Scattering and binding of different atomic species in a one-dimensional   optical lattice
  The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average discrete coordinates applies and makes the problem analytically tractable, and we present a number of new results and features compared to the case of identical atoms. 
R. T. Piil, N. Nygaard, and K. Molmer