Transition quadrupole moments in γ-soft nuclei and the triaxial projected shell model

Transition probabilities of the ground-state bands in γ-soft nuclei are studied for the first time using the triaxial projected shell model approach. It is observed that the angular-momentum dependence of the transition quadrupole moment Qt is related to the triaxial deformation of the nuclear mean-field potential. The introduction of the γ-degree of freedom in the shell model basis is shown to have a little influence on the constant behavior of the low-spin Qt in a well-deformed nucleus. However, the increasing collectivity with spin for the low-spin states in a γ-soft nucleus can only be explained by considering the triaxial mean-field deformation. The study of the nuclear shape as a function of angular-momentum has remained in the forefront of the nuclear physics research. The study of transition probabilities plays an important role in our understanding of the shape evolution. For instance, probability of the electric quadrupole transition directly reflects the deformation of a nuclear system. For a spherical nucleus, the electric quadrupole transition is of the order of a Weisskopf unit, whereas for a deformed system the transition is several hundred times the Weisskopf estimate [1]. Nuclear deformation is also believed to be one of the most important physical quantities in the astrophysical interest [2]. Many nuclei in nuclear periodic table exhibit axially symmetric deformation in their ground-state, with the projection of angular-momentum on the symmetry-axis as a conserved quantum number. This is referred to as the K-quantum number and the rotational bands are labelled with this quantum-number. In fact, the majority of electromagnetic transitions in nuclei are found to strictly obey the selection rules based on the K quantum-number [1]. The violation of K-selection rules is an indication that the system is not axially symmetric. This has been demonstrated, for example, in high-K isomeric states [3].