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# Energy of the 229Th nuclear clock transition

## Abstract

Owing to its low excitation energy and long radiative lifetime, the first excited isomeric state of thorium-229, 229mTh, can be optically controlled by a laser1,2 and is an ideal candidate for the creation of a nuclear optical clock3, which is expected to complement and outperform current electronic-shell-based atomic clocks4. A nuclear clock will have various applications—such as in relativistic geodesy5, dark matter research6 and the observation of potential temporal variations of fundamental constants7—but its development has so far been impeded by the imprecise knowledge of the energy of 229mTh. Here we report a direct measurement of the transition energy of this isomeric state to the ground state with an uncertainty of 0.17 electronvolts (one standard deviation) using spectroscopy of the internal conversion electrons emitted in flight during the decay of neutral 229mTh atoms. The energy of the transition between the ground state and the first excited state corresponds to a wavelength of 149.7 ± 3.1 nanometres, which is accessible by laser spectroscopy through high-harmonic generation. Our method combines nuclear and atomic physics measurements to advance precision metrology, and our findings are expected to facilitate the application of high-resolution laser spectroscopy on nuclei and to enable the development of a nuclear optical clock of unprecedented accuracy.

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## Data availability

Drawings of the spectrometer are available from the corresponding author on request.

## References

1. Kroger, L. A. & Reich, C. W. Features of the low-energy level scheme of 229Th as observed in the α-decay of 233U. Nucl. Phys. A 259, 29–60 (1976).

2. von der Wense, L. et al. Direct detection of the 229Th nuclear clock transition. Nature 533, 47–51 (2016).

3. Peik, E. & Tamm, C. Nuclear laser spectroscopy of the 3.5 eV transition in 229Th. EPL 61, 181–186 (2003).

4. Campbell, C. J. et al. Single-ion nuclear clock for metrology at the 19th decimal place. Phys. Rev. Lett. 108, 120802 (2012).

5. Mehlstäubler, T. E. et al. Atomic clocks for geodesy. Rep. Prog. Phys. 81, 064401 (2018).

6. Derevianko, A. & Pospelov, M. Hunting for topological dark matter with atomic clocks. Nat. Phys. 10, 933–936 (2014).

7. Flambaum, V. V. Enhanced effect of temporal variation of the fine structure constant and the strong interaction in 229Th. Phys. Rev. Lett. 97, 092502 (2006).

8. Reich, C. W. & Helmer, R. G. Energy separation of the doublet of intrinsic states at the ground state of 229Th. Phys. Rev. Lett. 64, 271–273 (1990).

9. Helmer, R. G. & Reich, C. W. An excited state of 229Th at 3.5 eV. Phys. Rev. C 49, 1845–1858 (1994).

10. Beck, B. R. et al. Energy splitting of the ground-state doublet in the nucleus 229Th. Phys. Rev. Lett. 98, 142501 (2007).

11. Beck, B.R. et al. Improved Value for the Energy Splitting of the Ground-State Doublet in the Nucleus 229m Th. Report No. LLNL-PROC-415170 (Los Alamos National Laboratory, 2009).

12. Tkalya, E. V. et al. Radiative lifetime and energy of the low-energy isomeric level in 229Th. Phys. Rev. C 92, 054324 (2015).

13. Minkov, N. & Pálffy, A. Reduced transition probabilities for the gamma decay of the 7.8 eV isomer in 229Th. Phys. Rev. Lett. 118, 212501 (2017).

14. Rellergert, W. D. et al. Constraining the evolution of the fundamental constants with a solid-state optical frequency reference based on the 229Th nucleus. Phys. Rev. Lett. 104, 200802 (2010).

15. Karpeshin, F. F. & Trzhaskovskaya, M. B. Impact of the electron environment on the lifetime of the 229Thm low-lying isomer. Phys. Rev. C 76, 054313 (2007).

16. Burke, D. G., Garrett, P. E., Qu, T. & Naumann, R. A. Nuclear structure of 229,231Th studied with the 230,232Th(d, t) reactions. Nucl. Phys. A 809, 129–170 (2008).

17. Raeder, S. et al. Resonance ionization spectroscopy of thorium isotopes – towards a laser spectroscopic identification of the low-lying 7.6 eV isomer of 229Th. J. Phys. At. Mol. Opt. Phys. 44, 165005 (2011).

18. Jeet, J. et al. Results of a direct search using synchrotron radiation for the low-energy 229Th nuclear isomeric transition. Phys. Rev. Lett. 114, 253001 (2015).

