Nuclear spin polarization of $^{37,41}K$ by optical pumping

Precision measurements of observables in nuclear $\beta$-decay are capable of imposing meaningful constraints on physics beyond the standard model complementary to those obtained at high-energy collider experiments. In particular, measuring the $\beta$-asymmetry parameter ($A_{\beta}$) in the $\beta^{+}$-decay of spin-polarized $^{37}K$ constrains the possible admixture of a hypothetical $V+A$ current in the weak interaction. At TRINAT (TRIUMF's Neutral Atom Trap), atoms are confined and cooled in a magneto-optical trap and highly spin-polarized by optical pumping. I will show that we have determined the average nuclear polarization of optically pumped $^{41}K$ to be $\left\langle P\right\rangle =98.8(6)\%$. Furthermore, I will present a comparison of optical pumping models as it pertains to our application, demonstrating that a quantum mechanical approach based on the density matrix formalism is necessary to accurately account for the various depolarizing mechanisms.