How strongly do electrons interact with the atomic nucleus via the weak force? For electromagnetism the answer is easy: the electron and nuclear charges determine the strength. However, the weak force is more complicated, having two effective types of charge for each particle. The strength of the weak force must be measured in parts.

The parity-violating parts of the weak force in an atom or molecule can be split into two groups: nuclear spin dependent effects (NSD-PV) and nuclear spin independent effects. The spin independent effects are much easier to measure since they grow proportionally with the number of nucleons, while NSD-PV effects arise only from the unpaired spins in a nucleus—of which there is typically only one. Consequently, nuclear spin independent parity violation is stronger and has been measured well while NSD-PV effects are weaker and largely unmeasured.

The two NSD-PV effects that we are principally interested in are **Z boson exchange** between electrons and nucleons, and the **nuclear anapole moment**. Z boson exchange is a fundamentally simpler process (it corresponds to a tree level Feynman diagram) and directly addresses the question of how strong the electron-nucleon weak force is. However, the strengths of these two effects are roughly the same order of magnitude and the contribution of the nuclear anapole moment cannot be distinguished from Z boson exchange in a measurement from a single isotope.

Although the nuclear anapole moment complicates the measurement of the strength of the weak force, it is interesting in its own right. Inside the nucleus, the weak force causes the spin of the unpaired nucleon to point in its direction of motion as it orbits the nuclear core. The magnetic moment associated with the nuclear spin is equivalent to a current loop; its orbit around the nuclear core results in an effectively toroidal current. This toroidal current gives rise to an **anapole moment**, analogous to how a current loop gives rise to a dipole moment. Atomic electrons then interact magnetically with the anapole moment. Measuring nuclear anapole moments will give valuable insight into the strength of the nucleon-nucleon weak force. Furthermore, the magnitude of the nuclear anapole moment is unique to each nucleus, so having a table of these values may be useful in a way analogous to that in which nuclear magnetic moment measurements have been useful to NMR.

Our novel approach to measuring these small effects uses diatomic molecules. The NSD-PV effects cause levels of opposite parity to be mixed, and it is this mixing that we directly measure in order to deduce the NSD-PV strengths. The mixing is very small, but is amplified if the levels are closely spaced in energy. Due to their large moment of inertia, diatomic molecules have rotational levels that are very closely spaced and are thus an ideal system for measuring NSD- PV. The levels are brought even closer together using a magnetic field and associated Zeeman shifts of the levels. Finally, the mixing is amplified through interference with an oscillating electric field, and detected using laser-induced fluorescence from the molecules.

Recently, we assembled a complex “interaction region” which will allow us to apply an electric field and laser beams to the molecules flying through the small confines of our superconducting magnet. We plan to soon make NSD-PV measurements in ^{138}BaF as a test of possible systematic errors in our approach; this system should not exhibit NSD-PV because ^{138}Ba does not have an unpaired nucleon spin. Later, after improvements to our molecular beam flux, we will measure NSD-PV in ^{137}BaF, where the predicted size of the effect is large enough to detect.