Shell model analysis of multiple SU(3) algebras in nuclei

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. Numerical results showed that one of the SU(3) algebras generates prolate shape, one oblate shape and the other two also generate prolate shape with one of them giving small quadrupole moments for low-lying levels. Conclusions from the shell model studies are also substantiated using sdg interacting boson model.