On the measurability of true coincidence summing in the GRIFFIN spectrometer

The measurement of gamma-rays from decaying nuclei allow for the investigation into nuclear structure. True coincidence summing occurs when two gamma-rays from a single decay get detected in a single detector and their energies sum together to give false peaks in the energy spectrum. Corrections to this summing effect are crucial for an accurate determination of nuclear decay events. The summing correction formalism of Semkow et al. (1990) is generalized here into the Semkow matrix formalism and is extended into a multiplicity expansion. This formalism is used to calculate the matrix probabilities for 180-degree coincidence events as a method for correcting coincidence summing. In doing so, the deviation between the full correction and this 180-degree correction is shown as a function of multiplicity. This formalism is extended to the partitioned matrix formalism, to calculate probabilities for gated gamma rays, where two gamma-rays of interest are taken in multi-detector coincidence. The summing correction probabilities for gated gamma-rays are provided and the deviation is shown in a manner similar to that of the singles. Terms such as measurability, event equivalence, and ontic and epistemic events are defined. It is shown that within these definitions, the sufficient measurability of coincidence summing is statistically bounded by the deviations derived. A toy model nuclear level scheme results in deviations on the order of 10^-3%. These results show that the 180-degree coincidence method is sufficient for most gamma-ray spectroscopy experiments.