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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.
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Stimulated by the still puzzling competition between spin-singlet and spin-triplet pairing in nuclei, the 3SD1 neutron-proton pairing is investigated in the framework of BCS theory of nuclear matter. The medium polarization effects are included in the single particle spectrum and also in the pairing interaction starting from the G-matrix, calculated in the Brueckner-Hartree-Fock approximation. The vertex corrections due to spin and isospin collective excitations of the medium are determined from the Bethe-Salpeter equation in the RPA limit, taking into account the tensor correlations. It is found that the self-energy corrections confine the superfluid state to very low-density, while remarkably quenching the magnitude of the energy gap, while the induced interaction has an attractive effect. The interplay between spin-singlet and spin-triplet pairing is discussed in nuclear matter as well as in finite nuclei.
We discuss the effect of changes in meson properties in a nuclear medium on physical observables, notably, $J/Psi$ dissociation on pion and $rho$ meson comovers in relativistic heavy ion collisions, and the prediction of the $omega$-, $eta$- and $eta$-nuclear bound states.
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