Search

Optical atomic clocks are the most accurate measurement devices ever constructed and have found many applications in fundamental science and technology. The use of highly charged ions (HCI) as a new class of references for highest accuracy clocks and precision tests of fundamental physics has long been motivated by their extreme atomic properties and reduced sensitivity to perturbations from external electric and magnetic fields compared to singly charged ions or neutral atoms. Here we present the first realisation of this new class of clocks, based on an optical magnetic-dipole transition in Ar$^{13+}$. Its comprehensively evaluated systematic frequency uncertainty of $2.2\times10^{-17}$ is comparable to that of many optical clocks in operation. From clock comparisons we improve by eight and nine orders of magnitude upon the uncertainties for the absolute transition frequency and isotope shift ($^{40}$Ar vs. $^{36}$Ar), respectively. These measurements allow us to probe the largely unexplored quantum electrodynamic nuclear recoil, presented as part of improved calculations of the isotope shift which reduce the uncertainty of previous theory by a factor of three. This work establishes forbidden optical transitions in HCI as references for cutting-edge optical clocks and future high-sensitivity searches for physics beyond the standard model., Comment: Main: 20 pages, 3 figures. Supplement: 19 pages, 2 figures

A theoretical study of the K-shell ionization of hydrogen-like ions, colliding with bare nuclei, is performed within the framework of the time-dependent Dirac equation. Special emphasis is placed on the ionization probability that is investigated as a function of impact parameter, collision energy and nuclear charge. To evaluate this probability in a wide range of collisional parameters we propose a simple analytical expression for the transition amplitude. This expression contains three fitting parameters that are determined from the numerical calculations, based on the adiabatic approximation. In contrast to previous studies, our analytical expression for the transition amplitude and ionization probability accounts for the full multipole expansion of the two-center potential and allows accurate description of nonsymmetric collisions of nuclei with different atomic numbers, $Z_1 \neq Z_2$. The calculations performed for both symmetric and asymmetric collisions indicate that the ionization probability is reduced when the difference between the atomic numbers of ions increases., 8 pages, 6 figures

Physical review / A 107(4), 042814 (2023). doi:10.1103/PhysRevA.107.042814, Published by APS, Woodbury, NY

Physical review / A 107, 012805 (2023). doi:10.1103/PhysRevA.107.012805, We perform a study on Rayleigh scattering of highly linearly polarized hard x rays on a thin Au foil target. Inthe study the angular distribution of the scattered radiation is analyzed in a relativistic regime both within and outof the plane of polarization of the incident beam. Within this experiment we scatter a synchrotron beam with aphoton energy of 175 keV on a high-Z target foil, namely, gold. Our findings correlate well with state-of-the-artcalculations of the scattering process performed in the framework of quantum electrodynamics and may haveconsiderable impact on future experiments regarding a polarization-resolved analysis of Delbrück scattering.Furthermore, we show that the angular distribution of Rayleigh scattering can be used for a highly sensitivedetermination of the degree and orientation of the linear polarization of the incident hard-x-ray beam, if we relyon the theoretical framework., Published by Inst., Woodbury, NY

We present an experimental study of the quasi-elastic Raman scattering (QES) of plane-wave and twisted light by liquid crystals. Depending on their temperature, these crystals can exhibit isotropic, nematic and chiral nematic phases. The question is addressed of how the phase of a crystal and the state of incident light can affect the quasi-elastic energy spectra of the scattered radiation, whose shape is usually described by the combination of Lorentzian and Gaussian components. Special attention is paid to the \textit{chiral phase}, for which the Raman QES spectrum is dominated by a Lorentzian with reduced linewidth, pointing to diminished disorder and configurational entropy. Moreover, this phase is also known for a regime of iridescence (selective backscattering) which arises when the wavelength of incident light becomes comparable with the chiral pitch length. Detailed measurements, performed in this \textit{resonant} regime and by employing twisted light, carrying various projections of the orbital angular momentum (OAM), have indicated a low-energy scattering surplus depending on OAM. We argue that this observation might indicate a transfer of angular momentum between light and the liquid crystal., 4 figures, two References added and ACKNOWLEDGMENT, submitted to Low Temperature Physics/Fizika Nizkikh Temperatur 47, No. 11, (2021)

