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Precision Studies with Ions and Nuclei

High-precision experiments with ions and nuclei enable a direct access to fundamental physics. In a highly charged ion, inner-shell electrons experience the strongest electromagnetic fields accessible nowadays, providing an ideal testing ground to prove weather quantum electrodynamics, the field theory of the electromagnetic interaction, is valid in intense external fields. Precision measurements with these systems, when combined with sufficiently accurate theoretical calculations, also yield the values of fundamental constants or can test whether these vary in space and time. Such studies are also anticipated to provide access to tests of physical phenomena beyond the Standard Model of particle physics. Furthermore, nuclei become also attractive in this direction being both increasingly accessible with advanced light sources and stable against external perturbations. Due to their typical MeV energy scale, they appear attractive for applications such as compact nuclear batteries or quantum information devices.

An external static magnetic field gives rise to the Zeeman splitting of atomic energy levels, with a strength characterized by the dimensionless g-factor of the atomic state. The theory of the g-factor of an electron bound in the attractive potential of an atomic nucleus is investigated in the group around Zoltán Harman. These studies are paralleled with a quantum leap in the experimental accuracy in the investigation of the g-factor, especially in Penning trap measurements performed by the division headed by Klaus Blaum. Measuring the electron's g-factor in highly charged ions provide an exciting possibility for testing fundamental theories. Effects of strong-field quantum electrodynamics (QED) are increasingly relevant at higher and higher ionic charges. Bound-state QED effects are scrutinized to the highest precision in recent trapped-ion experiments, which have reached the 10-11 level in terms of relative precision with hydrogenlike ions. From a combined analysis of experimental and theoretical data for carbon ions, an improved value of the atomic mass of the electron has been determined, representing an improvement in accuracy by more than an order of magnitude as compared to the previously established value. The recently constructed ALPHATRAP Penning-trap setup also enables the experimental investigation of highly charged ions in virtually arbitrary charge states, which, in collaboration with theoretical calculations, largely enriches the field of applications. Penning-trap measurements have very recently also enabled a novel determination of electronic binding energies via the comparison of measured ionic cyclotron frequencies. The achieved experimental accuracy on the 1eV precision level is matched by our large-scale atomic structure calculations, forshadowing exciting future applications.

The g-factor experiments are currently being extended to a range of ions along the periodic table, including the heaviest stable elements. An essential motivation of such studies is that g-factor measurements with highly charged ions are anticipated to yield a new value of the fine-structure constant, i.e. the fundamental constant defining the strength of any kind of electromagnetic interactions in the Universe. We have found that a combination of the experimental g-factors of light one- and three-electron ions allows one to substract detrimental nuclear uncertainties, and thus one can extract this constant to unprecedented precision. This necessitates also a continuous improvement in the theoretical description of electron correlation effects and radiative corrections. In recent studies, we calculated the g-factor of the five-electron argon ion with a 6-digit accuracy, which was found to be in perfect agreement with the very first ALPHATRAP experiment on the same atomic system. Furthermore, we put forward the use of high-precision measurements of the g-factor of few-electron ions and its isotope shifts as a probe for physics beyond the Standard Model. The contribution of a hypothetical fifth fundamental force is calculated, and we found that, combining measurements from different ions at accuracy levels projected to be accessible in the near future, one may constrain the new physics coupling constant by more than one order of magnitude further than the best current atomic data.

Optical and x-ray spectroscopy of highly charged ions for testing fundamental theories

Highly charged ions do not only allow the precision determination of the values of physical constants, but they have also been proposed as improved optical clocks, and ideal systems for testing a potential variation in time of fundamental constants. Open-shell ions near level crossings have been predicted to be particularly sensitive to a variation of the fine-structure constant, and their optical and extreme ultraviolet spectra are being investigated by ion trap experiments by the group of José Crespo López-Urrutia. We perform large-scale calculations of the atomic structural properties of these ions to accompany the experiments, and put forward further ions and transition schemes for an efficient testing of the potential variation of the fine-structure constant and the electron-proton mass ratio. To extend the studies with highly charged ions, recently we also theoretically describe nuclear effects such as the hyperfine splitting of optical transitions in neutral atoms or singly charged ions, in collaboration with collinear laser spectroscopic measurements of the division of Klaus Blaum at the ISOLDE radioactive ion beam facility at CERN.

