Multiple SU(3) Algebras in Interacting Boson Model and Shell Model

Abstract

Rotational SU (3) algebraic symmetry continues to generate new results in the shell model (SM). Interestingly, it is possible to have multiple SU (3) algebras for nucleons occupying an oscillator shell η. Several different aspects of the multiple SU (3) algebras are investigated using shell model and also deformed shell model based on Hartree-Fock single particle states with nucleons in sdg orbits giving four SU (3) algebras. Results show that one of the SU (3) algebra generates prolate shapes, one oblate shape and the other two also generate prolate shape but one of them gives quiet small quadrupole moments for low-lying levels. These are inferred by using the standard form for the electric quadrupole transition operator and using quadrupole moments and B(E2) values in the ground K = 0 + band in three different examples. Multiple SU (3) algebras extend to interacting boson model and using sdgIBM, the structure of the four SU (3) algebras in this model are studied by coherent state analysis and asymptotic formulas for E2 matrix elements.The results from sdgIBM further support the conclusions from the sdg shell model examples.