${\Delta}{I=1}$ Staggering Effect in the Energy Spectrum of the ${\gamma}$ Band of Heavy Even–Even Nuclei

Abstract

Quadrupole-type collective excitations of even–even nuclei are studied in the free-triaxiality approximation. The zigzagging behavior of the $\Delta I=1$ staggering effects in the energy spectrum of collective excitations of the $\gamma$ bands of heavy even–even ${}^{152}$Sm, ${}^{156}$Dy, ${}^{164,166}$Er, and ${}^{230}$Th nuclei is considered in this approximation. The first- and second-order terms in the expansion of the rotational-energy operator in the variable $\gamma$ are taken into account in describing the energies of levels of these nuclei. It is shown that the $\Delta I=1$ staggering effect occurs in the case of a strong coupling between the ground-state and $\gamma$ bands in the limit of $SU$(3) dynamical symmetry.