Shape Phase Transitions In The Proton-neutron Interacting Boson Model

The proton-neutron interacting boson model（IBM2）has a very good microscopic founda-tion of shell model and it is considered as one of the standard models for heavy and intermediate-heavy nuclei.In this work,we have investigated three types of shape phase transitions including the spherical to prolate（U（5）-SU（3））,the spherical to triaxially-deformed（U（5）-SU（3）*）and the prolate to triaxailly-deformed（SU（3）-SU（3）*）shape phase transitions in the IBM-2 based on the algorithm of solving the IBM-2 in terms of the weak-coupling SU（3）basis developed by us.Specifically,we have compared the evolutional behaviors of the typical energy ratios,B（E2）transitional rate ratios and electronic quadrupole moments in these shape phase transi-tions,which may occur as functions of the control parameters.It is shown that most of them can present clearly the critical features in these transitions thus being able to be applied to iden-tify and distinguish nuclear shape phase transitions in different mass regions.In addition,we have derived the matrix elements of the Majorana term,which reflects the mixing-symmetry in the IBM-2,under the weak-coupling SU（3）basis.Since the SU（3）*phase is a special phase uniquely appearing in the IBM-2,the effects of the Majorana term on the critical structure in the U（5）-SU（3）*shape phase transition have been analyzed quantitatively.Finally,we applied the consistent-Q Hamiltonian to fit the data for¹⁵⁴Sm.The results indicate that the low-lying properties of this nucleus can be reasonably reproduced by the theoretical calculations,which thus provides an example of the IBM2 applications.