The ground-state hyperfine splitting structure in heavy hydrogen-like and lithium-like ions resides in the visible and the infrared part of the electromagnetic spectrum, respectively. Even though it is a highly forbidden M1 transition, it is possible to probe it by using standard atomic-spectroscopy techniques, like laser spectroscopy. At the experimental storage rings at GSI/FAIR, like ESR or CRYRING, heavy highly charged ions can be stored for long periods of time at relativistic energies. At these energies the Doppler shift of light is huge, e.g., up to few hundreds of nanometers. This enables us to probe atomic transitions, which are in the deep ultraviolet or infrared part of the electromagnetic spectrum, by using visible laser beams when they are superimposed either counter- or co-propagating to the ion beam, respectively.

The so-called “specific difference”, a weighted difference between the hyperfine transition energies in hydrogen-like and lithium-like ions, provides the means to test QED in the strongest magnetic fields in the laboratory [1] by eliminating most of the nuclear structure effects that are not well under control. In 2017 we measured the specific difference at ESR using the stable isotope ²⁰⁹Bi [2]. Surprisingly we found a 7s deviation from the theoretical prediction at that time. This, so-called, “hyperfine puzzle” was solved shortly after by a new measurement of the nuclear magnetic moment in ²⁰⁹Bi [3].

Since then, it was proposed to investigate the specific difference using another isotope. Predictions on this regard were performed by Schmidt et al. using measurement in the neutral atom of the isotope ²⁰⁸Bi [4]. Therefore, completing a measurement of the specific difference on this isotope can confirm the effectiveness of this approach and therefore allow us to test bound-state strong-field QED.

In a collaboration with several universities and research centers, in our most recent beam time at the ESR, we succeeded to produce and separate a sufficient amount of hydrogen-like ²⁰⁸Bi⁸²⁺, about 10⁵ ions, to observe for the first-time ever the laser resonance signal of a highly-charged ion of an accelerator-produced radioactive isotope. The results are now being published [5]. Here we have been able to measure this hyperfine splitting with an accuracy of few times 10^-5. This result benefit us twofold: it can help us to predict the position of the 2s-hyperfine splitting in lithium-like ²⁰⁸Bi⁸⁰⁺ and it will enable us in the future to determine the specific difference in ²⁰⁸Bi experimentally. A campaign for measuring the 2s hyperfine-splitting in lithium-like ²⁰⁸Bi⁸⁰⁺ will take place in Mai 2025. Finding this hyperfine line will bring new insights of the QED effects in the strongest magnetic fields.

1] Volotka, A.V., Glazov, D.A., Andreev, O.V., Shabaev, V.M., Tupitsyn, I.I., Plunien, G.: Test of many-electron QED effects in the hyperfine splitting of heavy high-Z ions. Phys. Rev. Lett. 108(7), 073001 (2012) https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.073001

[2] Ullmann, J., Andelkovic, Z., Brandau, C., Dax, A., Geithner, W., Geppert, C., Gorges, C., Hammen, M., Hannen, V., Kaufmann, S., König, K., Litvinov, Y., Lochmann, M., Maaß, B., Meisner, J., Murböck, T., Sánchez, R., Schmidt, M., Schmidt, S., Nörtershäuser, W.: High precision hyperfine measurements in Bismuth challenge bound-state strong-field QED. Nature Communications 8, 15484 (2017) https://doi.org/10.1038/ncomms15484

[3] Skripnikov, L.V., Schmidt, S., Ullmann, J., Geppert, C., Kraus, F., Kresse, B., Nörtershäuser, W., Privalov, A.F., Scheibe, B., Shabaev, V.M., Vogel, M., Volotka, A.V.: New nuclear magnetic moment of 209Bi: Resolving the bismuth hyperfine puzzle. Phys. Rev. Lett. 120, 093001 (2018) https://doi.org/10.1103/PhysRevLett.120.093001

[4] Schmidt, S., Billowes, J., Bissell, M.L., Blaum, K., Ruiz, R.F., Heylen, H., Malbrunot-Ettenauer, S., Neyens, G., N¨ortersh¨auser, W., Plunien, G., Sailer, S., Shabaev, V., Skripnikov, L., Tupitsyn, I., Volotka, A., Yang, X.: The nuclear magnetic moment of 208Bi and its relevance for a test of bound-state strong-field QED. Physics Letters B 779 (2018) https://doi.org/10.1016/j.physletb.2018.02.024

[5] Horst M., Andelkovic Z., Brandau C., Chen R. J., Freire Fernández D., Geppert C., Glorius J., Hannen V., Heß R., Imgram P., Klammes S., König K., Leckenby G., Litvinov S., Litvinov Y. A., Lorentz B., Meisner J., Mohr K., Müller P., Passon S., Ratajczyk T., Rausch S., Roßbach J., Sánchez R., Sanjari S.,Singh Sidhu R., Spillmann U., Steck M., Stöhlker T., Ueberholz K., Weinheimer C., Winters D., Nörtershäuser W.: Laser spectroscopy of accelerator-produced hydrogen-like ²⁰⁸Bi⁸²⁺ – a test of strong-field QED with 10⁵ ions. Nature Physics. In Press.