Dispersion relations in which the scattering angle $\theta$ 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.

• Received 16 January 1959

DOI:https://doi.org/10.1103/PhysRev.114.1633