Basis Generator for M-Scheme SU(3) Shell Model Calculations

Abstract

A FORTRAN code for generating the leading SU(3) irreducible representation (irrep) of N identical spin 1/2 fermions in a harmonic oscillator mean field is introduced. The basis states are labeled by N--the total number of particles, the SU(3) irrep labels ($\lambda ,\mu $), and S -- the total spin of the system. The orthonormalized basis states have two additional good quantum numbers: $\epsilon $ -- the eigenvalue of the quadruple operator, $Q_{0}$; and $M_{J}$ -- the eigenvalues of the projection of the total angular momentum operator, $J_{0}=L_{0}+S_{0}$. The approach that is developed can be used for a description of nuclei in a proton-neutron representation and is part of a larger program aimed at integrating SU(3) symmetry into the best of the currently available exact shell-model technologies.