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Molecular Parity Nonconservation in Nuclear Spin Couplings

The weak interaction does not conserve parity, which is apparent in many nuclear and atomic phenomena. However, thus far, parity nonconservation has not been observed in molecules. Here we consider nuclear-spin-dependent parity nonconserving contributions to the molecular Hamiltonian. These contributions give rise to a parity nonconserving indirect nuclear spin-spin coupling which can be distinguished from parity conserving interactions in molecules of appropriate symmetry, including diatomic molecules. We estimate the magnitude of the coupling, taking into account relativistic corrections. Finally, we propose and simulate an experiment to detect the parity nonconserving coupling using liquid- or gas-state zero-field nuclear magnetic resonance of electrically oriented molecules and show that $^{1}$H$^{19}$F should give signals within the detection limits of current atomic vapor-cell magnetometers.