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

We develop a model of off-mass-shell pairing correlations in nuclear systems, which is based on the meson-exchange picture of nuclear interactions. The temporal retardations in the model are generated by the Fock-exchange diagrams. The kernel of the complex gap equation for baryons is related to the in-medium spectral function of mesons, which is evaluated nonperturbatively in the random phase approximation. The model is applied to the low-density neutron matter in neutron star crusts by separating the interaction into a long-range one-pion-exchange component and a short-range component parametrized in terms of Landau Fermi liquid parameters. The resulting Eliashberg-type coupled nonlinear integral equations are solved by an iterative procedure. We find that the self-energies extend to off-shell energies of the order of several tens of MeV. At low energies the damping of the neutron pair correlations due to the coupling to the pionic modes is small, but becomes increasingly important as the energy is increased. We discuss an improved quasiclassical approximation under which the numerical solutions are obtained