Theoretical Study Of The Interacting Boson Fermion Model With Multi-j Single Particle Orbits

The interacting boson model（IBM）has been widely applied to describe the low-lying properties of even-even nuclei with heavy or intermediately-heavy mass.For odd nuclei,the IBM should be extended by coupling an unpaired nucleon,which is assumed to occupy some given single-particle orbits.The resulting model is called the interacting boson-fermion model（IBFM）.In this thesis,we will conduct a theoretical analysis of the IBFM involving multiplejorbits.Specifically,an algorithm for building the Hamiltonian matrix in terms of the SU（3）basis has been build,by which the IBFM is further applied to describe¹⁵¹Eu.The results indicate that the low-lying spectrum and（2）transitions in this nucleon can be well reproduced in the IBFM.Based on a dynamic supersymmetry scheme of the IBFM,we also investigated the prolate-oblate shape phase transition in the odd A system,and the results confirm the improtance of the IBFM in understanding shape phase transitions in odd nuclei.