Fixed Angle Dispersion Relations for Nucleon-Nucleon Scattering

Dispersion relations in which the scattering angle θ is kept constant are proposed for nucleon-nucleon scattering. These relations are a direct consequence of a general representation proposed by Mandelstam (see reference 4) and can be checked directly up to the fourth-order perturbation theory. An extrapolation procedure based on these dispersion relations is proposed with the purpose of obtaining an independent determination of the pion-nucleon coupling constant and the possibility of discriminating between the different available sets of phase shifts.A first determination of the pion-nucleon coupling constant from these fixed-angle dispersion relations is attempted by means of a more direct extrapolation procedure, closely analogous to the effective range approximation, and a result in good agreement with the currently accepted value is obtained.