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Modern applications of atomic physics, including the determination of frequency standards and the analysis of astrophysical spectra, require prediction of atomic properties with exquisite accuracy. For complex atomic systems, high-precision calculations are a major challenge due to the exponential scaling of the involved electronic configuration sets. This exacerbates the problem of required computational resources for these computations and makes indispensable the development of approaches to select the most important configurations out of otherwise intractably huge sets. We have developed a neural-network (NN) tool for running high-precision atomic configuration interaction (CI) computations with iterative selection of the most important configurations. Integrated with the established atomic codes, our approach results in computations with significantly reduced computational requirements in comparison with those without NN support. We showcase a number of NN-supported computations for the energy levels of ${\mathrm{Fe}}^{16+}$and ${\mathrm{Ni}}^{12+}$and demonstrate that our approach can be reliably used and automated for solving specific computational problems for a wide variety of systems. Published by the American Physical Society2024 

Abstract Optical atomic clocks are the most accurate and precise measurement devices of any kind, enabling advances in international timekeeping, Earth science, fundamental physics, and more. However, there is a fundamental tradeoff between accuracy and precision, where higher precision is achieved by using more atoms, but this comes at the cost of larger interactions between the atoms that limit the accuracy. Here, we propose a many-ion optical atomic clock based on three-dimensional Coulomb crystals of order one thousand Sn²⁺ions confined in a linear RF Paul trap with the potential to overcome this limitation. Sn²⁺has a unique combination of features that is not available in previously considered ions: a¹S₀ ↔ ³P₀clock transition between two states with zero electronic and nuclear angular momentum (I = J = F = 0) making it immune to nonscalar perturbations, a negative differential polarizability making it possible to operate the trap in a manner such that the two dominant shifts for three-dimensional ion crystals cancel each other, and a laser-accessible transition suitable for direct laser cooling and state readout. We present calculations of the differential polarizability, other relevant atomic properties, and the motion of ions in large Coulomb crystals, in order to estimate the achievable accuracy and precision of Sn²⁺Coulomb-crystal clocks. 

We used the monochromatic soft-x-ray beamline P04 at the synchrotron-radiation facility PETRA III to resonantly excite the strongest $2p\text{−}3d$transitions in neonlike $\mathrm{Ni}$ions, ${\left[2p^6\right]}_{J=0}\to {\left[{\left(2p^5\right)}_{1/2}3d_{3/2}\right]}_{J=1}$and ${\left[2p^6\right]}_{J=0}\to {\left[{\left(2p^5\right)}_{3/2}3d_{5/2}\right]}_{J=1}$, respectively dubbed $3C$and $3D$, achieving a resolving power of 15 000 and signal-to-background ratio of 30. We obtain their natural linewidths, with an accuracy of better than 10%, as well as the oscillator-strength ratio $f\left(3C\right)/f\left(3D\right)=2.51\left(11\right)$from analysis of the resonant fluorescence spectra. These results agree with those of previous experiments, earlier predictions, and our own advanced calculations. Published by the American Physical Society2024 

Abstract We improve by a factor of 4–20 the energy accuracy of the strongest soft X-ray transitions of Fexviiions by resonantly exciting them in an electron beam ion trap with a monochromatic beam at the P04 beamline of the PETRA III synchrotron facility. By simultaneously tracking instantaneous photon-energy fluctuations with a high-resolution photoelectron spectrometer, we minimize systematic uncertainties down to 10–15 meV, or velocity equivalent ±∼5 km s⁻¹in their rest energies, substantially improving our knowledge of this key astrophysical ion. Our large-scale configuration-interaction computations include more than 4 million relativistic configurations and agree with the experiment at a level without precedent for a 10-electron system. Thereby, theoretical uncertainties for interelectronic correlations become far smaller than those of quantum electrodynamics (QED) corrections. The present QED benchmark strengthens our trust in future calculations of many other complex atomic ions of interest to astrophysics, plasma physics, and the development of optical clocks with highly charged ions.