Using cumulants and spectra to model nuclear radiation detectors

A general mathematical methodology is presented to model a nuclear radiation detector. This is accomplished by using a proposed generalization of Campbell´s theorem, which employs nth-order cumulants and spectra analysis and a vector of random parameters to describe the current pulses. This allows a more elaborate, higher order statistical characterization of the radiation detection process, as compared to the usual second order treatment. To demonstrate the method, it is applied to a neutron ionization chamber (fission or ¹⁰B). A deterministic model for the chamber current pulses is developed and their probability density functions are used to define the characteristics of the vector of random parameters. Computer simulations of the proposed theoretical methodology are presented and potential applications suggested.