Effects of impurity vertex correction on the NMR coherence peak in s-wave superconductors

We study the effects of nonmagnetic impurity vertex correction on nuclear spin-lattice relaxation rate 1/T1 of conventional s-wave superconductors within the Eliashberg formalism. We obtain, with a self-consistent t-matrix treatment of impurity scatterings, the expression for impurity vertex function and nuclear spin-lattice relaxation rate. The 1/T1 is evaluated with a simple approximation on angular average, and found to agree in clean limit with the previous result that 1/(T1T) remains unrenormalized under the impurity vertex correction. As dirtiness is increased, on the other hand, the coherence peak in 1/(T1T) is found to increase due to the impurity vertex correction. This result is discussed in connection with the experimental observations on conventional superconductors