Energy of the $^{229}$Th nuclear clock transition

Abstract: The first nuclear excited state of $^{229}$Th offers the unique opportunity for laser-based optical control of a nucleus. Its exceptional properties allow for the development of a nuclear optical clock which offers a complementary technology and is expected to outperform current electronic-shell based atomic clocks. The development of a nuclear clock was so far impeded by an imprecise knowledge of the energy of the $^{229}$Th nuclear excited state. In this letter we report a direct excitation energy measurement of this elusive state and constrain this to 8.28$\pm$0.17 eV. The energy is determined by spectroscopy of the internal conversion electrons emitted in-flight during the decay of the excited nucleus in neutral $^{229}$Th atoms. The nuclear excitation energy is measured via the valence electronic shell, thereby merging the fields of nuclear- and atomic physics to advance precision metrology. The transition energy between ground and excited state corresponds to a wavelength of 149.7$\pm$3.1 nm. These findings set the starting point for high-resolution nuclear laser spectroscopy and thus the development of a nuclear optical clock of unprecedented accuracy. A nuclear clock is expected to have a large variety of applications, ranging from relativistic geodesy over dark matter research to the observation of potential temporal variation of fundamental constants.

• The paper presents a direct measurement of the 229Th nuclear isomer energy at 8.28 ± 0.17 eV using internal conversion decay.
• It employs an innovative experimental setup with ion extraction, graphene-based neutralization, and a magnetic bottle retarding field spectrometer achieving a 3% FWHM resolution.
• The results lay a critical foundation for developing nuclear optical clocks with transformative applications in precision metrology and fundamental physics.

Measurement of the Energy of the $^{229m} \text{Th}$ Nuclear Clock Transition

The paper discusses the precise measurement of the energy of the first nuclear excited state of $^{229m} \text{Th}$, which holds significant promise for developing a nuclear optical clock. Previous attempts to determine the energy of this state have relied on indirect methods, often with considerable uncertainty due to the limitations of detector resolution. This research presents a direct measurement using the internal conversion (IC) decay channel in neutral $^{229} \text{Th}$ atoms, providing an energy constraint of $8.28 \pm 0.17$ eV.

Experimental Setup and Findings

The authors employed a comprehensive experimental setup including ion extraction, neutralization, and electron spectrometry to achieve the direct measurement. The ion beam was generated from a $^{233} \text{U}$ source, followed by neutralization of the $^{229(m)} \text{Th}$ ions in graphene layers. The decay of the isomeric state was monitored through IC electron emission, where the kinetic energy of emitted electrons was analyzed using a magnetic bottle-type retarding field spectrometer. This novel spectrometry technique allowed the authors to achieve a first width half maximum (FWHM) resolution of about 3%, revealing the transition energy with significant precision.

Implications and Applications

The ability to manipulate nuclear states via optical transitions offers an intriguing alternative to electronic shell transitions. An optical clock based on $^{229m} \text{Th}$ could significantly surpass existing atomic clock technologies due to the extraordinary properties of the nuclear excited state, particularly its narrow linewidth and long radiative lifetime. Such a nuclear clock could have transformative applications ranging from relativistic geodesy to dark matter research, as well as monitoring potential temporal variations in fundamental physical constants.

Theoretical Considerations

The theoretical considerations hinge on the electron spectrometer’s ability to discern electronic state contributions to the IC process, helping resolve the spectrum's complex structure. Density functional theory (DFT) calculations played a crucial role, simulating possible electron configurations in the decay process. Selecting accurate initial states is vital as their distributions impact the measurement's systematic uncertainty significantly.

Future Outlook

This achievement sets a foundation for high-resolution nuclear laser spectroscopy and the eventual realization of a nuclear optical clock demonstrating unprecedented accuracy. It opens pathways for further exploration into nuclear transitions and their utility in precision metrology. The methodological advancements demonstrated by the authors will also likely spur new developments in the instrumentation required for such measurements, potentially bridging atomic and nuclear precision metrics.

Conclusion

The paper offers a substantial step forward in nuclear metrology by directly measuring the energy of the $^{229m} \text{Th}$ isomer. This provides the critical parameters needed for advancing nuclear clock technology, promising enhancements in the reliability and precision of time measurement standards. It is a landmark in the cross-disciplinary integration of atomic physics methodologies into nuclear science, with prospective benefits across a range of scientific and practical domains.