SU₃ symmetry and effective interactions in the s-d shell

Abstract

The effective interaction in the s-d shell can be characterized in terms of diagonal radial matrix elements I_nlS in relative states of orbital angular momentum l of two nucleons. The symmetry properties of radial matrix elements in l=0 states are investigated. The parameters I_0s and I_2s are shown to give exact SU₃ symmetry of the eigenfunctions. The SU₃-symmetry-breaking property of I_1s is explicitly demonstrated, but it is also found that in realistic calculations such an effect is somewhat suppressed by the single-particle spin-orbit force. We also show that whereas the T=1 eigenfunctions (for J=0, 2, 4 for two nucleons) can be very well generated from a suitable deformed intrinsic state, the T=0 eigenfunctions (J=1, 2, 3) generated from deformed states have poor overlaps with shell-model eigenfunctions in the absence of spin-orbit splitting of single-particle orbits. Inclusion of single-particle spin-orbit force improves very strikingly the overlaps between the generated and the shell-model T=0 states.