Studying The Higher-order Term In Interacting Boson Model

We systematically investigate the transitional nuclei from vibration to rotation by replac-ing the SU(3) quadrupole-quadrupole interaction into the SO(6) cubic [Q(0) x Q(0)×Q(0)]0 interaction. Firstly, the different energy levels and ratios, d boson expectation value, isomer shift ratios andβ,γvalues are calculated. The results show that the behavor of phase transition is enhanced after consid-ering the SO(6) cubic interaction. Secondly, we further study the difference for the SU(3) limit and SO(6) cubic interaction, and find that [Q(0) xQ(0)xQ(0)]0 could solve the intra-band E2 transitions. Thirdly, we discuss the application to some interesting X(5) nuclei. It is clearly shown that the results are better than those obtained from the traditional U(5) - SU(3) transitional description. Finally, we discuss the relation of U(5),SU(3) and [Q(0) x Q(0) x Q(0)]0 in coherent states. The results show that the first-order transition can occur at the point of [0.25,0] for U(5)-SU(3) case, and [0,±1.4] for U(5)-[Q(0)×Q(0)×Q(0)]0 case.