Detector energy resolution corrections for X-ray spectrum measurements

Abstract

A method was described for measuring the energy resolution dependence of NaI(Tl), Si(Li) and Ge(Li) X- and gamma -ray spectrometer systems. The method is based upon the observed Gaussian response of the spectrometer systems, when exposed to a monoenergetic photon source. A curve was derived relating the observed energy resolution dependence of the spectrometer systems with photon energy. From the energy resolution dependence curve, the normalized Gaussian was derived that describes the spectrometer system's energy resolution dependence as a function of energy. The normalized Gaussian was used to derive a matrix Gij(E), describing the distortions introduced into the incident X- or gamma -ray spectrum by the energy resolution dependence of the spectrometer system as N'j(E)=Gij(E)Nj(E), where N'j(E) and Nj(E) are the observed and true spectra, respectively. The matrix Gij(E) cannot be inverted in normal fashion to obtain Nj(E) and must be solved by an iterative procedure that avoids direct inversion. A digital computer was used in these calculations. A method was described whereby the effects of spectrometer energy resolution upon an incident spectrum can be calculated. Energy resolution distortions of incident X-ray spectra were compared for NaI(Tl), Si(Li) and Ge(Li) detectors.