Density dependence of the Σ nucleus optical potential derived from Σ^- atom data

We study phenomenologically the density dependence of the Σ nucleus optical potential V_opt(r) at zero kinetic energy by fitting it to a comprehensive set of atomic data across the periodic table. The best fit solutions for V_opt depart considerably from a standard t_effρ{variant}(r) form in that Re V_opt tends to flip sign from attraction outside the nucleus to repulsion in the surface region. However, the quality of the atomic data is too poor to determine unambiguously V_opt inside the nucleus. For such density dependent potentials, well defined single-particle hypernuclear states are unlikely to exist.