Off-shell pairing correlations from meson-exchange theory of nuclear forces

A model is developed for treating off-mass-shell pairing correlations in nuclear systems. These correlations are described by a coupled set of meson-exchange normal and anomalous Fock self-energies of baryons. The kernel of the complex gap equation for baryons is related to the in-medium spectral function of mesons, which is evaluated non-perturbatively in the random phase approximation. The model is applied to the low density neutron matter in neutron star crusts by modeling the interaction as a sum of a long-range one-pion exchange component and a short range component parameterized in terms of Landau Fermi-liquid parameters. An efficient algorithm is described for the self-consistent solution of the resulting Eliashberg type non-linear integral equations. We find that the off-shell pairing correlations extend to rather high energies - of the order of 100 MeV - with the real and imaginary parts of the pairing gap showing a complicated structure. At low energies the damping of the neutron pair correlations due to the coupling to the pionic modes is small, but becomes increasingly important, and eventually dominant as the energy is increased