Level crossing of particle-hole and mesonic modes in eta mesic nuclei

The prominent feature of the η meson is that it couples dominantly to the N(1535) (S11) resonance at threshold energies. The low-momentum η meson would then mainly excite N–nucleon-hole (N-h) states in nuclear matter. Therefore the η meson nuclear dynamics is sensitive to modifications of nucleon and N properties in medium. If some medium effects and/or a density increase bring the N-h state down below the eta state, so that mη > m ∗ N∗(ρ) − mN ∗ (ρ) , the optical potential of the eta meson becomes repulsive [1]. Thus it is not sufficient to treat the η meson in a nucleus in terms of an energyindependent optical potential. In our study we describe the eta mode with the frequencyω and the momentum ~k propagating in nuclear medium with the density ρ by the Green’s function Gη(ω, k; ρ) = 1/(ω − k −mη − Πη(ω, k, ρ)) with the polarization operator