The proton mass
The mass of the lightest nucleus, the proton, is essential in hydrogen and muonic hydrogen spectroscopy, as it is required for the determination of the Rydberg constant or the proton radius with high precision . Actually, in various atomic physics experiments, the ratio of the proton mass, mp to the electron mass, me (rather than the individual masses) is a pivotal parameter and thus needs to be determined with high precision and consistency, see Figure 1. The proton's mass was the first measurement campaign of the LIONTRAP experiment with a relative precision of 3·10-11 [2, 3]. The most precise value of the electron mass was measured with a relative accuracy of 3·10-11 at the bound-electron g-factor experiment for highly charged ions, which is the direct predecessor of LIONTRAP experiment .
The deuteron mass
The deuteron, the nucleus of the deuterium atom, is the second lightest atomic nucleus, consisting of one proton and one neutron. The mass of deuteron in combination with its measured nuclear binding energy enables the mass of the neutron to be determined with high precision. This, in turn, is significant for more precise tests of the equivalence of mass and energy (E = mc2) within special relativity at low energies .
The masses of helion and triton
For a central consistency check of the KATRIN (KArlsruhe TRItium Neutrino) experiment, the mass difference of triton (atomic nucleus consisting of one proton and two neutrons) and helion (atomic nucleus of 3He, consisting of two protons and one neutron) is necessary with the highest precision [8, 9]. The aim of KATRIN is to determine the mass of the electron antineutrino m(νe), with an accuracy of 0.2eV/c2 (=2·10-10 u) . The distribution of the kinetic energy (Ekin) of the electron emitted during the beta decay of tritium to helium-3 is measured very precisely, see Figure 2. The maximum energy of this distribution, E0, also called the endpoint energy, depends essentially on the mass of the electron antineutrino, where: E0= [m(T)−m(He3)−me−m(νe)]∙c2. This Q-value (mass difference) is of great importance for the energy calibration of KATRIN.
Light ion mass puzzle
The combination of high precision mass measurements of light nuclei such as proton, deuteron, and helion with 12C ion as reference together with a mass ratio measurement of HD+ molecular ion to 3He+ ion provides a consistency check for all these mass measurements, see Figure 3. However, currently this check fails with an inconsistency of 5 standard deviations. This "light ion mass puzzle", is thus a significant inconsistency of the values of light masses from different world-leading experiments. In other words, the mass difference of 3He+ and HD+ , measured in the group led by Prof. Myers at the Florida State University, deviates by five standard deviations from the one calculated based on the atomic masses of proton, deuteron and helion [2, 12]. The values for the atomic masses of deuteron and helion have been measured in the UW-PTMS experiment (University of Washington Penning-Trap Mass Spectrometer) by Prof. Van Dyck Jr at the University of Washington (UW), whereas the proton mass has been measured by the LIONTRAP group. To resolve this puzzle, an independent check of these measurements is needed, which is performed in our experiment.
|||S. G. Karshenboim and V. G. Ivanov, "Quantum Electrodynamics, High-Resolution Spectroscopy and Fundamental Constants" , in Exploring the World with the Laser, 2018, ch. Chapter 15, pp. 237-265.|
|||F. Heiße, F. Köhler-Langes, S. Rau, J. Hou, S. Junck, A. Kracke, A. Mooser, W. Quint, S. Ulmer, G. Werth, K. Blaum, and S. Sturm, "High-Precision Measurement of the Proton's Atomic Mass" , Phys. Rev. Lett., vol. 119, no. 3, p. 033001, Jul 21 2017.|
|||F. Heiße et al., "High-precision mass spectrometer for light ions" , Physical Review A, vol. 100, no. 2, 2019.|
|||S. Alighanbari, M. G. Hansen, V. I. Korobov, and S. Schiller, "Rotational spectroscopy of cold and trapped molecular ions in the Lamb–Dicke regime" , Nature Physics, vol. 14, no. 6, pp. 555-559, 2018.|
|||M. Hori, H. Aghai-Khozani, A. Soter, D. Barna, A. Dax, R. Hayano, T. Kobayashi, Y. Murakami, K. Todoroki, H. Yamada, D. Horvath, L. Venturelli, "Buffer-gas cooling of antiprotonic helium to 1.5 to 1.7 K, and antiproton-to–electron mass ratio" , Science, vol. 354, no. 6312, pp. 610-614, 04 Nov 2016 2016.|
|||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.|
|||M. Jentschel and K. Blaum, "Balancing energy and mass with neutrons" , Nature Physics, vol. 14, no. 5, pp. 524-524, 2018.|
|||KATRIN Collaboration, "KATRIN Design Report 2004" , 2005.|
|||E. Otten, "Searching the absolute neutrino mass in tritium β-decay—interplay between nuclear, atomic and molecular physics" , Hyperfine Interactions, vol. 196, no. 1-3, pp. 3-23, 2010.|
|||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.|
|||S. Hamzeloui, J. A. Smith, D. J. Fink, and E. G. Myers, "Precision mass ratio of 3He+ to HD+" , Physical Review A, vol. 96, no. 6, 2017.|
|||S. L. Zafonte and R. S. Van Dyck, "Ultra-precise single-ion atomic mass measurements on deuterium and helium-3" , Metrologia, vol. 52, no. 2, pp. 280-290, 2015.|