A quantitative explanation of the observed enhancements of the Korringa product and the ratio of Zeeman to dipolar spin-lattice relaxation times in sodium is given. The explanation is based on an extension of the theories of Moriya and Wolff, using for the generalized paramagnetic susceptibility the expression given by the self-consistent theory of Singwi et al. of spin correlations in a low-density interacting electron gas. The theory also predicts that the Korringa constant in the alkali metals is almost constant - a result in agreement with experiment.