Perturbations in angular correlations as an interference phenomenon

A complete derivation of the new formulation of the theory of perturbed angular correlations of time-independent interactions (H. J. Leisi, in “Angular Correlations in Nuclear Disintegration” (H. van Krugten and B. van Nooijen, Eds.), p. 375, Rotterdam University Press, Rotterdam, Holland, 1971.) is presented. Gamma-gamma directional correlation experiments are explicitly considered. The directional correlation functions for time-differential and time-integrated experiments are derived, including expressions for the general class of isotropic systems (powder sources). The formula for the interference amplitude which depends on the nuclear parameters and on the eigenfunctions of the interaction Hamiltonian is derived for an arbitrary (time-independent) interaction. Properties of the interference terms that follow from symmetries of the interaction Hamiltonian are discussed. A general proof of the theorem concerning the interference of time reversed states is given. The new approach is demonstrated by considering three angular correlation problems explicitly, namely the coupling between the nuclear magnetic moment and a magnetic field, the (axially symmetric) quadrupole interaction in a crystal and the hyperfine interaction in a free atom in the Zeeman region. The results (some of which are well known) are derived with a particular emphasis on the close relationship between the angular correlation function and the level structure of the system in the intermediate state. The results are also relevant to a number of recent experiments which clearly demonstrate the quantum-mechanical interference nature of the angular correlation process. These experiments are briefly discussed. An extension of the present theory in order to include time-dependent perturbations is suggested.