  We present some recent developments on the nuclear many-body problem, such as
the treatment of high-order correlations and finite temperature in the
description of in-medium two-nucleon propagators. In this work we discuss
two-time propagators of the particle-hole type, which describe the response of
finite nuclei to external probes without nucleon transfer. The general theory
is formulated in terms of the equation of motion method for these propagators
with the only input from the bare nucleon-nucleon interaction. The numerical
implementation was performed on the basis of the effective mason-nucleon
Lagrangian in order to study the energy-dependent kernels of different
complexity. The finite-temperature extension of the theory with $ph\otimes
phonon$ configurations is applied to a study of the multipole response of
medium-mass nuclei.
