Interrelations between the pairing and quadrupole interactions in the microscopic Shell Model

Abstract

Abstract. The symmetry-adapted Pairing-plus-Quadrupole Model (PQM) is explored in the framework of the Elliott's SU(3) Model with the aim to obtain the complementary and competing features of the pairing and quadrupole interactions in the model Hamiltonian, containing both of them as limiting cases or dynamical symmetries. The probability distribution of the SU(3) basis states within the SO(8) pairing states is obtained through a numerical diagonalization of the PQM Hamiltonian. In an application of the model for the description of the 20 Ne and 20 O spectra, we investigate systematically the relative strengths of dynamically symmetric quadrupole-quadrupole interaction with the isoscalar, isovector and total pairing interactions. The approach allows for an extension of the model space for two oscillator shells and introduction of more elaborate pairing interaction. The new effects that come with this generalization will also be discussed as a future development.

Phases and phase transitions in the algebraic microscopic shell model

“…This allows us to investigate the influence of these residual interactions on the spectra in real nuclear systems, which will be presented in the talk of Dr. K.P. Drumev [22]. In it we consider as V 2 always the quadrupole-quadrupole interaction V 2 = χQ · Q.…”