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The Zeeman splittings and EPR frequencies of alkali-metal atoms are shiftedin the presence of a polarized noble gas. For a spherical geometry, the shiftis enhanced over what is expected classically by a dimensionless atomicparameter $\kappa_0$ that is unique to each alkali-metal atom - noble-gas pair.We present a precise measurement of $\kappa_0$ for the $^{39}$K-$^3$He systemwith a relative accuracy of better than 1\%. A critical component of achievingsub-percent accuracy involved characterizing the shape of our samples usingboth MRI and CT medical-imaging techniques. The parameter $\kappa_0$ plays animportant role in establishing the absolute polarization of $^3$He in a varietyof contexts, including polarized targets for electron scattering experimentsand MRI of the gas space of the lungs. Our measurement more than doubles theaccuracy possible when using $\kappa_0$ for polarimetry purposes. Just asimportant, the work presented here represents the first {\it direct}measurement of $\kappa_0$ for the $^{39}$K-$^3$He system; previous values for$\kappa_0$ in the $^{39}$K-$^3$He system relied on a chain of measurements thatwere benchmarked by previous measurements of $\kappa_0$ in the Rb-$^3$Hesystem.

Frequency shifts in the EPR spectrum of $^{39}$K due to spin-exchange collisions with polarized $^3$He and precise $^3$He polarimetry