Extended microscopic theory for N ∼ Z nuclei

A symmetry adapted realization of the Pairing-plus-Quadrupole Model /PQM/ has been explored in the framework of the Elliott's SU(3) Model. The aim is to obtain the complementary and competing features of the pairing and quadrupole interactions in the model Hamiltonian, containing both of them as limiting cases of dynamical symmetries. For the purpose, one or two control parameters are introduced which account for the relative importance of each term in the Hamiltonian and serve to describe the effect of phase transition. The calculations are performed for nuclei in a single oscillator shell