In-medium T matrix in case of pairing instability

The diagonalization technique for two-body propagator in nuclear matter is generalized by inclusion of the two-hole continuum. In the approach, the total effective two-body Hamiltonian is introduced which allows us to find the complete propagator as well as the reaction $T$ matrix at many energies and relative momenta simultaneously from a single diagonalization procedure for the Hamiltonian matrix. Explicit treatment of bound and continuum states allows us to determine forward- and backward-propagating parts of the $T$ matrix in a closed form which simplifies strongly the evaluation of single-particle and single-hole self-energies. Special attention is paid to the bound-state contribution to the reaction matrix in case of pairing instability when complex conjugated eigenvalues of the effective Hamiltonian appear. A generalization of the approach to calculation of pairing gaps in case of nonzero center-of-mass momentum of the pair is also presented.