19. Yamaguchi, A. et al. Experimental search for the low-energy nuclear transition in 229Th with undulator radiation. New J. Phys. 17, 053053 (2015).

20. Stellmer, S. et al. Attempt to optically excite the nuclear isomer in 229Th. Phys. Rev. A 97, 062506 (2018).

21. Borisyuk, P. V. et al. Experimental studies of thorium ion implantation from pulse laser plasma into thin silicon oxide layers. Laser Phys. Lett. 15, 056101 (2018).

22. Stellmer, S. et al. Toward an energy measurement of the internal conversion electron in the deexcitation of the 229Th isomer. Phys. Rev. C 98, 014317 (2018).

23. Campbell, C. J., Radnaev, A. G. & Kuzmich, A. Wigner crystals of 229Th for optical excitation of the nuclear isomer. Phys. Rev. Lett. 106, 223001 (2011).

24. Kazakov, G. A. et al. Prospects for measuring the 229Th isomer energy using a metallic magnetic microcalorimeter. Nucl. Instrum. Meth. A 735, 229 (2014).

25. Bilous, P. V. et al. Internal conversion from excited electronic states of 229Th ions. Phys. Rev. A 95, 032503 (2017).

26. von der Wense, L. et al. A laser excitation scheme for 229mTh. Phys. Rev. Lett. 119, 132503 (2017).

27. Masuda, T. et al. X-ray pumping of the 229Th nuclear clock isomer. Nature https://doi.org/10.1038/s41586-019-1542-3 (2019).

28. Seiferle, B., v. d. Wense, L. & Thirolf, P. G. Lifetime measurement of the 229Th nuclear isomer. Phys. Rev. Lett. 118, 042501 (2017).

29. Thielking, J. et al. Laser spectroscopic characterization of the nuclear-clock isomer 229mTh. Nature 556, 321–325 (2018).

30. Yamakita, Y. et al. A highly sensitive electron spectrometer for crossed-beam collisional ionization: a retarding-type magnetic bottle analyzer and its application to collision-energy resolved Penning ionization electron spectroscopy. Rev. Sci. Instrum. 71, 3042–3049 (2000).

31. Seiferle, B. et al. Towards a precise determination of the excitation energy of the Thorium nuclear isomer using a magnetic bottle spectrometer. Preprint at https://arxiv.org/abs/1812.04621 (2018).

32. Arnau, A. et al. Interaction of slow multicharged ions with solid surfaces. Surf. Sci. Rep. 27, 113 (1997).

33. Lias S. G. Ionization energy evaluation. NIST Chemistry WebBook, NIST Standard Reference Database Number 69 (eds Linstrom P. J. & Mallard, W. G.) (National Institute of Standards and Technology, 2005).

34. van der Wense, L. et al. Determination of the extraction efficiency for 233U source α-recoil ions from the MLL buffer-gas stopping cell. Eur. Phys. J. A 51, 29 (2015).

35. van der Wense, L. On the Direct Detection of 229m Th (Springer, 2018).

36. Eberhardt, K. et al. Actinide targets for fundamental research in nuclear physics. AIP Conf. Proc. 1962, 030009 (2018).

37. Haettner, E. et al. A versatile triple radiofrequency quadrupole system for cooling, mass separation and bunching of exotic nuclei. Nucl. Instrum. Meth. A 880, 138–151 (2018).

38. Amersdorffer, I. Charge-exchange of 229(m)Th ions in carbon foils. BSc thesis, Ludwig-Maximilians Univ. (2018).

39. Eland, J. H. D. Photoelectron Spectroscopy (Elsevier, 1984).

40. Harada, K., Wada, T. & Tanaka, T. Near-infrared diode laser spectroscopy of the (2, 0) band of the $${A}^{{\rm{2}}}{\Pi }_{{\rm{u}}}-{X}^{2}{\Sigma }_{{\rm{g}}}^{+}$$ system of the $${{\rm{N}}}_{2}^{+}$$ion. J. Mol. Spectrosc. 163, 436–442 (1994).

41. Gardner, J. L. & Samson, J. A. R. Calibration of electron spectrometers. J. Electron Spectrosc. 8, 469–474 (1976).

42. Karpeshin, F. F. & Trzhaskovskaya, M. B. Impact of the ionization of the atomic shell on the lifetime of the 229mTh isomer. Nucl. Phys. A 969, 173 (2018).

