Space symmetry in light nuclei. I Application to the 2s−1d shell

The Wigner supermultiplet scheme is studied in the 2s?1d shell using the spectral distribution methods of French. Expressions for the average expectation value of H and H² over states belonging to a definite SU(4) symmetry are derived. Numerical results for these averages are given for the 2s?1d shell. These averages are then used to predict ground state energies and low energy spectra for nuclei in this shell, using Ratcliff's procedure; a comparison with shell model and observed spectra is made. Mixing intensities of SU(4) representations near the ground state are also evaluated. These provide us with a measure of symmetry breaking. It appears from our calculations that the symmetry is strongly mixed. Finally a preliminary application to the theory of level densities is made.