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.

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Multiple quantum nuclear magnetic resonance (NMR) transitions were observed on polarized 8Li nuclei, which were produced by capture of polarized neutrons in a single crystal of LiTaO 3. The asymmetric SLi/3-radiation distribution was used for the detection of NMR. A quadrupole moment ratio IQ(SLi)/Q(VLi)] = 0.78(1) was determined. Saturation of multiple quantum transitions in nuclear radiation detected NMR may lead to a reduction in measuring time of up to two orders of magnitude, as compared to single quantum detection methods. The measured spectra agree well with an exact lineshape calculation. The same measurements were also performed on a LiTaO 3 powder sample. This was done to test a method to obtain quadrupole coupling constants from high field NMR multiple quantum powder patterns, which are easily detectable, also for higher nuclear spins. This latter method may be applicable also to conventional NMR detection techniques.

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