Relativistic, Three-Dimensional Equations for Low-Energy Two-Nucleon Systems

Abstract

The manifestly covariant Bethe-Salpeter equation is reduced to relativistic, three-dimensional integral equations suitable for the dynamical treatment of the two-nucleon system at low energies. The reduction is achieved by restricting one of the nucleons to the mass shell. The resulting twonucleon scattering equations and bound state equations are Schrödinger-like field equations containing relativistic kinematical corrections. The transformation of these equations to the ordinary Schrödinger (or Lippmann -Schwinger)-equation is discussed. Intimately connected with the reduction is the derivation of a meson field mediated two-nucleon potential containing meson retardation effects and adequate for the application to the two-nucleon system and nuclear structure problems.