𝒞𝒫-violation sensitivity of closed-shell radium-containing polyatomic molecular ions

Abstract

Closed-shell atoms and molecules such as Hg and TlF provide some of the best low-energy tests of hadronic 𝒞𝒫 violation beyond the standard model of particle physics, which is considered to be a necessary ingredient to explain the observed excess of matter over antimatter in our universe. 𝒞𝒫 violation is expected to be strongly enhanced in octupole-deformed nuclei such as ²²⁵$\mathrm{Ra}$. Recently, closed-shell radium-containing symmetric-top molecular ions were cooled sympathetically in a Coulomb crystal [Fan et al., Phys. Rev. Lett. 126, 023002 (2021)] and shown to be well suited for precision spectroscopy in the search for fundamental physics [Yu and Hutzler, Phys. Rev. Lett. 126, 023003 (2021)]. In closed-shell molecules hadronic $\mathrm{CP}$ violation contributes to a net electric dipole moment (EDM) that violates parity and time-reversal symmetries (𝒫$,$𝒯), which is the target of measurements. To interpret experiments, it is indispensable to know the electronic-structure-enhancement parameters for the various sources of 𝒫$,$𝒯 violation which contribute to the net 𝒫$,$𝒯-odd EDM. We employ relativistic density-functional-theory calculations to determine relevant parameters for interpretation of possible EDM measurements in ${\mathrm{RaOCH₃}}_{\mathrm{⁺}},{\mathrm{RaSH⁺}}^{},{\mathrm{RaCH}}^{+⁺},{\mathrm{RaCN⁺}}^{}$, and ${\mathrm{RaNC⁺}}^{}$ and perform accurate relativistic coupled-cluster calculations of the Schiff-moment enhancement in ${\mathrm{RaSH⁺}}^{}$ to gauge the quality of the density-functional-theory approach. Finally, we project to bounds on various 𝒫$,$𝒯-odd parameters that could be achievable from an experiment with ${\mathrm{RaOCH₃}}_{\mathrm{⁺}}$ in the near future and assess its complementarity to experiments with Hg and TlF.

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