We present a theoretical study of photoexcitation of highly charged ions from their ground states, a process which can be realized at the Gamma Factory at CERN. Special attention is paid to the question of how the excitation rates are affected by the mixing of opposite-parity ionic levels, which is induced both by an external electric field and the weak interaction between electrons and the nucleus. In order to reinvestigate this "Stark-plus-weak-interaction" mixing, well-known in neutral atomic systems, we employ relativistic Dirac theory. Based on the developed approach, detailed calculations are performed for the ${\rm 1s}_{1/2} \to {\rm 2s}_{1/2}$ and ${\rm 1s}^2 \; {\rm 2s}_{1/2} \to {\rm 1s}^2 \; {\rm 3s}_{1/2}$ (M1 + parity-violating-E1) transitions in hydrogen- and lithium-like ions, respectively. In particular, we focus on the difference between the excitation rates obtained for the right- and left-circularly polarized incident light. This difference arises due to the parity violating mixing of ionic levels and is usually characterized in terms of the circular-dichroism parameter. We argue that future measurements of circular dichroism, performed with highly charged ions in the SPS or LHC rings, may provide valuable information on the electron-nucleus weak-interaction coupling., Comment: 14 pages, 6 figures

We report a measurement of the radiative lifetime of the $^{2}{F}_{7/2}$ level of $^{171}{\mathrm{Yb}}^{+}$ that is coupled to the $^{2}{S}_{1/2}$ ground state via an electric octupole transition. The radiative lifetime is determined to be $4.98(25)\ifmmode\times\else\texttimes\fi{}{10}^{7}\text{ }\text{ }\mathrm{s}$, corresponding to 1.58(8) yr. The result reduces the relative uncertainty in this exceptionally long excited state lifetime by 1 order of magnitude with respect to previous experimental estimates. Our method is based on the coherent excitation of the corresponding transition and avoids limitations through competing decay processes. The explicit dependence on the laser intensity is eliminated by simultaneously measuring the resonant Rabi frequency and the induced quadratic Stark shift. Combining the result with information on the dynamic differential polarizability permits a calculation of the transition matrix element to infer the radiative lifetime.

We present a theoretical investigation of the resonant elastic scattering of twisted light, carrying angular momentum, by partially stripped ions. Special emphasis is placed on a question of whether the scattered radiation is also twisted. In order to investigate such an "angular momentum transfer", we develop an approach that allows us to find a quantum state of the final photon without projecting it onto a detector state. A general expression for this so--called \textit{evolved} state of outgoing radiation is derived and it can be used to analyze the resonant scattering by any ion, independently of its shell structure. Here, we illustrate our approach with the strong electric dipole $n S_{0} \to n' P_{1} \to n S_{0}$ transitions, which play an important role for the Gamma Factory project at CERN. For the incident Bessel light, the scattered radiation is shown to be in a superposition of twisted modes with the projections of the total angular momentum $m_f = 0, \pm 1$. The larger values of $m_f$ can be efficiently generated by inducing transitions of higher multiplicity. This angular momentum transfer, together with a remarkable cross section that is many orders of magnitude larger than that of the backward Compton scattering, makes the resonant photon scattering an effective tool for the production of twisted x-- and even gamma--rays at the Gamma Factory facility., 10 pages, 1 figure

