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Magnetic hyperfine structure constants of $^{137}$BaF in the $^2Π_{1/2}$ and $^2Π_{3/2}$ excited states

Yuly Chamorro, Felix Kogel, Tim Langen, Anastasia Borschevsky

TL;DR

This work addresses the problem of predicting the hyperfine structure constants for the excited states of $^{137}$BaF, essential for interpreting symmetry-violation experiments and enabling laser cooling. It employs a relativistic four-component Dirac-Coulomb FSCC method with a finite-field perturbation and CBS extrapolation to compute $A_{ ext{parallel}}$ and $A_{ ext{perp}}$ for the states $^2Π_{1/2}$ and $^2Π_{3/2}$. The key contributions include a systematic assessment of basis-set quality, electron-correlation effects (including triples), vibrational averaging, and a transparent uncertainty budget, yielding final values $A_{ ext{parallel}}(^{2}Π_{1/2}) = 399.0 ext{ MHz}$, $A_{ ext{perp}}(^{2}Π_{1/2}) = 239.1 ext{ MHz}$, and $A_{ ext{parallel}}(^{2}Π_{3/2}) = 34.6 ext{ MHz}$ with stated uncertainties; these are in good agreement with experimental measurements and improve the foundation for BaF-based NSD-PV and eEDM searches. The work demonstrates the predictive power of the FSCC approach for excited-state hyperfine properties in heavy molecules and informs future precision spectroscopy and laser-cooling schemes.

Abstract

High-precision molecular experiments testing the Standard Model of particle physics require an accurate understanding of the molecular structure at the hyperfine level, both for the control of the molecules and for the interpretation of the results. In this work, we calculate the hyperfine structure constants for the excited states $^2Π_{1/2}$ and $^2Π_{3/2}$ of $^{137}$BaF due to the $^{137}$Ba nucleus. We use the 4-component relativistic Fock-space coupled-cluster method, extrapolating our results to the complete basis set limit. We investigate the effect of the basis sets and electron correlation, and estimate the uncertainty in our final results. Our results are used in the interpretation of the experimental spectroscopy of the hyperfine and rovibrational spectra of BaF, and the planning of laser-cooling schemes for future parity-violating anapole moment measurements [1].

Magnetic hyperfine structure constants of $^{137}$BaF in the $^2Π_{1/2}$ and $^2Π_{3/2}$ excited states

TL;DR

This work addresses the problem of predicting the hyperfine structure constants for the excited states of BaF, essential for interpreting symmetry-violation experiments and enabling laser cooling. It employs a relativistic four-component Dirac-Coulomb FSCC method with a finite-field perturbation and CBS extrapolation to compute and for the states and . The key contributions include a systematic assessment of basis-set quality, electron-correlation effects (including triples), vibrational averaging, and a transparent uncertainty budget, yielding final values , , and with stated uncertainties; these are in good agreement with experimental measurements and improve the foundation for BaF-based NSD-PV and eEDM searches. The work demonstrates the predictive power of the FSCC approach for excited-state hyperfine properties in heavy molecules and informs future precision spectroscopy and laser-cooling schemes.

Abstract

High-precision molecular experiments testing the Standard Model of particle physics require an accurate understanding of the molecular structure at the hyperfine level, both for the control of the molecules and for the interpretation of the results. In this work, we calculate the hyperfine structure constants for the excited states and of BaF due to the Ba nucleus. We use the 4-component relativistic Fock-space coupled-cluster method, extrapolating our results to the complete basis set limit. We investigate the effect of the basis sets and electron correlation, and estimate the uncertainty in our final results. Our results are used in the interpretation of the experimental spectroscopy of the hyperfine and rovibrational spectra of BaF, and the planning of laser-cooling schemes for future parity-violating anapole moment measurements [1].

Paper Structure

This paper contains 10 sections, 8 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Computational details
  4. Results and discussion
  5. Basis set quality
  6. Electron correlation
  7. Vibrational effects
  8. Final results and uncertainty estimation
  9. Conclusions
  10. Acknowledgments

Figures (3)

  • Figure 1: HFS constants (MHz) as a function of the cardinality of the dyall.v$n$z basis set, $n=3,4$. The dashed lines represent the curve fitted through the calculated HFS values and the CBS limit obtained using the Helgaker scheme; the latter is shown by the solid line. The shadowed interval is limited by the upper and lower CBS(M) and CBS(L) limits.
  • Figure 2: Variation (%) of the HFS constants relative to the values at the equilibrium bond length ($r_e$) as a function of $\Delta r$.
  • Figure 3: Contributions of the different sources to the total uncertainty on the final calculated HFS constants. The percentage is relative to the final value shown in \ref{['tab:uncertainty']}.