On the Directional Correlation of Successive Nuclear Radiations

Abstract

The theory of angular correlation is given in a form applicable to the successive emissions of any nuclear radiations. It is shown that the theoretical specification of angular correlation requires two kinds of information; namely, the angular momenta of the nuclear states and emitted radiations, and the Hamiltonian interaction between the outgoing particles and nucleus. The former information enters in the same way in all angular correlations while the latter, differing with the kind of particles emitted, is needed to obtain the angular distributions associated with each component of a line. The structure of such angular distributions is studied in relation to isotropy requirements and an explicit construction to exhibit them is given. Systematic simplifications in the calculation of angular correlation functions $W\left(\vartheta \right)$ are shown to result from several theorems relating to the combinations of transformation coefficients occurring in $W\left(\vartheta \right)$. These make possible a complete tabulation of $W\left(\vartheta \right)$ in canonical forms applicable, on proper specialization, to any angular correlation in which the angular momentum of the decay products in either transition is 1 or $2\hslash$. The specializations for $\alpha$- and $\gamma$-emission are given.