Mathematical Treatment of Digitized Data Containing Instrument Response and Statistical Deviations

Abstract

<p> Two methods of approach are presented for the analysis of digitized data containing instrument response effects. The first method corrects the data vector by means of multiplication by the inverse response matrix. In order to accomodate large size data fields, a special effort is made to obtain expressions for the inverse. matrix elements in closed form. Reduction of statistical uncertainties is accomplished by application of non-negativity conditions. The second approach is based on the method of least squares. Applications to two-dimensional coincidence spectra and nonlinear model functions are discussed in some detail. Although the main emphasis is placed on analysis of nuclear spectra, the techniques presented need· not be limited to this application alone. </p>