The electronic structure parameter (W-M) of the nuclear magnetic quadrupole moment (MQM) interaction in numerous open-shell metal monofluorides (viz., MgF, CaF, SrF, BaF, RaF, and PbF) is computed in the fully relativistic coupled-cluster framework. The electron-correlation effects are found to be very important for the precise calculation of W-M in the studied molecular systems. The molecular MQM interaction parameter scales nearly as Z(2) in the alkaline earth metal monofluorides, where Z is the nuclear charge of metal. Our study identifies (RaF)-Ra-223 as a good candidate for the experimental search of the nuclear MQM, which can help unravel the physics beyond the standard model in the hadron sector of matter.

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