Laser spectroscopy and CP-violation sensitivity of actinium monofluoride

Abstract

The apparent invariance of the strong nuclear force under combined charge conjugation and parity (CP) remains an open question in modern physics. Precision experiments with heavy atoms and molecules can provide stringent constraints on CP violation via searches for effects due to permanent electric dipole moments and other CP-odd properties in leptons, hadrons, and nuclei. Radioactive molecules have been proposed as highly sensitive probes for such searches, but experiments with most such molecules have so far been beyond technical reach. Here we report the first production and spectroscopic study of a gas-phase actinium molecule, $^{227}$AcF. We observe the predicted strongest electronic transition from the ground state, which is necessary for efficient readout in searches of symmetry-violating interactions. Furthermore, we perform electronic- and nuclear-structure calculations for $^{227}$AcF to determine its sensitivity to various CP-violating parameters, and find that a realistic, near-term experiment with a precision of 1 mHz would improve current constraints on the CP-violating parameter hyperspace by three orders of magnitude. Our results thus highlight the potential of $^{227}$AcF for exceptionally sensitive searches of CP violation.

Figures (4)

• Figure 1: Schematic of the experiment. From top left: (a) Target and ion-source unit releasing Ac to form AcF$_x$ molecules from injected CF$_4$. (b) All species are ionized by accelerated electrons within the anode volume and extracted across a voltage difference (40 kV) to ground potential. The ion beam is then (c) mass-separated, (d) cooled and bunched before (e) neutralization via charge exchange with sodium vapor and laser resonance ionization. Inset (f) shows the time-of-flight (TOF) spectrum of the ion beam after 2000 revolutions in a multi-reflection TOF mass spectrometer Wolf2013Au2024AcFx. Expected TOF for $^{227}$Ac$^{19}$F$^+$ ($t_{1/2}=21.7$ y) and $^{227}$Ra$^{19}$F$^+$ ($t_{1/2}=42.5$ min) shown in red and blue lines, respectively. The x-axis is offset by the expected TOF for $^{227}$Ac$^{19}$F$^+$. No molecules other than $^{227}$Ac$^{19}$F$^+$ were identified in the beam.
• Figure 2: Spectroscopy of AcF and molecular sensitivity to nuclear CP-odd properties. (a) Two-step laser resonance ionization scheme used to search for electronic transitions in AcF. (b) Spectrum of the measured vibronic transitions from the ground state in AcF, and simulation based on the contour-fitted molecular constants. (c) Assigned vibronic transitions observed in the spectrum shown in (b). (d) Fortrat diagrams for the measured vibronic transitions, showing the evolution of the $P$, $Q$, and $R$ branches along the diagonal vibrational progression. (e) Ion count rate as a function of the wavenumber of the first excitation laser across the full scanning range. A cubic Savitzky-Golay de-noising filter with a 10-point window length is applied to the raw data to assist in the visualization of data trends. The complete spectrum is constructed from multiple shorter scans. A vertical offset is applied to each scan to compensate for their different background rates due to long-term variations in the beam intensity. The $y$-axis is thus in arbitrary units. The red band marks the region of the spectrum in (b), and the gray bands mark regions investigated and excluded as resonant features. (f) Comparison of excitation wavenumbers to different electronic states calculated with FS-RCC Skripnikov2023AcF and the upper state in the spectrum of (b). The error bars correspond to the theoretical uncertainty in the excitation wavenumber calculations, as reported in Ref. Skripnikov2023AcF.
• Figure 3: Sensitivity of the $^{227}$Ac nucleus to CP violation. (a) Comparison of molecular sensitivity to the nuclear Schiff moment ($W_\mathcal{S}$), tensor-pseudotensor electron-nucleon interaction ($W_\mathrm{T}$), electric dipole moment of the electron ($W_\mathrm{d}$), and scalar-pseudoscalar electron-nucleon interaction ($W_\mathrm{sps}$) for the $^3\Delta_1$ electronic states in $^{229}$ThO and $^{229}$ThF$^+$, and for the $^1\Sigma^+$ electronic ground states in $^{227}$AcF, $^{205}$TlF, and $^{225}$RaOCH$^+_3$. (b) Comparison of the sensitivity coefficients (in units of $e$ fm$^3$) of the laboratory nuclear Schiff moment to the CP-odd pion-nucleon (isoscalar $a_0$, isovector $a_1$, isotensor $a_2$) and heavy-meson-exchange ($b_1$, $b_2$) interactions for different nuclei. Values for $^{227}$Ac are from this work, and for all other nuclei from Ref. Dobaczewski2018. (c) Comparison of the nuclear Schiff moment in the intrinsic body-fixed frame ($S_{\rm{int}}$) for $^{227}$Ac and $^{225}$Ra, calculated with nuclear density functional theory in this work and in Ref. Dobaczewski2018. (d) Expected magnitude of the CP-odd molecular energy shift in the laboratory due to the Schiff moment as a function of the QCD constant $\bar{\theta}$ for different molecules, taking into account the calculated $W_\mathcal{S}$ constant for each species. The teal line marks the precision needed to place a new bound on $\bar{\theta}$ using $^{227}$AcF.
• Figure 4: Cuts of selected two-dimensional subspaces of the full seven-dimensional CP-odd parameter space for different values of experimental precision of a proposed $^{227}$AcF experiment -- top: 0.1 mHz, bottom: 1 mHz. The electronic sensitivity factors for $^{227}$AcF used in the analysis, computed at the level of ZORA-cGKS-BHandH, are shown in Table \ref{['tab:ptodd_cghf']}, the calculated nuclear structure parameters are given in Table \ref{['tab:Schiff_coefficients_227Ac']}, and for the volume interaction with the short-range contribution to the proton EDM we use $R_\mathrm{vol} \approx 3.22\,\mathrm{fm}^2$, as discussed in the text. A theoretical uncertainty of 20% is considered, and the molecular sensitivity factors to all CP-odd properties in the hyperspace are conservatively scaled by a factor of $0.8$. The impact of a proposed $^{227}$AcF experiment is shown in a global analysis including existing experiments using $^{129}$Xe allmendinger:2019sachdeva:2019, $^{171}$Yb zheng:2022, $^{133}$Cs murthy:1989, $^{199}$Hg Graner2016, $^{205}$Tl regan:2002, $^{255}$Ra parker:2015Bishof2016, $^{174}$YbF hudson:2002hudson:2011, $^{180}$HfF$^{+}$roussy:2023, $^{205}$TlF cho:1991, $^{207}$PbO eckel:2013, and $^{232}$ThO andreev:2018, employing the experimental data given in the respective references within the global analysis. All electronic structure parameters for these experiments are taken from Ref. Gaul2024GlobalCP_new and were combined, where available, with nuclear structure data from Ref. Chupp2019. In other cases, rough estimates of nuclear structure parameters from Ref. Gaul2024GlobalCP_new were employed. The seven-dimensional ellipsoid is computed at the 95$\%$ confidence level.