Vertex corrections and the Korringa ratio in strongly correlated electron materials

We show that the Korringa ratio, associated with nuclear magnetic resonance in metals, is unity if vertex corrections to the dynamic spin susceptibility are negligible, the hyperfine coupling is momentum independent, and there exists an energy scale below which the density of states is constant. In the absence of vertex corrections we also find a Korringa behaviour for T-1, the nuclear spin relaxation rate, i.e., 1/T-1 proportional to T, and a temperature independent Knight shift. These results are independent of the form and magnitude of the self-energy (so far as is consistent with neglecting vertex corrections) and of the dimensionality of the system.