  Response functions in nuclear matter at finite temperature are considered
beyond the usual Hartree-Fock (HF) plus Random Phase Approximation (RPA)
scheme. The contributions due to the propagator for the dressed nucleons and
the corresponding vertex corrections are treated in a consistent way. For that
purpose a semi-realistic Hamiltonian is developed with parameters adjusted to
reproduce the nucleon self-energy as derived from realistic nucleon-nucleon
interactions. For a scalar residual interaction the resulting response
functions are very close to the RPA response functions. However, the collective
modes, if present, get an additional width due to the coupling to multi-pair
configurations. For isospin dependent residual interactions we find strong
modifications of isospin response functions due to multi-pair contributions in
the response function. Such a modification can lead to the disappearance of
collective spin or isospin modes in a correlated system and shall have an
effect on the absorption rate of neutrinos in nuclear matter.
