We report systematic ^{75}As-NQR and ^{139}La-NMR studies on nickel-pnictide superconductors LaNiAsO_{1-x}F_x (x=0, 0.06, 0.10 and 0.12). The spin lattice relaxation rate 1/T_1 decreases below T_c with a well-defined coherence peak and follows an exponential decay at low temperatures. This result indicates that the superconducting gap is fully opened, and is strikingly different from that observed in iron-pnictide analogs. In the normal state, 1/T_1T is constant in the temperature range T_c sim 4 K < T <10 K for all compounds and up to T=250 K for x=0 and 0.06, which indicates weak electron correlations and is also different from the iron analog. We argue that the differences between the iron and nickel pnictides arise from the different electronic band structure. Our results highlight the importance of the peculiar Fermi-surface topology in iron-pnictides.
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