Angular Distributions of Gamma Rays in Terms of Phase-Defined Reduced Matrix Elements

The theory of angular distributions of $\gamma$ rays is developed systematically, aiming at a phase consistent derivation of angular distribution formulas for gamma rays emitted in the decay of an aligned initial state. The development starts from first principles, that is, the angular distribution formulas are derived directly from perturbation theory and all quantities introduced are carefully and explicitly defined. In particular the mixing ratios are phase consistently related to reduced matrix elements of interaction multipole operators which again are well defined in phase. Hence the mixing ratios become physical quantities which can be extracted from angular distribution measurements and then compared in both magnitude and sign with the predictions of nuclear models (especially the independent particle model). Critical stages in the theoretical development at which either a choice of phase convention has to be made or transformation properties enter are emphasized.