Locally Energy Dependent Phase Shift Analysis of Proton-Proton Scattering in the 20 — 750 MeV Region

Abstract

Our approach to phase shift analysis is characterized as being intermediate between a conventional analysis at a fixed energy, and an analysis with energy dependence of the phase shifts through the entire interval 1,2). We use the usual formalism 3) together with corrections due to the electromagnetic effects 4). Our method consists in approximating the real part of each phase shift, within a given interval of incident particle energies T, by a cubic function where To is a fixed energy within this interval and where the fitted parameters aℓo, ..., aℓ3 represent the value and the first three derivatives of δℓ(T) at T = To. The imaginary parts are parametrized by where the threshold energy Toℓ for each phase shift is treated as a variable parameter, and where the coefficient bℓ2 is required to be non-negative. If the threshold is below the lower limit of the interval, the form of the energy dependence of Im δℓ coincides with that of Re δℓ.