  Local spectral functions and Nuclear Magnetic Relaxation (NMR) rates, 1/T1,
for the spin-half Heisenberg antiferromagnet on the Kagome Lattice are
calculated using Moriyas Gaussian approximation, as well as through an
extrapolation of multiple frequency moments. The temperature dependence of the
calculated rates is compared with the oxygen 1/T1 NMR data in Herbertsmithite.
We find that the Gaussian approximation for 1/T1 shows behavior qualitatively
similar to experiments with a sharp drop in rates at low temperatures,
consistent with a spin-gapped behavior. However, this approximation
significantly underestimates the magnitude of 1/T1 even at room temperature.
Rates obtained from extrapolation of multiple frequency moments give very good
agreement with the room temperature NMR data with J = 195 +/- 20 K and
hyperfine couplings determined independently from other measurements. The use
of multiple frequency moments also leads to additional low frequency weight in
the local structure factors. The convergence of our calculations with higher
frequency moments breaks down at low temperatures suggesting the existence of
longer range dynamic correlations in the system despite the very short-range
static correlations.
