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Test of quantum electrodynamics circumvents insufficient knowledge of nuclear structure
Many atomic nuclei have a magnetic field, similar to that of the Earth. However, directly at the surface of a heavy nucleus such as lead or bismuth, it is trillions of times stronger than the Earth's field and more comparable to that of a neutron star. Whether we understand the behaviour of an electron in such strong fields is still an open question. A research team led by TU Darmstadt at the GSI Helmholtz Centre for Heavy Ion Research has now taken an important step towards clarifying this question. Their findings have been published in Nature Physics. The results confirm the theoretical predictions.
Hydrogen-like ions, i.e. atomic nuclei to which only a single electron is bound, are theoretically particularly easy to describe. In the case of heavy nuclei with a high proton number – bismuth, for example, has 83 positively charged protons in its nucleus – the strong electrical attraction binds the electron close to the nucleus and thus within this extreme magnetic field. There, the electron aligns its own magnetic field with that of the nucleus like a compass needle. By supplying exactly the right amount of energy, this compass needle can be flipped in the opposite direction. This is precisely what the researchers have achieved. They were able to apply the method for the first time to a radioactive isotope for which there was a particularly accurate theoretical prediction of the amount of energy required.
The energy required can be calculated using quantum electrodynamics (QED) – the quantum theory of electromagnetism. However, insufficient knowledge of the structure of such heavy atomic nuclei makes accurate predictions difficult and has so far prevented a precise and unambiguous test of the theory. Measurements on the stable isotope Bi-209 were recently consistent with the theoretical prediction. However, there were still doubts as to whether the influence of the nuclear structure on the theoretical prediction could really be eliminated to the extent assumed. To close this loophole in the experimental test, it was proposed to measure another bismuth isotope with a different nuclear structure. Unfortunately, bismuth does not have a second stable isotope, so the research team led by Professor Wilfried Nörtershäuser had to resort to a radioactive isotope. The isotope Bi-208 was a suitable candidate, as it has one neutron less than the stable isotope and therefore exhibits an even stronger magnetic field.
‘The initial challenge in this experiment was to generate and isolate the hydrogen-like ion of the desired isotope Bi-208,’ explains Dr. Max Horst, lead author of the study. To do this, a neutron was knocked out of the stable Bi-209 in a nuclear reaction and the fragments of this reaction were collected in the ESR experimental storage ring. At the same time, all but one of the initially 83 electrons must be stripped off the atom to generate the hydrogen-like system. The fragments circle in the storage ring at about 72 percent of the speed of light, or around 200,000 kilometres per second. The hydrogen-like ions of the isotope Bi-208 among them were identified and all unwanted reaction products were removed. ‘In earlier measurements of the stable isotope Bi-209, we had around 1,000 times more ions available,’ explains Horst, ’which is why all aspects of the experiment had to be optimised in terms of efficiency and sensitivity.’
The measurement principle is based on flipping the electron's magnetic field by irradiating it with a laser beam of the correct energy. The ion absorbs an elementary particle of light – a photon – from the laser beam. The photon’s energy is then transferred to the electron and is used to flip its magnetic field, such that the state with the unfavourable alignment in the nuclear magnetic field is reached. To get rid of this energy, the electron flips back after about half a millisecond on average, emitting another photon. By this point, the ion has already circled the storage ring many hundreds of times, and these emitted photons are detected by sensitive detectors at a particularly dark spot along the storage ring to have as little background as possible.
Due to the small number of ions present, it was crucial to predict very accurately at which photon energy or wavelength (‘colour’) of the laser the process should take place. ‘Searching a large wavelength range at such a low signal rate would have taken a lot of time,’ says Nörtershäuser. A few years ago, he therefore initiated measurements at the CERN research centre in Switzerland on neutral atoms of the two Bi isotopes, which allowed the influence of the different nuclear structures to be estimated. The theoretical physicists combined this information with the earlier measurement of the hydrogen-like ion of the stable isotope to make a very precise prediction of the transition energy in hydrogen-like Bi-208. This value agreed with a full quantum mechanical calculation but was about ten times more accurate. The experimental value measured at the storage ring and reported in the new publication agrees excellently with this prediction. The result can now be used to predict the influence of the nuclear structure on other charge states of the isotope Bi-208, and the method can be applied analogously to other isotopes of bismuth or other elements.
The results published in "Nature Physics" are largely based on a collaboration between TU Darmstadt, with researchers at the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt and the Universities of Münster and Jena, which was funded by the German Federal Ministry of Education and Research (BMBF) as part of the APPA Research Focus. Furthermore, the research contributions of TU Darmstadt, the GSI Helmholtz Centre and the Justus Liebig University Giessen were supported by the Helmholtz Research Academy Hesse for FAIR (HFHF).
Prof. Dr. Wilfried Nörtershäuser
Working area: wnoertershaeuser@ikp.tu-darmstadt.de
+49 6151 16-23575
M. Horst, Z. Andelkovic, C. Brandau, R.J. Chen, D. Freire Fernandez, Ch. Geppert, J. Glorius, V. Hannen, R. Heß, P. Imgram, S. Klammes, K. König, G. Leckenby, S. Litvinov, Y. A. Litvinov, B. Lorentz, J. Meisner, K. Mohr, P. Müller, S. Passon, T. Ratajczyk, S. Rausch, J. Roßbach, R. Sánchez, S. Sanjari, R. S. Sidhu, U. Spillmann, M. Steck, T. Stöhlker, K. Ueberholz, C. Weinheimer, D. Winters, and W. Nörtershäuser: „Storage-ring laser spectroscopy of accelerator-produced hydrogen-like 208Bi82+“, in: Nature Physics (2025)
DOI: https://doi.org/10.1038/s41567-025-02885-x
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