Studies on nuclear structure in the 2s - 1d shell: (I). Methods of group theory and a model interaction

Abstract

The purpose of this series of papers is to carry out systematic calculations in nuclear structure in the 2s-1d shell, considering a model interaction which is a linear combination of a spin-orbit coupling (W_s.o.) plus a quadrupole-quadrupole (Q²) and an orbital pairing (P) term, the last two terms taking into account, respectively, the long and short-range correlations of the residual central interaction. In this paper we discuss methods of group theory that would allow us to classify the states in relation with a chain of subgroups in such a way that each of the interactions Q², P and W_s.o. becomes diagonal, and then we discuss how to obtain transformation brackets that take us from states classified by one chain of subgroups to states classified by another, so that it is possible to obtain the matrix elements for the model interaction. In the next papers of this series we shall apply the present techniques to specific nuclei, starting with those of A=18 and A=20.