  We consider Feshbach scattering of fermions in a one-dimensional optical
lattice. By formulating the scattering theory in the crystal momentum basis,
one can exploit the lattice symmetry and factorize the scattering problem in
terms of center-of-mass and relative momentum in the reduced Brillouin zone
scheme. Within a single band approximation, we can tune the position of a
Feshbach resonance with the center-of-mass momentum due to the non-parabolic
form of the energy band.
