Evaluation of accidental coincidences for time-differential Mِssbauer-spectroscopy

The accidental coincidences of a measuring system based on time-to-amplitude conversion are considered in some detail for the case of low starting and high stopping rates. Two types of accidental coincidences are distinguished, those carrying time information and those without time information. Neglecting any deadtime effects of the detectors, analytical expressions for the calculation of the time distribution of the random coincidences are evaluated. The analytical expressions have been confirmed by Monte Carlo simulations. The procedure is applied to time-differential Mِssbauer spectroscopy in order to extract the time spectra of true coincidences. The measured spectrum in a time channel turns out to be a superposition of the true spectrum (true coincidences), a time integral spectrum (random coincidences), and a weighted superposition of true spectra of other time channels (random but time carrying information). A measurement with a single line 57Co/Rh-source and single line K[Fe(CN)6]·3H2O-absorber with stopping rates of 1 MBq shows agreement between the theoretical time-filtered spectra and the corrected measured spectra of true coincidences.