Quasiparticle and collective nucleon degrees of freedom in nuclei and its correlation in structure of Hf isotopes

Structure of energy spectra and backbending phenomena of the isotope string of Hf with mass number between 162 and 170 have been investigated. Extend of SU(3)-limits of interacting boson model to allow a boson to break to form a quasiparticle pair, which can occupy h11/2 and i13/2 orbitals. The calculated energy levels, intensity of the electromagnetic transitions, including the ground state, β and γ band are in satisfactory agreement with observed values for the whole string of Hf isotopes. Backbending of the moment inertia of the yrast and β bands can be reproduced reasonably. Recently, very high spin states up to J=40 and a double backbending have been observed in some nuclei in rare-earth region. This phenomena might hopefully be interpreted by considering two or more bosons to break to form more quasiparticle pairs and make more bands crossing to form the double backbending