Photoproduction of mesons on nucleons: Phase shift analysis and dispersion relations

Abstract

A phase shift analysis of the dispersion relations obtained in ref. 1) for photoproduction of mesons is carried out. It is assumed that the integrals in the dispersion relations converge with sufficient rapidity. The dependence of the photoproduction amplitude on the spin and isobaric variables and also the relation between the photoproduction and scattering amplitudes which follows from the unitary condition are considered. The range of unobservable angles, cos θ < − 1, in the dispersion relations is examined in the c.m.s. Phase shift analysis of the photoproduction amplitude is investigated and dispersion relations for partial waves have been obtained on the assumption of rapid convergence of the integrals. In this case the equations for S and P waves have been completely determined in the first approximation differing from the static one (that is, to terms of the order of μ/ m).