Broken Symmetries and Chaotic Behavior inAl26

Fluctuation properties of positive-parity states in ${}_{}{}^{26}{}_{}{}^{}\mathrm{Al}$ from the ground state to the resonance region (0-8 MeV excitation energy) are found to be consistent with the Gaussian-orthogonal-ensemble version of random-matrix theory. Although isospin is an approximately good quantum number in this system, the fluctuation properties of the combined sequence ($T=0\mathrm{}$ and $T=1\mathrm{}$ states) are consistent with those of a single Gaussian-orthogonal-ensemble sequence. This agrees with earlier predictions by Dyson and Pandey and with recent analysis by Guhr and Weidenmüller.