Revisited $\mathcal{T}$, $\mathcal{P}$-odd spin-rotational Hamiltonian of HfF$^+$ for precise $e$EDM measurements

TL;DR

This paper refines the theoretical understanding of the HfF$^+$ molecule's spin-rotational Hamiltonian, crucial for precise electron EDM measurements, by validating models against recent experimental data and ensuring accurate interpretation of high-precision experiments.

Contribution

It provides a revisited and validated $ ext{T}$, $ ext{P}$-odd spin-rotational Hamiltonian for HfF$^+$, supporting more accurate electron EDM experiments.

Findings

Theoretical models match recent experimental spectroscopy data.

Validation of first-principles approaches for molecular Hamiltonians.

Enhanced understanding of systematic uncertainties in EDM measurements.

Abstract

The current constraint on the electron electric dipole moment ($e$EDM), $|d_e|<4.1\times 10^{-30}$ ${e {\cdotp} {\rm cm}}$ (90\% confidence), was recently established using the trapped $^{180}$Hf$^{19}$F$^+$ molecular ions in the $J=1$ rotational level of its $ ^3\Delta_1$ electronic state [T. S. Roussy, L. Caldwell, T. Wright, et al., arxiv:2212.11841]. The extensive experimental study of the HfF$^+$ cation provides detailed spectroscopy of the $\Omega-$doublet levels in the external rotating electric and magnetic fields. We showed that previously developed theoretical approaches can fully reproduce the latest experimental data. Their justification from the first principles is very important for the examination of both modern molecular theory and possible systematic uncertainties in the interpretation of the experimental data obtained with high accuracy.