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Penning trap mass measurements of the deuteron and the HD+ molecular ion

Abstract

The masses of the lightest atomic nuclei and the electron mass1 are interlinked, and their values affect observables in atomic2, molecular3,4,5 and neutrino physics6, as well as metrology. The most precise values for these fundamental parameters come from Penning trap mass spectrometry, which achieves relative mass uncertainties of the order of 10−11. However, redundancy checks using data from different experiments reveal considerable inconsistencies in the masses of the proton, the deuteron and the helion (the nucleus of helium-3), suggesting that the uncertainty of these values may have been underestimated. Here we present results from absolute mass measurements of the deuteron and the HD+ molecular ion using 12C as a mass reference. Our value for the deuteron mass, 2.013553212535(17) atomic mass units, has better precision than the CODATA value7 by a factor of 2.4 and differs from it by 4.8 standard deviations. With a relative uncertainty of eight parts per trillion, this is the most precise mass value measured directly in atomic mass units. Furthermore, our measurement of the mass of the HD+ molecular ion, 3.021378241561(61) atomic mass units, not only allows a rigorous consistency check of our results for the masses of the deuteron (this work) and the proton8, but also establishes an additional link for the masses of tritium9 and helium-3 (ref. 10) to the atomic mass unit. Combined with a recent measurement of the deuteron-to-proton mass ratio11, the uncertainty of the reference value of the proton mass7 can be reduced by a factor of three.

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Fig. 1: Overview of cyclotron frequency ratio (RCF) measurements on light ions.
Fig. 2: Details of the LIONTRAP setup.
Fig. 3: Averages of cyclotron frequency ratios.
Fig. 4: Most precise mass values for md.

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Data availability

The datasets analysed for this study are available from the corresponding author on reasonable request. Source data are provided with this paper.

Code availability

The analysis codes are available from the corresponding author on reasonable request.

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Acknowledgements

This study comprises parts of the PhD thesis work of S.R. We acknowledge discussions on the nuclear binding energy with M. Jentschel. This project received funding from the Max-Planck Society, from the International Max Planck Research School for Precision Tests of Fundamental Symmetries (IMPRS-PTFS) and Quantum Dynamics (IMPRS-QD), from the Max Planck–RIKEN–PTB Center for Time, Constants and Fundamental Symmetries and from the Helmholtz Excellence Network ExNet020, Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA+) of the Helmholtz Initiative and Networking Fund.

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Contributions

The experiment was performed by S.R., F.K.-L. and S. Sasidharan. The data were analysed by S.R, F.K.-L. and S. Sturm. The manuscript was written by S.R. The deuterated target was prepared by R.H., D.R. and C.E.D. All authors discussed and approved the data as well as the manuscript.

Corresponding author

Correspondence to Sascha Rau.

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The authors declare no competing interests.

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Extended data figures and tables

Extended Data Fig. 1 Averages of cyclotron frequency ratios.

a, b, Averages of cyclotron frequency ratios with equal parameters, after correction to zero-excitation amplitude using the fit described in the main text, for the data obtained with AWG2 for the deuteron campaign (a) and for HD+ (b). Each point corresponds to a setting used in the PNA method. On the x axis, the corresponding cyclotron radii of the deuteron (rd) and carbon (rC) and the number of cyclotron ratios N are given. The error bars denote the standard error of the mean and are estimated from the standard deviations divided by the square root of N. The grey band with dashed borders denotes 1σ uncertainty for the fitted frequency ratio.

Source data

Extended Data Table 1 Systematic effects in the HD+ measurement
Extended Data Table 2 Constants used in this work

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Rau, S., Heiße, F., Köhler-Langes, F. et al. Penning trap mass measurements of the deuteron and the HD+ molecular ion. Nature 585, 43–47 (2020). https://doi.org/10.1038/s41586-020-2628-7

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