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We show that it is possible to reconcile NMR and neutron scatteringexperiments on both LSCO and YBCO, by making use of the Millis-Monien-Pinesmean field phenomenological expression for the dynamic spin-spin responsefunction, and reexamining the standard Shastry-Mila-Rice hyperfine Hamiltonianfor NMR experiments. The recent neutron scattering results of Aeppli et al onLSCO (x=14%) are shown to agree quantitatively with the NMR measurements of$^{63}T_1$ and the magnetic scaling behavior proposed by Barzykin and Pines.The reconciliation of the $^{17}T_1$ relaxation rates with the degree ofincommensuration in the spin fluctuation spectrum seen in neutron experimentsis achieved by introducing a new transferred hyperfine coupling $C'$ betweenoxygen nuclei and their next nearest neighbor $Cu^{2+}$ spins; this leads to anear-perfect cancellation of the influence of the incommensurate spinfluctuation peaks on the oxygen relaxation rates of LSCO. The inclusion of thenew $C'$ term also leads to a natural explanation, within the one-componentmodel, the different temperature dependence of the anisotropic oxygenrelaxation rates for different field orientations, recently observed byMartindale $et~al$. The measured significant decrease with doping of theanisotropy ratio, $R= ^{63}T_{1ab}/^{63}T_{1c}$ in LSCO system, from $R =3.9$for ${\rm La_2CuO_4}$ to $R ~ 3.0$ for LSCO (x=15%) is made compatible with thedoping dependence of the shift in the incommensurate spin fluctuation peaksmeasured in neutron experiments, by suitable choices of the direct andtransferred hyperfine coupling constants $A_{\beta}$ and B.Comment: 24 pages in RevTex, 9 figures include

NMR and neutron-scattering experiments on the cuprate superconductors: A critical re-examination