η′ nucleus optical potential and possible η′ bound states

Starting from a recent model of the ηN interaction, we evaluate the η-nucleus optical potential, including the contribution of lowest order in density, tρ/2mη′ , together with the second order terms accounting for η absorption by two nucleons. We also calculate the formation cross section of the η bound states from (π, p) reactions on nuclei. The η-nucleus potential suffers from uncertainties tied to the poorly known ηN interaction, which can be partially constrained by the experimental modulus of the ηN scattering length and/or the recently measured transparency ratios in η nuclear photoproduction. Assuming an attractive interaction and taking the claimed experimental value |aη′N | = 0.1 fm, we obtain a η optical potential in nuclear matter at saturation density of Vη′ = −(8.7 + 1.8i) MeV, not attractive enough to produce η bound states in light nuclei. Larger values of the scattering length give rise to deeper optical potentials, with moderate enough imaginary parts. For a value |aη′N | = 0.3 fm, which can still be considered to lie within the uncertainties of the experimental constraints, the spectra of light and medium nuclei show clear structures associated to η-nuclear bound states and to threshold enhancements in the unbound region. PACS numbers: 21.85.+d; 21.65.Jk; 25.80.-e