Global isotopic analysis of hyperfine-resolved rotational spectroscopic data for barium monofluoride, BaF

TL;DR

This work presents sub-kHz precision FTMW measurements of pure rotational transitions in BaF for five isotopologues, integrated with prior microwave data through a global SPFIT fit to refine the $X^2\Sigma^{+}$ state Hamiltonian. A comprehensive Born-Oppenheimer breakdown analysis reveals that both nuclear-size field shifts and a smaller mass-dependent term govern the observed offsets in the leading rotational constant $Y_{01}$, with the odd-even nuclear-radius staggering playing a crucial role. The study delivers improved hyperfine constants, notably $\gamma$, $b_F(F)$, $c(F)$, and $eQq_0$ for odd isotopologues, and introduces refined $C_I$ terms for Ba and F nuclei. These results enhance BaF’s utility as a benchmark for fundamental-physics tests such as the electron EDM and nuclear anapole moment searches and corroborate King-plot interpretations of nuclear-size effects.

Abstract

New high-precision microwave spectroscopic measurements and analysis of rotational energy level transitions in the ground vibronic state of the open-shell BaF molecule are reported with the purpose of contributing to studies of physics beyond the Standard Model. BaF is currently among the key candidate molecules being examined in the searches for a measurable electron electric dipole moment, eEDM, as well as the nuclear anapole moment. Employing Fourier-transform microwave spectroscopy, these new pure rotational transition frequencies for the 138Ba19F, 137Ba19F, 136Ba19F, 135Ba19F, and 134Ba19F isotopologues are analyzed here in a combined global fit with previous microwave data sets for 138Ba19F (v = 0 - 4), 137Ba19F, and 136Ba19F using the program SPFIT. As a result, hyperfine parameters are significantly improved, and we observe a distinctive structure in a Born-Oppenheimer breakdown (BOB) analysis of the primary rotational constant. This can be understood using the nuclear field shifts due to the known isotopic variation in the size of barium nuclei and in combination with the smaller linear mass-dependent BOB terms.

Figures (2)

• Figure 1: Examples of BaF spectra, including the strong $^{138}$Ba$^{19}$F transition near 12988.1 MHz (the 5th $^{138}$Ba$^{19}$F entry in Table \ref{['tab:BaF Data']}) and a pair of weaker transitions from $^{136}$Ba$^{19}$F near 12977.2 MHz and $^{135}$Ba$^{19}$F near 12977.5 MHz (the 3rd entry for both isotopologues in Table \ref{['tab:BaF Data']}). All three signals exhibit the characteristic double-peak feature as a result of the Doppler shifted components within the resonator; the rest frequency is the arithmetic mean of the two peak frequencies COBRA_1. Experimental conditions were optimized for the central transitions, and the TEM-mode's Gaussian envelope function reduces the relative intensity of the $^{136}$Ba$^{19}$F transition compared to the more central $^{135}$Ba$^{19}$F transition.
• Figure 2: Visualization of the $Y_{01}$ offsets in the final fit (black solid line) as the sum of mass shift BOB (dotted) and field shift (dashed) contributions. The black data points represent the free floating offsets and associated 1$\sigma$ uncertainties from Table \ref{['tab:Mass and Field Shift Table']}. Note that the staggered trend of the field shift values (scaled on the right axis using the linear relationship in Eq. \ref{['eq:Y01massdep']}