Energy dependence of the optical-model potential for fast-neutron scattering from bismuth

Neutron differential-elastic-scattering cross sections of bismuth were measured at ≊0.5 MeV intervals from ≊4.5 to 10.0 MeV. At each incident energy 40 or more differential values were obtained between ≊18° and 160°. These data were combined with lower-energy results previously reported from this laboratory, and others available in the literature, to provide a detailed data base extending from ≊1.5 to 10.0 MeV. This data base was interpreted in terms of the conventional optical-statistical model and also using a model which included the surface-peaked real potential predicted by the dispersion relation. Particular attention was given to the energy dependence of the volume-integral-per-nucleon of the real potential, $J_v$, to see if there was evidence of the Fermi surface anomaly. In the range 3.0–10.0 MeV, the present study indicates that ${\mathrm{dJ}}_v$/dE is essentially constant, with a relatively large negative value of -6.0 to -9.0 ${\mathrm{fm}}^3$, depending on the model used in the analysis. Below 3.0 MeV, there is some evidence for a decrease in the magnitude of ${\mathrm{dJ}}_v$/dE. However, the effect is very small, and it is only when this trend is combined with considerations of the $J_v$ values needed to give correct bound-state energies that evidence for the Fermi surface anomaly emerges. $J_v$ and the geometry of the optical potentials found for ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ become equal to those explaining the higher-energy ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ data at about 10.0 MeV. Since ${\mathrm{dJ}}_v$/dE for the latter is smaller in magnitude than that for ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$, a change in ${\mathrm{dJ}}_v$/dE is clearly indicated near 10.0 MeV.