Symmetry Theorems for Isospin-Invariant Reactions

Symmetry theorems, analogous to those well known for angular distributions and correlations, are given for isospin-invariant reactions starting from an initial state of limited complexity. Detailed calculations are carried out when the initial-state isospin does not exceed $\frac{3}{2}$. A statistical generalization is given for averages over experiments starting from different charge states. Some properties of the irreducible tensor operators which arise from recoupling the angular momentum operator to itself are discussed.