  We are concerned with few-particle correlations in a fermionic system at
finite temperature and density. Within the many-body Green functions formalism
the description of correlations is provided by the Dyson equation approach that
leads to effective few-body equations. They contain the dominant medium
effects, which are self energy corrections and the Pauli blocking. Hence the
effective two-body interactions between quasiparticles are
momentum/energy-dependent and therefore they can be usesed in the medium
modified, momentum space, integral AGS equations for three- and four-body
systems. To investigate correlations and clusters beyond four-body, we employ,
instead, the configuration space two-variable integro-differential equations
(IDEA) for $A$-body bound systems which are based on Hyperspherical Harmonics
and the Faddeev decomposition of the wave function in two-body amplitudes. This
requires the transformation of the energy dependent two-body interactions to
equivalent local, energy independent, ones. To achieve this we use inverse
scattering techniques the resulting interactions being, on-- and (to all
practical purposes) off--shell equivalent to the energy dependent potentials.
In this way we obtain binding energy results for the 2--, 3--, 4--, and
16--particle in a medium at a finite temperature and various densities. Several
aspects of the problem are discussed and the behavior of the potential surfaces
obtained in the extreme adiabatic approximation, below and above the Mott
transition, is investigated.
