  In this work we fit $neutron$ - $^{12}C$ elastic scattering angular
distributions in the energy range 12 to 20 MeV, by adding a velocity dependent
term to the optical potential. This term introduces a wave function gradient,
whose coefficient is real and position dependent, and which represents a
nonlocality. We pay special attention to the prominent backscattering minima
which depend sensitively on the incident energies, and which are a tell-tale of
nonlocalities. Reasonable fits to the analyzing power data are also obtained as
a by-product. All our potentials have the form of conventional Woods - Saxon
shapes or their derivatives. The number of our parameters (12) is smaller than
the number for other local optical potentials, and they vary monotically with
energy, while the strengths of the real and imaginary parts of the central
potential are nearly constants. Our nonlocality is in contrast to other forms
of nonlocalities introduced previously.
