Self-consistency and quasi-particle approximation in π- and Δ-propagation in nuclear matter

Abstract

The equations for the self-consistent π- and Δ-propagation in nuclear matter are solved numerically in the quasi-particle approximation. We have taken into account the full complexity of nucleon recoil and Fermi motion as well as the effects of binding and short-range correlations. Because of the much smoother behaviour of the self-consistent π and Δ self-energies it turns out that the quasi-particle approximation is still a good one even at normal nuclear density, whereas for k F ⩾ 1 fm −1 the first-order solution displays a multiple eigenmode propagation for the pion in the resonance region. The self-consistent π- and Δ-dispersion relations in the medium are then obtained for increasing densities by an iterative procedure which takes as a starting point, each time, the final result at the preceding density.