Effect of inelastic scattering on the nuclear magnetic relaxation rate 1/T1T in iron-based superconductors

We present a microscopic study of the nuclear magnetic relaxation rate 1/T1 based on the five-orbital model for iron-based superconductors. We mainly discuss the effect of the "inelastic" quasi-particle damping rate {\gamma} due to many-body interaction on the size of the coherence peak, for both s++ and s+- wave superconducting states. We focus on Ba(Fe1-xCox)2As2, and systematically evaluate {\gamma} in the normal state from the experimental resistivity, from optimally to over-doped compounds. Next, {\gamma} in the superconducting state is calculated microscopically based on the second order perturbation theory. In optimally doped compounds (Tc ~ 30 K), it is revealed that the coherence peak on 1/T1T is completely suppressed due to large {\gamma} for both s++ and s+- wave states. On the other hand, in heavily over doped compounds with Tc < 10 K, the coherence peak could appear for both pairing states, since {\gamma} at Tc is quickly suppressed in proportion to Tc^2. By making careful comparison between theoretical and experimental results, we conclude that it is difficult to discriminate between s++ and s+- wave states from the present experimental results.