The interacting boson model with isospin （IBM-3） has been used to study the isospin excitation states and electromagnetic transitions for 24Mg nucleus. The mixed symmetry states at low spin are also analyzed. The theoretical calculations are in agreement with experimental data. The present calculations indicate that the 3^＋ state is the lowest mixed symmetry state.
The E-Gamma Over Spin （E-GOS） analysis method is applied to the study of the shape phase transition of neutron-rich even-even light nuclei with Z=20-28. Some valuable results are gained through analysing E-GOS curves of Ca, Ti, Cr, Fe and Ni nuclei.
Spectra and E2 transition rates for the 160-170Er isotopes are studied in the framework of the interaction boson model. A schematic Hamiltonian able to describe their spectra and B(E2) transition is used. It is found that the 160-170Er isotopes are in the transition from the vibrational limit to rotational limit.
The interacting boson model with isospin （IBM-3） is applied to study the band structure and electromagnetic transition properties of the low-lying states in the cross-conjugate nuclei 44Ti and S2Fe. The isospin excitation states with T=0, 1 and 2 are identified and compared with available data. The E2 and M1 matrix elements for the low-lying states have been investigated. According to this study, the 2＋3 state is the lowest mixed symmetry state in the cross-conjugate nuclei 44Ti and 52Fe. The excitation energy of the second 0＋2 and 2＋2 states with T=0 in the nucleus 52Fe are identified. The agreement between the model calculations and data is reasonably good.
The interacting boson model-3(IBM-3) has been used to study the low-energy level structure and electromagnetic transitions of 68Ge nucleus. The main components of the wave function for some states are also analyzed respectively. The theoretical calculations are in agreement with experimental data, and the 68Ge is in transition from U(5) to SU(3).
The interacting boson model with isospin (IBM-3) has been used to study the isospin excitation states and mixed symmetry states at low spin for 28Si. The theoretical calculations are in agreement with experimental data. The theoretical results show that the 81+ energy is 14.73 MeV.
