Differential neutron elastic- and inelastic-scattering cross sections of vanadium were measured from 4.5 to 10 MeV. These results were combined with previous 1.5 to 4.0 MeV data from this laboratory, the 11.1 MeV elastic-scattering results obtained at Ohio University, and the reported neutron total cross sections to energies of approx. 20.0 MeV, to form a data base which was interpreted in terms of the spherical optical-statistical model. A fit to the data was achieved by making both the strengths and geometries of the optical-model potential energy dependent. This energy dependence was large below approx. 6.0 MeV. Above approx. 6.0 MeV the energy dependencies are smaller, and similar to those characteristic of global models. Using the dispersion relationship and the method of moments, the optical-model potential energy deduced from 0.0 to 11.1 MeV neutron-scattering data was extrapolated to higher energies and to the bound-state regime. This extrapolation leads to predicted neutron total cross sections that are within 3% of the experimental values throughout the energy range 0.0 to 20.0 MeV. Furthermore, the values of the volume-integral-per-nucleon of the real potential are in excellent agreement with those needed to reproduce the observed binding energies of particle- and hole-states. The latter gives clear evidence of the Fermi surface anomaly. Using only the 0.0 to 11.1 MeV data, the predicted E