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The Hamiltonian Theory of the fractional quantum Hall effect is an operatordescription that subsumes many properties of Composite Fermions, applies togapped and gapless cases, and has been found to provide results in quantitativeaccord with data on gaps, relaxation rates and polarizations at temperatures of$300mK$ and above. The only free parameter is $\lambda$, which is related tothe sample thickness and appears in the Zhang-Das Sarma potential $v(q) = {2\pie^2\over \kappa q} e^{-ql\lambda}$ where $l$ and $\kappa $ are the magneticlength and dielectric constant. Here we examine the recent data of Tracy andEisenstein on the nuclear magnetic resonance relaxation rate at filling factor$\nu=\half$ deduced from resistivity measurements at temperatures as low as$45mK$. We find that their results can be satisfactorily described by thistheory, if in addition to a $v(q)$ with $\lambda \simeq 2$, a constant disorderwidth $\Gamma\simeq 100 mK$ is incorporated.

Hamiltonian theory of the half-filled Landau level with disorder: Application to recent NMR data