The local-density approximation to the expression for the generalized
complex spin susceptibility is used to treat simultaneously the effect
s of core polarization and of susceptibility enhancement on the Knight
shift and on the nuclear spin-lattice relaxation rate in metals. The
resulting equations can be considered as refinements of the Yafet-Jacc
arino (YJ) theory for transition metals, and retain the structure of a
sum of terms related to partial densities of states at the Fermi leve
l. The original YJ theory correctly identified the importance of core
polarization, but was unable to provide good fits to experimental data
in transition metals (specifically Pt and Pd). To obtain satisfactory
agreement, later workers found it necessary to introduce empirically
factors taking account of enhancement effects. This paper provides a t
heoretical basis for doing so.