Statistical properties and broken symmetries within the shell model

Shell-model calculations in the s-d shell have been utilized to examine how the statistical behavior of eigenvalues and reduced transition probabilities are affected by broken isospin symmetry. Calculations have been performed for the nuclides 22Na, 26Al, and 34Cl and have been compared to existing experimental data for 26Al and 30P. The eigenvalue statistics depend on the magnitude of the Coulomb matrix element, and this is reflected in a sensitivity to the choice of single-particle energies. The distributions of reduced transition probabilities are not universal but depend upon the particular transition mode chosen; this behavior is qualitatively similar to experimental results.