The use of the pairing-quadrupole connections in PQM for application in nuclear systems

Within the algebraic realization of the Pairing-plus-Quadrupole Model /PQM/ in the framework of the Elliott’s SU(3) Model,we present some particular applications for realistic nuclear systems. The probability distribution of the SU(3) basis states within the isovector, isoscalar and total pairing eigenstates is obtained through a numerical diagonalization of the PQM Hamiltonian in each limit. This allows the investigation of the interplay between the pairing and quadrupole interactions in the Hamiltonian of the PQM, containing all of them as limiting cases. The relative strengths of the dynamically symmetric quadrupole-quadrupole interaction with the considered types of pairing interactions are investigated systematically for systems like the 20Ne.