43. Pálffy, A., Scheid, W. & Harman, Z. Theory of nuclear excitation by electron capture for heavy ions. Phys. Rev. A 73, 012715 (2006).

44. Blaise, J. & Wyart, J.-F. Database of Selected Constants, Energy Levels and Atomic Spectra of Actinides http://web2.lac.u-psud.fr/lac/Database/Tab-energy/Thorium/ (2014).

45. Jönsson, P. et al. New version: Grasp2k relativistic atomic structure package. Comput. Phys. Commun. 184, 2197–2203 (2013).

46. Bilous, P. V., Minkov, N. & Pálffy, A. Electric quadrupole channel of the 7.8 eV 229Th transition. Phys. Rev. C 97, 044320 (2018).

47. Fritzsche, S. The RATIP program for relativistic calculations of atomic transition, ionization and recombination properties. Comput. Phys. Commun. 183, 1525 (2012).

48. Burgdörfer, J., Lerner, P. & Meyer, F. W. Above-surface neutralization of highly charged ions: the classical over-the-barrier model. Phys. Rev. A 44, 5674 (1991).

49. Gruber, E. et al. Ultrafast electronic response of graphene to a strong and localized electric field. Nat. Commun. 7, 13948 (2016).

50. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996); erratum 78, 1396 (1997).

51. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

52. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1774 (1999).

53. Behrens, R. G. et al. Th Thorium: General Properties. Spectra. Recoil Reactions. Gmelin Handbook of Inorganic Chemistry (Springer, 1989).

54. Roy, S. K. Prasad, R. & Chandra, P. Electron correlation and relativistic effects in atomic structure calculations of the thorium atom. J. Chem. Phys. 134, 234302 (2011).

## Acknowledgements

We acknowledge discussions with D. Habs, J. Weitenberg, M. Laatiaoui, A. Ulrich, W. Plaß and colleagues, J. Crespo, C. Weber, F. Zacherl and K. Beeks and we thank K. Eberhardt, C. Mokry, J. Runke and N. Trautmann for producing the 233U and 234U sources. This work was supported by DFG (Th956/3-2), by the LMU Chair of Medical Physics via the Maier-Leibnitz Laboratory Garching and by the European Union’s Horizon 2020 research and innovation programme under grant agreement number 664732 (nuClock).

## Author information

Authors

### Contributions

B.S., L.v.d.W. and I.A. performed the experiments. B.S., L.v.d.W., P.V.B., I.A., S.S., C.L., F.L., T.S., C.E.D., A.P. and P.G.T. discussed the experimental results. P.V.B. and A.P. performed the theoretical calculations. The radioactive sources were produced in C.E.D.’s group. C.L. and F.L. performed the DFT calculations. B.S., L.v.d.W. and P.G.T. wrote the manuscript with input from all authors.

### Corresponding author

Correspondence to Benedict Seiferle.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Peer review information Nature thanks Jason Burke, Feodor Karpeshin and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

## Extended data figures and tables

### Extended Data Fig. 1 Sectional view of the focusing and bending electrodes and the collection region.

a, Top view. b, Lateral view. Ions are focused by focusing electrodes (labelled ‘1’, ‘2’, ‘3’ and ‘4’) onto graphene. A large fraction (50%) of the ions is neutralized. Secondary electrons, as well as ions that are not neutralized, are deflected by bending electrodes and cannot enter the spectrometer collection region. A grid placed at the entrance of the collection region is used to shield electric radiofrequency and d.c. fields. The collection region is accessible via several ports to allow calibration. For the calibration a gas discharge lamp is used and photoelectrons are generated along the line indicated by the arrow (labelled ‘He I radiation’). An MCP detector is used to monitor the ion and atom extraction.

### Extended Data Fig. 2 Sectional view of the magnetic-bottle-type retarding-field electron spectrometer.

The retarding-field voltage is applied to the central grid in the retarding-field unit. The outer grids are kept grounded and the electrodes between them are biased via a voltage divider chain.

### Extended Data Fig. 3 Experimental scheme.

a–c, A mixed-ion cloud (containing Th2+ and Th3+ ions) is trapped in a segmented RFQ magnet (blue area). The cloud/bunch (white) is released and injected into the QMS (red area), which serves as an ion guide. The difference in kinetic energy (Th3+ ions are faster than Th2+ ions) leads to a temporal separation of the two charge states. The ion bunches are then neutralized in graphene and continue their flight as atoms (black). The atoms are counted with an MCP detector (MCP II). A time-of-flight spectrum is shown in b (the corresponding measurement is presented in Extended Data Fig. 4b). The neutralization also triggers the internal conversion decay of the 229mTh nuclear isomer. When 229mTh decays inside the collection region of the electron spectrometer, the internal conversion (IC) electron is guided towards MCP I and generates a signal. The time-resolved signal, as well as the time windows that are used to count the internal conversion electrons, are shown in c (a measurement is shown in Extended Data Fig. 4a). cts, number of counts. Dimensions are not to scale.

