&Bullet; physics 14, 103

New research shows that radioactive molecules can be used to study the variation in shape and size of exotic nuclei, which are particularly sensitive to fundamental symmetry violations.

Since matter and antimatter have near-perfect symmetry with respect to the laws of physics as we know them, physicists expect that equal amounts of matter and antimatter were present in the early universe. But the agreement of increasingly precise astronomical and cosmological observations indicates that the visible universe is completely dominated by matter and that there is hardly any antimatter left. What caused the preponderance of matter? Physicists suspect that the answer to this question lies in fundamental symmetry violations, for example in subatomic particle interactions, which are not the same when the time arrow is reversed [1, 2] . A promising approach to finding these injuries is to study certain pear-shaped radioactive nuclei in polar molecules (see Viewpoint: Designer Molecules for Fundamental-Symmetry Tests). Research has shown that the energy spectra of such molecules are exceptionally sensitive probes for symmetry violations [3, 4] . To harness this discovery potential, researchers need to develop a better understanding of the energy spectra of these radioactive molecules. In particular, they need to quantify how the interactions between the nuclei of a molecule and the electrons affect the quantum mechanical energy levels of the molecule. Silviu-Marian Udrescu from the Massachusetts Institute of Technology and co-workers have now investigated this question by measuring the quantum mechanical energy levels of radium monofluoride (RaF) molecules with different Ra isotopes [5] . Taking into account the core sizes of the various Ra isotopes, the team determined the isotope shifts of these energy levels and tested quantum chemical models to predict molecular spectra [5] . This new approach will help researchers develop increasingly sensitive symmetry violation tests using molecules with this and other heavy nuclei.

Testing symmetry violations with these molecules requires a detailed understanding of molecular energy levels. Nuclei influence the energy levels of atoms through their interactions with the electrons. In heavy nuclei, the key factors influencing energy levels are the size and variation in electron density within the nucleus volume. Laser spectroscopic measurements of transitions between energy levels in atoms, in conjunction with atomic theory, make it possible to obtain quantitative information about the shapes and sizes of nuclei in a way that is independent of nuclear models [6] . This technique provides a powerful test of core structure theories aimed at predicting these properties. Changing the number of neutrons within the nucleus for a given chemical element results in a small but measurable shift in atomic energy levels known as an isotope shift. Measurements of isotope shifts in atoms for isotope chains have shown the variations in shape and size of atomic nuclei, as recent work in Nobelium showed (see Focus: Laser Bags a Giant Nucleus) [7] . Although these isotope shifts can also be observed in molecules, they have not yet been measured in molecules containing nuclei heavier than lead.

Udrescu and co-workers have now measured isotope shifts in RaF for a number of Ra isotopes (with atomic weights of 223–226 and 228) using laser spectroscopy. By combining these isotope shifts with literature values ​​for the size of Ra isotopes, the researchers extracted the isotope shift constant, a quantity that describes the influence of nucleus size on isotope shift. They then compared the measured isotope shift constant with that derived from quantum chemical calculations. Since this constant is critically sensitive to the overlap of the electronic quantum mechanical wave function with the core volume, this comparison with experiments offers a rigorous test of the quantum chemical theories.

The researchers produced Ra isotopes on the Isotope Separator Online Device (ISOLDE) at CERN by bombarding a uranium target with high-energy protons [8] . The team has formed

${\text{RaF}}^{+}$

Molecular ions by heating this target in the presence of carbon tetrafluoride gas. These molecular ions were then extracted, mass selected, cooled, focused and neutralized to form a pulsed beam of neutral RaF molecules with a specific Ra isotope. In order to carry out spectroscopic measurements of the energy transitions of interest, the researchers illuminated these neutral molecules with a laser, the frequency of which could be scanned through the molecular spectra. The resonantly excited molecules were then re-ionized with a second laser beam with a different, fixed frequency. An ion detector then counted the resulting RaF + molecular ions as a function of the tunable laser frequency. The experimental isotope shift constant was finally derived by fitting a line to a diagram of the measured shifts as a function of the core sizes of the Ra isotopes known from the literature.

The researchers also calculated the isotopic shift constant using relativistic molecular theory codes. Although the RaF molecule has only one valence electron, the researchers performed the calculations taking into account the 17 outermost electrons and their correlations. They also performed a limited set of more time-consuming and accurate calculations with 27 correlated electrons and used these results to scale the results of the 17-electron calculations. The calculations were not overly sensitive to the exact shape of the nuclear charge distribution and were in agreement with experimental results to within 10%. In addition, the team used the empirically determined isotopic shift constants to derive the difference in the effective electron density between the ground and excited states for the transition under study. This difference, which also agreed well with the quantum chemical calculations, is important because it largely determines the surprisingly high sensitivity of the molecular energy levels to nuclear size effects.

The results of this work show that the technique can measure molecular isotopic shifts with sufficient precision to study the variation of nuclear shapes and sizes along the isotopic chain of a heavy element. This conclusion has important implications for the study of the core structure of exotic actinide cores, which are more accessible in molecular form than as isolated atoms. In addition, the successful benchmarking of quantum chemical calculations with experimental data is particularly valuable, as the reliability of these calculations is the key to understanding the electron-nucleus interactions that determine the sensitivity of radioactive molecules to violations of fundamental symmetries.

Certain radioactive pear-shaped cores, such as B. Protactinium Cores [9] and the Ra cores [10] investigated by Udrescu and colleagues, have an excellent sensitivity to fundamental symmetry violations [11] . This sensitivity can be increased by examining these exotic nuclei inside polar molecules like RaF. By increasing the spectral resolution of the laser, the researchers can investigate nuclear spin-related effects in RaF and other radioactive molecules such as thorium monoxide (ThO) and protactinium monoxide (PaO). More accurate measurements of molecular isotopic shifts could also enable researchers to look for new types of exotic forces (see Synopsis: Hints of Dark Bosons).

## References

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${\text{RaOH}}^{+}$

and

${\text{RAOCH}}_{3}^{+}$

Phys. Rev. Lett.126, 023002 (2021).

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