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 k F51.36 fm 21 . 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 1 S0 and 3 S1- 3 D1 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 2e F this reduction corresponds to z kF 2 , where z kF is the strength of the quasiparticle pole at k F , and it can therefore be as large as 0.5. This reduction has significant consequences for the strength of pairing correlations both in the 3 S1- 3 D1 channel where it leads to a dramatic decrease of the attraction at the Fermi energy and for the 1 S0 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 1 S0 interactions deep in the Fermi sea. [S0556-2813~99!06612-1]