Effect of symmetry breaking on statistical distributions

The quantum numbers of states in P-30 have been determined for over 100 sta tes from the ground state to 8 MeV. Previous measurements had provided comp lete spectroscopy for over 150 states in Al-26 in a similar energy region. These N = Z = odd nuclei have the property that states of isospin T = 0 and T = 1 coexist from the ground state. Isospin is approximately conserved in these nuclei. Since the energy E, spin J, parity pi, and isospin T are kno wn for every level, these data provide a unique opportunity to test the eff ect of symmetry breaking on the level statistics and on the transition stre ngth distributions. The level statistics are strongly affected by the small symmetry breaking, in agreement with predictions of Random Matrix Theory ( RMT). In Al-26 the transition strength distributions differ from the standa rd Porter-Thomas distribution; deviations at a weaker level also appear in P-30. Until very recently there were no theoretical predictions for the eff ect of symmetry breaking on the transitions. Recent RMT calculations predic t a deviation from the Porter-Thomas distribution, in qualitative agreement with the measurements.