Photopeak shape function: formulation based on stochastic event analysis and parameter estimation by the maximum-likelihood estimation method

Abstract

A theoretical model to describe the photopeak shape function has been developed by introducing an instrument function, which is a convolution of the statistical fluctuation of the charge carriers and the stochastic process of escape of the charge-carrier collection by capture at trapping centers. The photopeak shape function is a convolution of the instrument function and a Poisson probability-density functional representation of a reduced random summing event. The functions have been tested by using three coaxial, high-purity Ge detectors of a conventional type. The parameters were estimated by the maximum-likelihood estimation method. The position indicating the incident photon energy appeared at the centroid of the intrinsic normal distribution. The most probable peak-height position is no more than a “conventional” one, though it is commonly used in spectroscopy. The theory predicts the photopeak shape of any photons by folding an input function of the subject. The theory provides standards for the detector and the detection system.