easily tractable by diagonalization of the Hamiltonian because the dimension of the original IBM space is at most about one hundred. At this stage, many phenomenological works were carried out, which showed that the low-lying states of many even-even nuclei can be explained by using six parameters of the IBM in a unified way. These parameters are considered to