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Effect of symmetry breaking on statistical distributions

The quantum numbers of states in 30P have been determined for over 100 states from the ground state to 8 MeV. Previous measurements had provided complete spectroscopy for over 150 states in 26Al 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 π, and isospin T are known for every level, these data provide a unique opportunity to test the effect of symmetry breaking on the level statistics and on the transition strength distributions. The level statistics are strongly affected by the small symmetry breaking, in agreement with predictions of Random Matrix Theory (RMT). In 26Al the transition strength distributions differ from the standard Porter-Thomas distribution; deviations at a weaker level also appear in 30P. Until very recently there were no theoretical predictions for the effect of symmetry breaking on the transitions. Recent RMT calculations predict a deviation from the Porter-Thomas distribution, in qualitative agreement with the measurements.