Triaxial projected shell model study of $$\gamma $$-bands in atomic nuclei

Abstract

A systematic study of $$\gamma $$ -bands observed in atomic nuclei is performed using the triaxial projected shell model (TPSM) approach. The staggering phase between the even and odd spin members of the $$\gamma $$ -band for most of the nuclei investigated in the present work is found to have even-I-below-odd-I, which in the framework of the collective model is considered as a signature of $$\gamma $$ -softness. It is observed that out of twenty-three systems studied, only four nuclei, namely, $$^{76}$$ Ge, $$^{112}$$ Ru, $$^{170}$$ Er and $$^{232}$$ Th depict staggering phase with odd-I-below-even-I, which is regarded as an indication of the static $$\gamma $$ -deformation in the collective model picture. The inclusion of the quasiparticle excitations in the framework of configuration mixing is shown to reverse the staggering phase from odd-I-down to the even-I-down for all the studied nuclei, except for the aforementioned four nuclei. Furthermore, by fitting a collective Bohr Hamiltonian to the TPSM energies, the differences between the two models are delineated through a comparison of the transition probabilities.