  The interdependence of antiferromagnetism and superconductivity in the
Bechgaard salts series of organic conductors is examined in the light of the
anomalous temperature dependence of the nuclear spin-lattice relaxation rate.
We apply the renormalization group approach to the electron gas model to show
that the crossover from antiferromagnetism to superconductivity along with the
anomalous nuclear relaxation rate of the Bechgaard salts can be well described
within a unified microscopic framework. For sizable nesting deviations of the
Fermi surface, scaling theory reveals how pairing correlations enhance
short-range antiferromagnetic correlations via magnetic Umklapp scattering over
a large part of the metallic phase that precedes superconductivity. These
enhanced magnetic correlations are responsible for the Curie-Weiss behavior
observed in the NMR relaxation rate.
