Phase shifts and in-medium cross sections for dressed nucleons in nuclear matter

Abstract

The dressing of nucleons as embodied in single-particle spectral functions is incorporated in the description of nucleon-nucleon scattering in nuclear matter at a density corresponding to kF= 1.36 fm-1. In order to clarify the new features associated with the complete off-shell behavior of the single-particle motion, results involving mean-field particles are also presented with special emphasis on the behavior of the phase shifts when bound pair states occur. Both the 1S0 and 3S1-3D1 channels exhibit this feature at the considered density for mean-field particles at zero temperature. An important tool to assess the effect of the dressing of the particles is the two-particle density of states. A sizable reduction with respect to the mean-field density of states is obtained. At 2∈F this reduction corresponds to Z2kF, where ZkF is the strength of the quasiparticle pole at kF, and it can therefore be as large as 0.5. This reduction has significant consequences for the strength of pairing correlations both in the 3S1-3D1 channel where it leads to a dramatic decrease of the attraction at the Fermi energy and for the 1S0 channel which no longer shows a pairing signal. Phase shifts and cross sections for dressed particles are determined based on expressions which fold the effective interaction with the dressed but noninteracting two-particle spectral function. This folding procedure yields similar results to an "on-shell" prescription reminiscent of the result for free or mean-field particles, except for cross sections deep in the Fermi sea. Comparison of phase shifts and cross sections to the case of mean-field particles indicates that smaller phase shifts in an absolute sense and considerable reductions of the in-medium cross sections for dressed particles are obtained. It is shown that while in many cases these results imply a weakening of the effective interaction, this is not the case for 1S0 interactions deep in the Fermi sea.