Nuclear Schiff moment of fluorine isotope $^{19}$F

Nuclear Schiff moments (NSMs) are sensitive probes for physics beyond the Standard Model of particle physics, signaling violations of time-reversal and parity-inversion symmetries in atomic nuclei. In this Letter, we report the first-ever calculation of a NSM in a nuclear ab initio framework, employing the no-core shell model to study the fluorine isotope $^{19}$F. We further perform quantum-chemistry calculations to evaluate the sensitivity of the hafnium monofluoride cation, HfF$^+$, to the NSM of $^{19}$F. Combined with recent high-precision measurements of the molecular electric dipole moment of HfF$^+$, our results enable the first experimental bound on the NSM of $^{19}$F. Although the resulting bounds on the pion-nucleon-nucleon ($π$NN) coupling constants are not yet the most stringent, this work establishes the foundation for constraining $π$NN interactions using nuclear ab initio methods.

💡 Research Summary

This paper presents the first ab initio calculation of a nuclear Schiff moment (NSM) for the fluorine‑19 nucleus and connects it to precision measurements of the electric dipole moment (EDM) of the hafnium monofluoride cation (HfF⁺). The authors employ the no‑core shell model (NCSM) with chiral effective‑field‑theory (χEFT) nucleon–nucleon (NN) and three‑nucleon (3N) interactions to solve the full 19‑body problem. Using the Lanczos strength method they evaluate the matrix elements of the P‑ and T‑violating NN interaction (dominated by one‑pion exchange) that induce the Schiff operator. Two χEFT interaction sets (NN‑N⁴LO+3N and NN‑N³LO+3N) are explored, and systematic variations of the model space size (N_max) and oscillator frequency (ℏΩ) are performed. The resulting NSM is expressed linearly in terms of the three isospin components of the P,T‑odd pion‑nucleon coupling constants (\bar g_{0,1,2}): \