eta-prime nucleus optical potential and possible eta-prime bound states

TL;DR

This paper evaluates the eta'-nucleus optical potential based on a recent eta'N interaction model, exploring the possibility of eta'-nuclear bound states and their experimental signatures, considering uncertainties in the interaction parameters.

Contribution

It provides a calculation of the eta'-nucleus optical potential and formation cross sections, incorporating second-order absorption effects and analyzing the impact of interaction uncertainties.

Findings

Attractive potential with |a_eta'N|=0.1 fm is not sufficient for bound states in light nuclei.

Larger scattering lengths (|a_eta'|=0.3 fm) produce observable eta'-nuclear bound states.

Potential depth and bound state signatures depend critically on eta'N scattering length values.

Abstract

Starting from a recent model of the eta'N interaction, we evaluate the eta'-nucleus optical potential, including the contribution of lowest order in density, t rho/2m_eta', together with the second order terms accounting for eta' absorption by two nucleons. We also calculate the formation cross section of the eta' bound states from (pi+,p) reactions on nuclei. The eta'-nucleus potential suffers from uncertainties tied to the poorly known eta'N interaction, which can be partially constrained by the experimental modulus of the eta'N scattering length and/or the recently measured transparency ratios in eta' nuclear photoproduction. Assuming an attractive interaction and taking the claimed experimental value |a_eta'N| = 0.1 fm, we obtain a eta' optical potential in nuclear matter at saturation density of V_eta' = -(8.7 + 1.8i) MeV, not attractive enough to produce eta' 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 |a_eta'| = 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 eta'-nuclear bound states and to threshold enhancements in the unbound region.