A new synthetic formalism for true coincidence summing calculations

Simultaneous detection in one sensing crystal of photons emitted in cascade from the same radioactive atom gives rise to true coincidence summing effects (excess and deficit counting). Presented in this paper is a general formula to correct for true coincidence summing. This analytical formula enables calculation of the correction factor and its associated uncertainty for any gamma-ray placed in a decay scheme of any radionuclide (all decay modes treated) in any measuring configuration. It takes account of any cascade of photons either through the nature of the involved photons (γ-rays, X-rays, and annihilation photons) or the unlimited number of photons emitted in cascade. The requirement for this calculation is twofold. From the radionuclide part, theoretical knowledge of the decay scheme is necessary along with its characteristics (gamma-ray intensities and internal conversion coefficients for instances). Some atomic quantities such as fluorescence yields have also to be known. From the detector part, calibrations for full-energy peak efficiency and total efficiency in the measuring configuration have to be available. The demonstration of the formula is done with restrictive conditions (point source, no angular correlation, and no metastable state between the initial and final energy states) but adaptation can be implemented to partially or totally lift these limitations or approximations. Implementation of the formula in a computer code named Coincal is mentioned. Its successful application to point sources of 152Eu placed 10 cm and 15 mm away from an n-type coaxial HPGe detector with 60% relative efficiency is also described.