Dressing two nucleons at the same time.

Abstract

At intermediate energies, the interaction of two nucleons with pions is often described in terms of nonrelativistic time-ordered perturbation theory. The field theory is usually further simplified by restricting the Hilbert space to states having some maximum number of pions. One outstanding difficulty with such approaches is an inconsistent treatment of the dressed two-nucleon propagator. In the [ital NN][minus][pi][ital NN] model, for example, states can have at mos t one pion, so that only one of the nucleons is allowed to undergo dressing at any one time. Thus each nucleon cannot obtain its full dressing and this leads to problems of wave function normalization. We have found a way to dress both nucleons at the same time, where each nucleon retains its full dressing. The method, involving a convolution integral, determines the full two-nucleon dressed propagator in a practical but exact way. Numerical calculations have been performed using a model of the [pi][ital N] interaction in the one-pion approximation. We find a significant difference between the fully dressed two-nucleon propagator and the different-time propagator as used in [ital NN]-[pi][ital NN] models.