Measurements

First result: determination of the proton mass in atomic mass units

In our first measurement campaign we determined the atomic mass of the proton with a relative accuracy of 3·10^-11 [1, 2]. One of the most challenging parts in this measurement is the quite different charge to mass ratio of the measured ion and the reference ion. In other words, a proton and a carbon ion form neither a mass doublet nor a charge over mass doublet. This results in very different modified cyclotron frequencies (ν_c(p) ≈ 57.4 MHz and ν_c(¹²C⁶⁺) ≈ 28.9 MHz, with B₀ ≈ 3.76 T) and axial frequencies (ν_z(p) ≈ 740 kHz and ν_z(¹²C⁶⁺) ≈ 525 kHz, where U_r ≈ -10 V). All frequency-dependent systematic frequency shifts therefore do not cancel in the cyclotron frequency ratio and make the determination of the proton mass a special challenge in high-precision mass spectroscopy. In a Penning trap, in order to store the two ions at the same position of the precision trap the identical trapping potential is applied. This leads to two very different axial frequencies due to which we have used two precisely matched axial detection systems. A further challenge is the relatively low electric charge of the proton, which results in a small measurement signal. At the same time, the trap radius cannot be too small to prevent a limitation of the precision by the interaction of mainly the heavy carbon ion with the electrodes, the so-called image charge effect. Only due to the novel double-compensated Penning trap it was possible to provide a sufficiently harmonic trap potential to reach the axial amplitudes for the proton necessary to determine the modified cyclotron frequency phase-sensitively with the PnA method. The relative statistical accuracy of the cyclotron frequency ratio after a single 50-minute measuring cycle was about 2·10^-10. The newly determined value of the proton mass is more accurate than the previous literature value of the CODATA [3] by a factor of three. However, it deviates significantly from this at 3 sigma and is 3·10^-10 u lighter, see Figure 1. The inconsistencies between the high-precision measurements of light atomic masses still remain despite this new, deviating value for the proton mass. However, they still give us a strong motivation to measure the other nuclei of light atoms with the highest precision.

Figure 1: Overview of proton mass measurements over the last 20 years. The value measured with LIONTRAP was three times more precise than the literature value at that time and deviated downwards from this 3σ.

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Ongoing experiment

In the current measurement project, we will determine the mass of deuteron with a relative accuracy of better than 10^-11.

For the determination of the deuteron mass, we were able to significantly reduce the prevailing systematic uncertainty due to the quadratic magnetic field inhomogeneity (B₂=0.24 T/m², where B≈B₀+B₂z²) for the first time by fully compensating the B₂ with a specially designed superconducting coil - placed directly around the trap chamber.

We have also succeeded for the first time in producing single deuterium atomic and molecular (HD⁺) ions with our ion source (mEBIS) discussed in the in-situ ion production section previously.

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Planned experiments

In the long run, we also plan to perform mass measurements of helium-3 and tritium. In the course of this project we will measure the ³He mass in relation to carbon in order to further investigate the light ion mass puzzle and later also determine the mass difference of ³He and T directly. We are expecting to obtain their mass difference with an accuracy of better than 20 meV and thus δm/m~5ppt, which will serve as an important cross-check for the KATRIN experiment [5].

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References

[1]	F. Heiße et al., "High-Precision Measurement of the Proton's Atomic Mass" , Phys. Rev. Lett., vol. 119, no. 3, p. 033001, Jul 21 2017.
[2]	F. Heiße et al., "High-precision mass spectrometer for light ions" , Physical Review A, vol. 100, no. 2, 2019.
[3]	P. J. Mohr, D. B. Newell, and B. N. Taylor, "CODATA recommended values of the fundamental physical constants: 2014" , Reviews of Modern Physics, vol. 88, no. 3, 2016.
[4]	S. Sturm et al., "High-precision measurement of the atomic mass of the electron" , Nature, vol. 506, no. 7489, pp. 467-70, Feb 27 2014.
[5]	M. Aker et al., "Improved Upper Limit on the Neutrino Mass from a Direct Kinematic Method by KATRIN" , Phys. Rev. Lett., vol. 123, no. 22, p. 221802, Nov 29 2019.