  The propagator of two nucleons in infinite nuclear matter is evaluated by a
diagonalization of the $pphh$ RPA Hamiltonian. This effective Hamiltonian is
non-Hermitian and, for specific density domains and partial waves, yields pairs
of complex conjugated eigenvalues representing in-medium bound states of two
nucleons. The occurrence of these complex poles in the two-particle Greens
function is tightly related to the well known BCS pairing approach. It is
demonstrated that these complex eigenvalues and the corresponding bound state
wavefunctions contain all information about the BCS gap function. This is
illustrated by calculations for $^1S_0$ and $^3PF_2$ pairing gaps in neutron
matter which essentially coincide with the corresponding gap functions
extracted from conventional solutions of the gap equation. Differences between
the bound states in the conventional BCS approach and the $pphh$ RPA are
arising in the case of $^3SD_1$ channel in symmetric nuclear matter at low
densities. These differences are discussed in the context of transition from
BEC for quasi-deuterons to the formation of BCS pairing.

Nuclear Theory