Observation of the distribution of nuclear magnetization in a molecule

TL;DR

We demonstrate that precision laser spectroscopy of $^{225}$Ra$^{19}$F, combined with high-level ab initio molecular calculations, probes the distribution of nuclear magnetization in $^{225}$Ra via the Bohr-Weisskopf effect reflected in hyperfine structure. The study reports 54 measured transitions, extracts the ground-state hyperfine constant $A_\perp$ and a ~5% BW contribution, and computes symmetry-violating electronic form factors ($E_{\rm eff}$, $W_{P,T}$, $W_a$, $W_S$), enabling quantitative predictions of hadronic CP-violation in RaF. The excellent agreement with theory validates the electronic wavefunction in the nuclear region and establishes RaF as a powerful platform for testing nuclear models and pursuing fundamental physics, including higher-order moments and CP-violation, with realistic prospects for mHz precision given sufficient molecular production and coherence time.

Abstract

Rapid progress in the experimental control and interrogation of molecules, combined with developments in precise calculations of their structure, are enabling new opportunities in the investigation of nuclear and particle physics phenomena. Molecules containing heavy, octupole-deformed nuclei such as radium are of particular interest for such studies, offering an enhanced sensitivity to the properties of fundamental particles and interactions. Here, we report precision laser spectroscopy measurements and theoretical calculations of the structure of the radioactive radium monofluoride molecule, $^{225}$Ra$^{19}$F. Our results allow fine details of the short-range electron-nucleus interaction to be revealed, indicating the high sensitivity of this molecule to the distribution of magnetization, currently a poorly constrained nuclear property, within the radium nucleus. These results provide a direct and stringent test of the description of the electronic wavefunction inside the nuclear volume, highlighting the suitability of these molecules to investigate subatomic phenomena.

Figures (3)

• Figure 1: Experimental setup. (A) Radium fluoride molecules are produced by impinging $1.4$-GeV protons on a high-temperature (T$=2000$ K) uranium carbide target, injected with CF$_4$ gas, then surfaced ionized and extracted using electrostatic fields (I). $^{225}$RaF is mass-selected (II) and trapped in a He-filled radiofrequency quadrupole (T = 300 K) for up to $20$ ms (III). The bunched RaF ions are guided using electrostatic deflectors (IV), neutralized in a Na-filled charge-exchange cell (V), then overlapped with 3 pulsed lasers in a collinear geometry (VI). The resulting RaF ions are deflected and detected using an ion detector (VII). (B) Example of energy levels involved in a transition between hyperfine levels in an R-branch (not to scale). N, J and F correspond to the rotational, electronic and total angular momentum quantum numbers of the molecule (N and J are not good quantum numbers when $\mathrm{I} > 0$). Experimentally observed transitions are shown by upwards-pointing arrows and numbered. (C) Example of measured spectra showing the ion rate in arbitrary units (a.u.) as a function of the wavenumber of the first laser, Doppler corrected to the molecular rest frame and shifted by $T_{\Pi}$. The error bars show one standard deviation statistical uncertainty. Data points are connected by straight lines to guide the eye. The numbering on the individual peaks corresponds to the transitions shown in (B).
• Figure 2: Nuclear effects in the RaF molecule due to the Ra nucleus. (A) Extracted values of the magnetic moment of $^{225}$Ra, $\mu\left(^{225}\mathrm{Ra}\right)$, in units of nuclear magnetons, $\mu_N$, assuming the Ra nucleus is a point-like magnetic dipole (left) and accounting for the distribution of the nuclear magnetization inside of the Ra nucleus (right). The difference between the two, $\mu_{BW}$($^{225}$Ra), corresponds to the effect of the distribution of the nuclear magnetization and amounts to $\sim 5\%$ of the total value of $\mu\left(^{225}\mathrm{Ra}\right)$. The black and blue error bars are the experimental and total (experimental plus theoretical) uncertainties, respectively. The center and thickness of the orange band correspond to the previously measured value and associated uncertainty of $\mu$($^{225}$Ra) in an atom arnold1987direct. (B) Evolution of the calculated $A_\perp$ for increasing levels of theoretical sophistication (see main text and the Supplementary Materials for more details) skripnikov2020nuclear. (C) Order-of-magnitude estimation of nuclear effects due to Ra nucleus on the energy levels of $^{223,225}$RaF. From left to right: changes in nuclear charge radius between Ra isotopes udrescu2021isotope, point-like magnetic dipole moment, electric quadrupole moment petrov2020energy, distribution of nuclear magnetization, anapole moment, nuclear Schiff moment flambaum2019enhancedgraner2016reduced, magnetic quadrupole moment flambaum2022enhanced. The electric and magnetic quadrupole moments are nonzero only for Ra isotopes with nuclear spin $\mathrm{I}>1/2$, such as $^{223}$Ra.
• Figure 3: Example of measured spectra for the $0' \leftarrow 0"$ transitions. In the center, in blue, the fitted combined hyperfine and rovibronic spectrum of $^{225}$RaF obtained for $J\le 100$, over a range of $\sim 50$ cm$^{-1}$ is presented. Figures in magnified views show measured spectra for different regions in frequency space. The connected red dots show the experimental data, while the continuous blue lines represents the best fits to the data. The errorbars show one standard deviation statistical uncertainty. The values on the x-axis correspond to the wavenumber of the first laser used in the resonance ionization scheme, Doppler corrected to the molecular rest frame. The rate on the y-axis is given in arbitrary units (a.u.).