# ${\cal{P,T}}$-Odd and Magnetic Hyperfine Interaction Constants and Excited-State Lifetime for HfF$^+$

## TL;DR

This paper reports precise calculations of symmetry-violating interaction constants and related properties for HfF$^+$, aiding the interpretation of experimental measurements searching for fundamental symmetry violations.

## Contribution

The study provides new relativistic multi-reference configuration interaction calculations of key symmetry-violating constants and hyperfine parameters for HfF$^+$.

## Key findings

- Nucleon-electron scalar-pseudoscalar interaction constant W_S = 20.0 kHz
- Effective electric field |E_eff| = 22.7 GV/cm
- Magnetic hyperfine interaction constants and G-tensor values

## Abstract

Parity- and time-reversal-symmetry violating interaction constants required for the interpretation of a recent measurement (arXiv:1704.07928 [physics.atom-ph]) of corresponding symmetry violations in the $\Omega=1$ (${^3\Delta}_1$) science state of the HfF$^+$ molecular ion are reported. Using a relativistic four-component all-electron multi-reference configuration interaction model the nucleon-electron scalar-pseudoscalar interaction constant is determined as $W_S = 20.0$ [kHz]. An updated result for the electron electric-dipole-moment effective electric field of $|E_{\text{eff}}| = 22.7 \left[\frac{\rm GV}{\rm cm}\right]$ is obtained. Further results of relevance in the context of the search for leptonic charge-parity violation such as magnetic hyperfine interaction constants and electronic $G$-tensor for HfF$^+$ are presented.