Off-shell NN potential and triton binding energy

Abstract

The NONLOCAL Bonn-B potential predicts 8.0 MeV binding energy for the triton (in a charge-dependent 34-channel Faddeev calculation) which is about 0.4 MeV more than the predictions by LOCAL NN potentials. We pin down origin and size of the nonlocality in the Bonn potential, in analytic and numeric form. The nonlocality is due to the use of the correct off-shell Feynman amplitude of one-boson-exchange avoiding the commonly used on-shell approximations which yield the local potentials. We also illustrate how this off-shell behavior leads to more binding energy. We emphasize that the increased binding energy is not due to on-shell differences (differences in the fit of the NN data or phase shifts). In particular, the Bonn-B potential reproduces accurately the $\epsilon_1$ mixing parameter up to 350 MeV as determined in the recent Nijmegen multi-energy NN phase-shift analysis. Adding the relativistic effect from the relativistic nucleon propagators in the Faddeev equations, brings the Bonn-B result up to 8.2 MeV triton binding. This leaves a difference of only 0.3 MeV to experiment, which may possibly be explained by refinements in the treatment of relativity and the inclusion of other nonlocalities (e.~g., quark-gluon exchange at short range). Thus, it is conceivable that a realistic NN potential which describes the NN data up to 300 MeV correctly may explain the triton binding energy without recourse to 3-N forces; relativity would play a major role for this result.