Energy dependence of the mean-field potential for neutron scattering from190,192Os and194,196Pt

An extensive set of neutron scattering cross sections for four shape-transitional nuclei, ${}_{}{}^{190}{}_{}{}^{}$,192Os and ${}_{}{}^{194}{}_{}{}^{}$,196Pt, have been examined to test recent mean-field concepts which relate scattering potentials to those which bind single particle levels in nuclei. Scattering observables for each of these four nuclei have been separately and exhaustively analyzed to fix the potential strengths and their dependence on incident neutron energy. The results of these analyses revealed potentials quite different than the usual ‘‘Hartree-Fock type’’ potentials arising from global analyses at higher particle energies. A dispersion relation, based on the imaginary parts of the optical model potential, is applied in these analyses. Not only can the nonlinear energy dependencies observed in the scattering potential be described with this method, the potential can be extrapolated to negative energies where it is constrained to fit bound states in the neutron-plus-nucleus system. This is the first report of dispersion corrections for potentials from coupled-channels analyses of scattering from highly collective nuclei.