Meson retardation, three-body forces, and medium modifications to the nucleon-nucleon interaction

We critically examine two formally equivalent approaches to the many-body problem, one of which is based on an effective energy-dependent interaction and the other on an effective energy-independent interaction (an instantaneous, but nonlocal, potential). The interactions are mediated by the same set of mesons, with common masses, coupling constants, and form factors, and they give similar reproductions of the two-body data. We examine the higher-order contributions in the many-body theory, and we are able to identify specific ingredients that could lead to different rates of convergence for the different interactions. For the three-body system, we find an important contribution to the three-body force that is large in the energy-dependent interaction and nearly cancels out of the instantaneous potential. For the many-body system we find numerous density-dependent terms that contribute to the energy-dependent interaction but not to the instantaneous one. We show numerical results for the binding energy per particle of nuclear matter based on the solution of the two-body Bethe-Goldstone equation. We find substantially less binding for the instantaneous potential, thus observing that in actual calculations the many-body theory converges at a different rate for the two types of interaction. We conclude that nuclear matter properties can be calculated with more reliability and less computational effort for the case of the instantaneous potential.