Generalized equation for the sum-peak method, accounting for random coincidences

For gamma cascade emitting radionuclides, the source activity can be determined by a single spectrometer from the sum peak area. At high count rates, random coincidence corrections must be considered. Starting from the equations of the peak and total count rates that consider random summing, a new equation for measurement of the activity is deduced. The results of the new formula are verified by Monte Carlo simulations.