### Extended Data Fig. 4 Internal conversion electron signal.

a, b, Internal conversion electron signal measured with MCP I at two different retarding voltages (a). Th3+ (Th2+) ions generate a signal at t ≈ 80 μs (t ≈ 97 μs) from the release of the ion bunch. 105 bunches were recorded for each retarding voltage. The number of counts from neutralized atoms measured with MCP II are shown in b (for 2.25 × 106 bunches recorded). We note that the ratio of the Th2+ and Th3+ peaks from a is not reflected in b. This can be explained as follows: in the Th2+ charged state, 229Th and 233U are extracted from the buffer-gas stopping cell at approximately equal rates, whereas the extraction rate in the Th3+ charged state is dominated by 229Th (see ref. 34). In our setup, thorium cannot be separated from uranium by the time-of-flight method; therefore, it can be expected that only 50% of the Th2+ peak in b results from neutralized 229Th2+ ions. By contrast, the internal conversion electron signal results solely from neutralized 229mTh ions.

### Extended Data Fig. 5 Comparative measurements.

Comparative measurement of 230Th and 229(m)Th at a blocking voltage of 0 V. For the 229(m)Th (230Th) measurement, 5,000 (>800,000) bunches were recorded. To compare 230Th with 229(m)Th, the number of counts was normalized to the number of extracted atoms measured with MCP II (see Extended Data Fig. 3). Constant background has been subtracted in the 230Th measurement.

### Extended Data Fig. 6 Calibration measurements.

Measured (integrated) calibration spectra (red) and their derivatives, shown together with a fitting function (black). For better visualization, data and derivatives are normalized to their respective maxima. The energy scale has been corrected for surface potentials. Measurements were obtained as detailed in ref. 31. a, Typical argon calibration spectrum used in the measurements (electron kinetic energies of 5.46 eV and 5.28 eV). b, Neon calibration spectrum, showing a clear separation of the two lines (electron kinetic energies of 1.52 eV and 1.43 eV). arb., arbitrary units.

### Extended Data Fig. 7 Monitoring of the applied blocking voltages.

a, Time-resolved behaviour of the applied retarding voltages. Retarding voltages between −0.5 V and −3.5 V are applied in steps of −0.1 V. Each retarding voltage is held for 1,000 bunches (about 100 s). Before incrementing the voltage, it is set to 0 V to make the measurement independent from the order in which the voltages are applied. b, Distribution of an exemplary retarding voltage over three days of measurement. The stability is better than 10 mV and limited by temperature fluctuations.

### Extended Data Fig. 8 Single-electron orbital energies for thorium.

Single-electron (Kohn–Sham) orbital energies for a thorium atom as a function of the distance from the topmost carbon layer, located at z = 0 Å. Screening of the core by the target’s electrons leads to distance-dependent shifts of the orbital energies. The 6s and 6p states (asymptotic energies of about −40 eV and −20 eV, respectively) remain atomic in graphene, whereas higher orbitals (7s, 6d, 5f) become resonant with the graphene valence bands (overlapping red and green shaded areas, indicating the region of high electron density in the target) at different distances. In the target, a prevalence of states with f characteristic (purple symbols) is observed. EF denotes the Fermi energy.

### Extended Data Fig. 9 Summary of internal conversion electron rates.

Bottom, possible values for IP − Ei + Ef, given by the internal conversion selection rules for even (blue) and odd (red) initial electronic states of Th. Initial states are numbered according to their state index (given in Extended Data Table 1). The ionization potential of the Th atom is shown by the black dashed line. The size of the symbols indicates the transition rate from an initial state to a final state. Top, projection of the data shown in the lower panel onto the horizontal axis (energy bin, 0.1 eV).

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Seiferle, B., von der Wense, L., Bilous, P.V. et al. Energy of the 229Th nuclear clock transition. Nature 573, 243–246 (2019). https://doi.org/10.1038/s41586-019-1533-4

• Accepted:

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• DOI: https://doi.org/10.1038/s41586-019-1533-4

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