THEORY OF REPRESENTATION OF SCATTERING DATA BY ANALYTIC FUNCTIONS

An extension is presented of a recently developed new method for analysis of differential cross section data. The method is designed to be the most powerful possible, given certain information about the relative degree of variability of the scattering amplitude. It is also designed to give a conservative estimate of systematic errors. The method is based on earlier work by Cutkosky and Deo and by Ciulli, and uses an expansion in terms of functions which are especially adapted both to the assumed analyticity properties and to the characteristics of the data. The amplitude is characterized, in addition to having a given analyticity domain, by a weighted Gaussian measure over the set of possible boundary values. For a given weight, for a given set of data, and for given parameters which are related linearily to the amplitude, there is a definite construction which will lead to the best convergence properties. The construction also provides a definite prescription for the form factors associated with poles. A test function, based on ratios of expansion coefficients, is constructed for the purpose of estimating truncation errors and the truncation point, and for distinguishing among various fits to the data. This test function is similar to χ2 and is to be used in conjunction with χ2 in analyzing data. © 1969.