Angular Correlation in the Triple Cascade Transitions

The theory of the angular correlation between the radiations involved in three successive nuclear transitions is presented. The formalism is applicable to the case of three successively emitted radiations as well as to the case in which one of the emission processes is replaced by an absorption process. Thus, applications are made to (1) the emission of three cascade gamma-rays and (2) to the double-cascade gamma-emission following capture of particles with nonzero orbital angular momentum. In some cases the angular correlation depends on the order of the transitions. Under process (2), special results are presented which are applicable to $B^{11}(p,\gamma ,\gamma )C^{12}$. It is also pointed out that the formalism properly describes the angular correlation in all processes wherein three directions are specified and is therefore applicable when one of these directions refers to a polarization state while the other two refer to propagation vectors. Results are given for the limitation on anisotropy for the triple cascade transition with two radiations parallel or antiparallel and for two radiations in cascade with intervening radiations unobserved.