Scattering of Correlated Nucleons in Nuclear Matter

Initial results on the scattering of dressed nucleons in the nuclear medium have been reported in publ.57, publ.67, and publ.76. Since little or no previous experience with this type of scattering process is available, the scattering of mean-field nucleons in nuclear matter has been studied to facilitate a comparison with studies using Brueckner theory ref.1 or a finite temperature Green's function formalism ref.2, ref.3. For the case of liquid 3He, the relevant description of the scattering process in terms of phase shifts and their behavior near threshold has been developed for mean-field fermions in ref.4. In this context it is important to emphasize the role of hole-hole propagation, which leads to a considerable enhancement of pairing correlations. As discussed in publ.24 and publ.42, a ladder summation is able to identify a pairing instability around twice the Fermi energy εF, for a sufficiently attractive interaction. We have shown that the solution of the scattering equation near twice the Fermi energy indicates this pairing feature by yielding phase shifts that tend to p when the continuum energy approaches 2εF on either side. This result mirrors Levinson's theorem for free particles. Both the 3S1-3D1 and 1S0 channels yield phase shifts that tend to π when the energy approaches 2εF in a wide range of densities. This feature of the effective interaction is responsible for the observed enhancement of the NN cross section at finite temperature as calculated in ref.3.

In order to treat the scattering of dressed particles in the nuclear medium, it is necessary to develop an appropriate scattering theory to deal with the new features that arise from the dressing of the participating nucleons. 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 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unique (on-shell) momentum characterizing the relative wave function of free or mean-field nucleons, this uniqueness is no longer maintained for dressed nucleons.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 of the scattering process in coordinate space which can be expressed as a healing of the correlated wave function to the noninteracting one. This property has been considered the physical justification of the mean-field-like properties observed in the presence of strong short-range correlations. Our present analysis publ.74, reconciles this healing concept for dressed nucleons with the substantial fragmentation of the nucleon single-particle strength observed in nuclei. The scattering process in nuclear matter involving mean-field nucleons always yields a phase shift and hence no healing. A realistic description of scattering processes in nuclear matter therefore requires the dressing of the nucleons in order bring into play this healing property of the relative wave function. The localization of the scattered wave implies that the particles no longer remember a scattering event beyond some finite distance. This feature suggests that the notion of a cross section in the medium is a tenuous one.

While the cross section of dressed particles cannot be written down formally, it is still possible to generate approximate expressions characterizing the strength of the interaction in the medium in terms of phase shifts and cross sections, which can be fruitfully compared to calculations involving mean-field nucleons publ.76. Results of calculations involving dressed nucleons generate phase shifts and cross sections which deviate substantially from the results for mean-field nucleons alluded to above. A detailed paper containing this information for a realistic NN interaction can be found in publ.78.


    1. G. Giansiracusa, U. Lombardo, and N. Sandalescu, Phys. Rev. C53, R1478 (1996).
    2. M. Schmidt, G. Röpke, and H. Schulz, Ann. Phys. 202, 57 (1990).
    3. T. Alm, G. Röpke, and M. Schmidt, Phys. Rev. C50, 31 (1994).
    4. R. F. Bishop, M. R. Strayer, and J. M. Irvine, Phys. Rev. A10, 2423 (1974).