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Resonance Scattering in Optical Lattices and Molecules: Interband versus Intraband Effects

We study the low-energy two-body scattering in optical lattices with all higher-band effects included in an effective potential, using a renormalization group approach. As the potential depth reaches a certain value, a resonance of low energy scattering occurs even when the negative s-wave scattering length $(a_s)$ is much shorter than the lattice constant. These resonances can be mainly driven either by interband or intraband effects or by both, depending on the magnitude of $a_s$. Furthermore the low-energy scattering matrix in optical lattices has a much stronger energy-dependence than that in free space. We also investigate the momentum distribution for molecules when released from optical lattices.