Polarization Correlation of Mixed Multipoles

Abstract

The directional polarization results of Hamilton are extended to cases in which one of the two photons emitted by a nucleus is described by a pure ${2}^{L}$ multipole and in which the second is described by two mixed multipoles. While these polarization functions are still quite simply related to the parameters occurring in the functions describing the correlation between two successive photons neither of whose polarizations is being measured, the relationship is more complicated than for pure multipole photons on account of the explicit dependence of the mixture polarization function on the mixture components and on the interference arising from the mixture. The net result is that the correlation parameters $Q$, $R$, $S$,... obtained from a correlation experiment without polarization are insufficient to describe a polarization correlation experiment when mixtures are involved. A table of polarization correlation functions is given for all pure-mixture transitions up to and including octupoles. Two examples briefly indicating how this table may be used, as well as a table of some useful combinations of the elements of the representations of the three-dimensional rotation group are included.