Dressed vertices P. Bo˙zek ∗

The response of a correlated nuclear system to an external field is discussed. The Bethe-Salpeter equation for the dressed vertex is solved. The kernel of the integral equation for the vertex is chosen consistently with the approximation for the self-energy. This guarantees the fulfillment of the f-sum rule for the response function. Processes occurring in dense nuclear matter are modified by the effects of the medium. In particular the effect of the off-shell propagation of nucleons in the medium is important for the subthreshold particle production in heavy ion collisions. The role of correlations for the neutrino emission could be especially important for processes in hot stars. Soft particle emission is influenced by the multiple scattering in the medium, which is equivalent to including vertex correction modifying the coupling of the external current to the dressed nucleons [13]. For the case of weak coupling of the external current or of the produced particles to the nucleons, the problem is equivalent to the calculation of the response function in the correlated medium. For the Hartree-Fock approximation the response function can be calculated from the random-phase approximation, which however is usually taken at the ring diagrams level only. The use of advanced approximations for the description of the many-particle system with in-medium propagators dressed by the interaction and scattering, raises the question of the correct treatment of the vertex corrections [14]. It is known that the density response function for the electron gas in the self-consistent GW approximation violates the f-sum rule [15, 16]. For a given approximation for the self-energy the corresponding vertex corrections can be obtained by solving the Bethe-Salpeter equation with a specific particle-hole irreducible kernel [17, 14]. The actual solution of the integral equation for the in-medium vertex is quite complex, a complete solution for dressed propagators was