  We report 75As-NQR/NMR studies on the oxygen-deficient iron(Fe)-based
oxypnictide superconductors LaFeAsO_{0.6} (T_c=28 K) along with the results on
LaFeAsO, LaFeAsO_{0.75}(T_c=20 K) and NdFeAsO_{0.6}(T_c=53 K). Nuclear
spin-lattice relaxation rate 1/T_1 of 75As NQR at zero field on LaFeAsO_{0.6}
has revealed a T^3 dependence below T_c upon cooling without the coherence peak
just below T_c, evidencing the unconventional superconducting state with the
line-node gap. We have found an intimate relationship between the nuclear
quadrupole frequencyof 75As and T_c for four samples used in this study. It
implies microscopically that the local configuration of Fe and As atoms is
significantly related to the T_c of the Fe-oxypnictide superconductors, namely,
the T_c can be enhanced up to 50 K when the local configuration of Fe and As
atoms is optimal, in which the band structure may be also optimized through the
variation of hybridization between As 4p orbitals and Fe 3d orbitals.
