Nuclear Spin-Dependent Parity Violation in Diatomic Molecules

Nuclear spin-dependent parity nonconservation (NSD-PNC) effects arise from exchange of the $Z^{0}$ boson (parameterized by the electroweak coupling constants $C_{2{\{P,N\}}}$) between electrons and the nucleus and from the interaction of electrons with the nuclear anapole moment, a parity-odd magnetic moment. The latter scales with the nucleon number $A$ of the nucleus as $A^{\frac{2}{3}}$, while the $Z^{0}$ coupling is independent of A; the former will be the dominant source of NSD-PNC in nuclei with $A \ge 20$. The most precise result on NSD-PNC to date comes from a measurement of the hyperfine dependence of atomic PNC in $^{133}$Cs, but this effect can be dramatically enhanced in diatomic molecules by bringing two levels of opposite parity close to degeneracy in a strong magnetic field. Level crossings have been observed in $^{138}$BaF as a precursor to the test for parity violation in $^{137}$BaF. We report on our measurements and planned design improvements to improve sensitivity in preparation for the parity violation experiment.