Influence of the Exclusion Principle on the Scattering Theory of Nonlocal, Separable Interactions

For a nonlocal, separable interaction which describes low-energy nucleon-nucleon scattering, the scattering-theory solution to the Brueckner-Bethe-Goldstone (BBG) equation is obtained analytically. The associated scattering amplitudes are evaluated for all momenta of the interacting pair. The off-energy-shell amplitudes are defined by analytic continuation to complex values of the relative momentum of the pair. The positions of singularities in the amplitudes are investigated for various values of both the two-body kinematical parameters and the density of the passive BBG Fermi gas. A comparison of the amplitudes calculated with and without incorporating the effects of the exclusion principle indicates that even for repulsive interactions the latter may differ from the former by as much as 50% for Fermi-gas densities as low as $\frac{1}{500}$ of the observed nuclear density.