Extrapolation of the dispersive optical model to the resonance region for neutrons onKr86

The neutron${\mathrm{-}}^{86}$Kr mean field is formulated in terms of a dispersive optical model potential in which the real part contains dispersive contributions derived from the imaginary part by the dispersion relation. The dispersive contribution is added to the Hartree-Fock potential, which is assumed to have a Woods-Saxon shape and a depth that decreases linearly with increasing energy. The shape parameters for all components of the potential are assumed to be independent of energy. The model is formulated in terms of the energy relative to the Fermi energy, and the imaginary potential is assumed to be symmetric about the Fermi energy, which is set equal to -7.7 MeV on the basis of the empirical level structure for n${\mathrm{-}}^{86}$Kr. All other parameters are taken from earlier analyses of other nuclei, particularly of ${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$. The model is shown to give good overall predictions for the n${\mathrm{-}}^{86}$Kr mean field by comparison to the following three sets of empirical data: (i) the observed energies of the occupied and unoccupied valence levels, (ii) the energy-averaged total cross section for neutron energies up to 25 MeV, and (iii) the averaged scattering functions for s-, p-, and d-wave neutrons in the resolved resonance region from 0.015 to 0.96 MeV. The latter comparison is the unique feature of this work; the partial-wave-scattering functions that are available for s, p, and d waves in the resonance region for ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$ make possible detailed comparisons to the scattering functions from the model.