Pairing-quadrupole connections in the algebraic shell model applied to sd-shell nuclear systems

We present some particular applications within the algebraic realization of the Pairing-plus-Quadrupole /PQM/ for realistic sd-shell nuclear systems. The PQM uses the framework of the Elliott's SU(3) model. The probability distribution of the SU(3) basis states within the dynamical symmetries, corresponding to 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. The relative strengths of the dynamically symmetric quadrupole-quadrupole interaction with the considered types of pairing interactions are investigated systematically. Specifically, we illustrate the evolution in the importance of different terms in the Hamiltonian by studying the chain of nuclei with 2 and 4 valence sd-shell particles going from the neutron-deficient to the neutron-rich part of the nuclear chart. (author)