η′-Nucleus optical potential and possible η′ bound states

Starting from a recent model of the η′N 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 η′N interaction, which can be partially constrained by the experimental modulus of the η′N 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|=0.1fm, we obtain an 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|=0.3fm, 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.