Parity, one of the three discrete spacetime symmetries of nature is broken by weak interactions. In atomic systems, parity violation is manifested in two ways: nuclear spin independent and spin dependent effects. The former is a relatively large effect that has been measured to better than 1%, whereas the nuclear spin dependent parity violation (NSD-PV) effect is smaller and remains poorly understood. To date the only nonzero measurement of NSD-PV effects in atoms was made in Cs, but the uncertainty in this measurement is substantial (~14%) and the result is in disagreement with other data from nuclear physics measurements. Precise measurements of NSD-PV effects will yield crucial information on the parameters that determine the strength of purely hadronic weak interactions, and potentially also on fundamental couplings of the Z0 boson.
We study NSD-PV effects using diatomic molecules. In this thesis, I discuss measurements that demonstrate a statistical sensitivity to NSD-PV surpassing that of any previous atomic PV measurement, using the test system 138Ba19F. With a total of ~168 hours of data, our statistical uncertainty for the NSD-PV weak matrix element, W, is ≤0.5 Hz. The sensitivity we demonstrate would be sufficient to measure NSD-PV effects of the size anticipated across a wide range of nuclei. We describe the details of data analysis and also an extensive study of systematic errors that can affect measurements using our technique, and show that these can be controlled at least at the level of the present statistical sensitivity.