An Exact Formula to Describe the Amplification Process in a Photomultiplier Tube

An analytical function is derived that exactly describes the amplification process due to a series of discrete, Poisson-like amplifications like those in a photo multiplier tube (PMT). A numerical recipe is provided that implements this function as a computer program. It is shown how the program can be used as the core-element of a faster, simplified routine to fit PMT spectra with high efficiency. The functionality of the method is demonstrated by fitting both, Monte Carlo generated and measured PMT spectra.