Some Comments on the Analysis of Excitation Functions Using Different Transforms

Abstract

The statistical theory of nuclear reactions (Brink and Stephen 1963; Ericson 1963) has been used successfully for some years. When it comes to determining properties like the mean level width r several authors (Bohning 1965; Ericson 1965, personal communication; Hellstrom and Dallimore 1969) have suggested and used a. Fourier analysis instead of the autocorrelation function C(E+?, E) because the former is associated with smaller errors, particularly when the average cross section has a slow variation with energy. The aim of this note is to elucidate some of the properties of the Fourier transform applied to analysis of excitation functions and also to point out that other transforms are possible. To fix notation, we take the Fourier transform F of the cross section a(E) over an energy interval I with middle point Eo as