Scattering of dressed nucleons in nuclear matter

The scattering of dressed nucleons in nuclear matter is studied. By casting the conventional asymptotic analysis of scattering in free space in the language of the two-body propagator, it becomes possible to develop modifications of this analysis due to the dressing of the scattering nucleons in the medium. While the scattering energy singles out a unique (on-shell) momentum characterizing the relative wave function of free or mean-field nucleons, this uniqueness is no longer maintained for dressed nucleons. The resulting distribution of momenta in the relative wave function leads to a localization in coordinate space of the influence of the scattering process which can be expressed as a healing of the wave function to the noninteracting one. An analytic approximation to the noninteracting propagator of the dressed nucleons is utilized to illustrate these points. The localization of the scattered wave implies that the particles no longer “remember” their scattering event beyond some finite distance. This feature suggests that the strict notion of a cross section in the medium is a tenuous concept. Approximate expressions are developed to characterize the strength of the interaction in the medium in terms of phase shifts and cross sections to facilitate comparisons with results of calculations involving mean-field nucleons.