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In the present work we discuss the effects of the medium polarization on the nuclear pairing, in the context of the relativistic Hartree-Fock-Bogoliubov (HFB) approximation. The medium polarization effects on the scalar and vector masses, as well on the pairing, as a function of Fermi momentum, are shown for several values of the coupling constants scaled by a parameter x. We find have obtained that the nuclear pairing is strongly affected by the medium polarization.For nearly three decades the nuclear pairing model has played an important role in the description of nuclear spectra. The mean field BCS method has been the most used approximation to solve this problem. However, the BCS theory is a very simple approximation which neglects any contribution to the nucleon-nucleon interaction beyond the bare potential. In order to account for many nuclear properties it is necessary to go beyond the pure BCS approach and add other effects to the nucleon-nucleon interaction, such as the medium polarization and other corrections to the selfenergy.In models of pairing, one of the most important quantities to be evaluated is the gap equation. In the BCS approach it is possible to obtain an analytical solution for the gap equation as opposed to potential models where this is possible only with a numerical treatment. However, going consistently beyond the BCS approximation including the medium polarization is a difficult task. Analytical results can be obtained only at low density where it has been noted that the medium effect modifies the effective nucleonnucleon interaction by adding a repulsive term, thus causing a reduction in the 1 S 0 gap.Understanding the role played by the nuclear medium in modifying hadronic properties is one of the most interesting problems facing nuclear physics today. One of the most interesting effects of the nuclear medium is the mixing of vector and scalar mesons. In lowest order this mixing is generated by the coupling of the mesons to particle-hole excitations. In the isoscalar channel, the coupling of the σ and ω fields through particle-hole excitations is extremely large and is therefore expected to strongly affect the propagation of mesons in nuclear matter [1].In this work, we intend to use the effective nucleonnucleon interaction in the 1 S 0 pairing channel to study the effect of the medium-modified meson masses. We use a relativistic Hartree-Fock-Bogoliubov formulation, developed in Ref. [2], in which, the QHD formulation is used to describe the nucleon-nucleon interaction in terms of the self-energy, Σ, and the pairing field, ∆. This model is an improvement over the non-relativistic formulation because it allows a simultaneous description of many nuclear matter properties such as the saturation point, the effective mass of the nucleon and the pairing energy.Using a Dirac-HFB approximation to pairing in symmetric nuclear matter, the self-consistency equation for the selfenergy and pairing field are written respectively as [2]andwhere, Γ jα represents the meson-baryon vertex ( we will ...

We analyse the renormalization of the of two-nucleon interaction with multiple subtractions in peripheral waves considering two chiral forces at N3LO. Phase shifts at low energies are then computed with several subtraction points below µ = 10 fm −1 . We show that for most peripheral waves the phase shifts have nearly no dependence on the renormalization scale. In two cases the phase shifts converge slowly as the renormalization scale approaches µ = 1 fm −1 and in one case the phase shifts presented oscillations with respect to the subtraction point µ.

Abstract. We apply five subtractions in the Lippman-Schwinger (LS) equation in order to perform a non-perturbative renormalization of chiral N3LO nucleon-nucleon interactions. Here we compute the phase shifts for the uncoupled peripheral waves at renormalization scales between 0.1 fm −1 and 1 fm −1 . In this range, the results are scale invariant and provide an overall good agreement with the Nijmegen partial wave analysis up to at least E lab = 150 MeV, with a cutoff at Λ = 30 fm −1 .

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