Dispersion representation for the nucleon-nucleon T matrix in the Bethe-Salpeter approach

The dispersion relations for the nucleon-nucleon $\mathrm{}\left(\mathrm{NN}\right)\mathrm{}$ T matrix in the framework of the Bethe-Salpeter equation for a two spin-one-half particle system with a separable kernel of interaction are considered. The developed expressions allow us to find explicit analytic connection between parameters of the separable kernel and low-energy scattering parameters and deuteron binding energy and to construct the rank-I separable kernel of interaction for S partial waves in singlet and triplet channels. The obtained kernel is used to calculate phase shifts. We presume that the approach can be extended—with a reasonable effort—to higher partial waves for $\mathrm{NN}$ scattering and other reactions $(\overline{N}N,$ $\pi N$ scattering).