On the field theoretical approach to the nucleon-nucleon scattering problem in the low-energy region

A relativistic three-dimensional Lippmann-Schwinger-type equation for the NN scattering matrix is derived from the field-theoretical Low equation. The potential of the latter nonlinear integral equation uniquely determines the potential of the suggested Lippmann-Schwinger-type equation and consists of two parts. The first part, calculated with the use of the simplest phenomenological meson-nucleon Lagrangians, reproduces the one-boson-exchange (OBE) NN potential. The second part of the potential of the Low equation is defined by the on-mass-shell meson-exchange terms and is a non-Hermitian operator. The numerical calculation carried out in the framework of the OBE model of NN interactions has demonstrated that the on-mass-shell meson-exchange terms give an essential contribution to the NN phase shifts, whereas the contribution from the non-Hermitian part of the potential can safely be neglected. (author)