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The Bethe-Goldstone-type formalism to determine a reaction matrix for two particles in medium (e.g. nucleons in nuclear matter) are reformulated in terms of a resolvent of the effective total Hamiltonian defined in the Pauli-allowed subspace. As a result, the reaction matrix at many relative momenta and energies can be found by using the respective Hamiltonian matrix diagonalization in the stationary wave packet basis which simplifies strongly the self-energy iterations. The proposed discrete approach is expected to open a new way to an accurate treatment of three-nucleon correlations in nuclear matter on the basis of the three-body Bethe-Faddeev equation by an effective Hamiltonian diagonalization procedure.