Abstract
WE derive and solve the Galilean covariant Dirac equation, also called "Levy-Leblond equation", for spin-1/2 particles in a Woods-Saxon potential. We obtain this wave equation with a Galilean covariant approach, which is based on a (4 + 1)-dimensional manifold with light-cone coordinates followed by a reduction to the (3 + 1)-dimensional Galilean space-time. We apply the Pekeris approximation and exploit the Nikiforov-Uvarov method to find the energy eigenvalues and eigenfunctions.