As these trapped-ion experiments are reaching extreme precision in the microwave and optical range, it would be desirable to also achieve high accuracy in a broader regime of the electromagnetic spectrum up to x-ray frequencies. While research with new x-ray free electron lasers has already produced remarkable results, the spectral qualities of these light sources are still far from those of optical lasers. In collaboration with the experimental group of Thomas Pfeifer at the Institute, we have developed x-ray pulse shaping schemes which are anticipated to decrease the bandwidth and improve the temporal coherence of the x-ray light. In recent studies, we have put forward a scheme to generate fully coherent x-ray lasers based on population inversion in highly charged ions, created by fast inner-shell photoionization using x-ray free-electron-laser pulses in a laser-produced plasma. Our numerical simulations show that one can obtain high-intensity, femtosecond x-ray pulses with bandwidths orders of magnitude narrower than in x-ray free-electron-laser pulses, at wavelengths down to the sub-ångström regime. Such x-ray lasers may be applicable in the study of x-ray quantum optics and metrology, investigating nonlinear interactions between x-rays and matter, or in high-precision spectroscopic studies in laboratory astrophysics.

The team around Natalia Oreshkina developed an accurate theoretical description of the structure of heavy muonic atoms and their corresponding x-ray emission spectra. The muons' probability density, due to their larger mass, greatly overlaps with the atomic nucleus, yielding access to the determination of nuclear parameters. As an example, in recent studies, the electric quadrupole moment of rhenium nuclei has been determined in collaboration with muonic x-ray spectroscopic measurements at the Paul Scherrer Institute in Switzerland. Since in these exotic atoms the energy scale of muonic and nuclear levels is comparable, a complex, unified treatment of muonic and nuclear structure is often mandatory in the theoretical modeling.

Nuclear transitions as accurate frequency standards

While usually ions and electrons are the typical candidates for precision studies, electromagnetic transitions in the atomic nucleus open new perspectives on the basis of their increased stability and long decoherence time. Due to the much smaller size, nuclei are less sensitive to the environment and their transition frequencies are remarkably stable. These qualities are most promising for the measurement of time and the development of ultra-precise clocks based on a nuclear transition. The lowest known nuclear transition connects the ground and the first excited states in the 229Th nucleus and lies in the vacuum ultraviolet range. The upper state at approx. 8 eV energy is a nuclear isomer, i.e., a long-lived excited nuclear state. Together with laser technology in the vacuum ultraviolet under development, this nuclear isomer may open the possibility to build incredibly precise nuclear clocks that may soon outperform the present atomic clocks defining the global time standard. In addition, this nuclear transition could also be used to shed light on fundamental questions about the time variation of physical questions, the equivalence principle, Lorentz invariance or dark matter search. So far, the low accuracy level on which the nuclear transition frequency has been determined is the main impediment on the way towards a new nuclear frequency standard and its compelling applications.

The group led by Adriana Pálffy is investigating theoretically the nuclear and atomic properties related to this low-lying nuclear transition. We are in particular interested in which are the most promising approaches to determine the nuclear transition energy on the required level of accuracy. Due to the small isomer energy, the coupling of the nuclear transition with the atomic shell is very strong. The coupling of the electronic and nuclear degrees of freedom can occur for instance in the process of internal conversion, when the nuclear excitation energy is transferred to an electron which leaves the atom. In the case of 229Th, due to the very low isomer energy, internal conversion can happen only in neutral atoms and expels one of the two outmost electrons from the atomic shell (see Fig. 4). A possible approach for a more precise energy determination involves ion or electron detection after the excited nucleus has undergone internal conversion. Our state-of-the-art internal conversion simulations rendered possible deducing a more precise isomer energy value in a direct experimental determination of the isomer decay performed by the group of Peter Thirolf at the Ludwig-Maximilians-Universität in Munich.

From a nuclear physics perspective, we have being working on nuclear models capable of predicting nuclear properties of this special isomer. The existence of the isomer appears to rely on a very fine interplay of collective and single-particle motion manifested in the actinide region of the nuclear chart. 229Th has an even number of protons and an odd number of neutrons. The nearly degenerated ground and isomeric state can be described theoretically by the collective motion of the even-even nuclear core which presents a complicated quadrupole-octupole deformation, together with the superimposed single-particle dynamics of the additional odd neutron. Using this model we could predict the radiative transition strength and the magnetic moment of the isomeric transition. Together with newly available experimental data for the isomer magnetic moment, our predictions suggest that the clock transition is weaker than so far expected, providing a possible justification on why so far all attempts to observe the radiative decay or excitation of the isomer have failed. The determination of the 229Th transition frequency is expected to pave the way for a whole range of applications in the newly emerging field of nuclear quantum optics.