We present a theoretical investigation of the resonant elastic scattering of laser photons by ultra-relativistic partially stripped ions, that is the core process of the Gamma Factory project. Special emphasis in our study is placed on the angular distribution and polarization of scattered photons as observed in the collider and ion-rest reference frames. In order to describe these (angular and polarization) properties for arbitrary relativistic many-electron ion, the general approach, based on the application of irreducible polarization tensors, is laid down. By making use of the polarization tensors we explore in detail the scattering of both, conventional plane-wave- and twisted (or vortex) photons. For the former case we show how the propagation directions and polarization states of incident and outgoing photons are related to each other for the $n S_{0} \to n' P_{1} \to n S_{0}$, $n S_{1/2} \to n' P_{1/2} \to n S_{1/2}$ and $n S_{1/2} \to n' P_{3/2} \to n S_{1/2}$ resonant transitions. For the scattering of initially twisted light, that carries non-zero orbital angular momentum, we explore the angular distribution of secondary photons and discuss the conditions under which they are also twisted., 16 pages, 4 figures

Molecules 26(9), 2660 (2021). doi:10.3390/molecules26092660, Published by MDPI, Basel

In this paper, we present an experimental and theoretical study of excitation processes for the heaviest stable helium-like ion, that is, He-like uranium occurring in relativistic collisions with hydrogen and argon targets. In particular, we concentrate on angular distributions of the characteristic Kα radiation following the K → L excitation of He-like uranium. We pay special attention to the magnetic sub-level population of the excited 1s2lj states, which is directly related to the angular distribution of the characteristic Kα radiation. We show that the experimental data can be well described by calculations taking into account the excitation by the target nucleus as well as by the target electrons. Moreover, we demonstrate for the first time an important influence of the electron-impact excitation process on the angular distributions of the Kα radiation produced by excitation of He-like uranium in collisions with different targets.

Promising searches for new physics beyond the current Standard Model (SM) of particle physics are feasible through isotope-shift spectroscopy, which is sensitive to a hypothetical fifth force between the neutrons of the nucleus and the electrons of the shell. Such an interaction would be mediated by a new particle which could in principle be associated with dark matter. In so-called King plots, the mass-scaled frequency shifts of two optical transitions are plotted against each other for a series of isotopes. Subtle deviations from the expected linearity could reveal such a fifth force. Here, we study experimentally and theoretically six transitions in highly charged ions of Ca, an element with five stable isotopes of zero nuclear spin. Some of the transitions are suitable for upcoming high-precision coherent laser spectroscopy and optical clocks. Our results provide a sufficient number of clock transitions for -- in combination with those of singly charged Ca$^+$ -- application of the generalized King plot method. This will allow future high-precision measurements to remove higher-order SM-related nonlinearities and open a new door to yet more sensitive searches for unknown forces and particles., 8 pages, 4 figures

We present a theoretical study on the elastic Rayleigh scattering of x-ray photons by closed-shell atoms. Special attention is paid to the transfer of linear polarization from the incident to the outgoing photons. To study this process, we apply the density-matrix formalism combined with the relativistic perturbation theory. This formalism enables us to find general relations between the Stokes parameters of the incident and scattered photons. By using these expressions, we revisit the recent proposal to use Rayleigh scattering for the analysis of the polarization purity of synchrotron radiation. We show that this analysis can be performed without any need for the theoretically calculated scattering amplitudes, if the linear polarization of the scattered light is measured simultaneously at the azimuthal angles ${0}^{\ensuremath{\circ}}$ and ${45}^{\ensuremath{\circ}}$ with respect to the plane of the synchrotron. To illustrate our approach, we present detailed calculations for scattering of 145 keV photons by lead atoms.

We present a theoretical investigation of the radiative recombination of twisted Bessel electrons with initially hydrogen-like (finally helium-like) heavy ions. In our study, we focus especially on the linear polarization of x-ray photons emitted in the electron capture into the ground $1{s}_{1/2}^{2}$ ionic state. Particular emphasis is placed on the question of how this polarization is affected if incident hydrogen-like ions are themselves spin-polarized. To explore such a ``polarization transfer'' we apply the density matrix theory and derive the Stokes parameters of recombination x rays for the realistic case of collisions between macroscopic electron and ion beams. Based on the developed general approach two scenarios are discussed that are of interest for the planned experiments at ion storage rings. First, we demonstrate how the use of twisted electrons can empower the known method for the diagnostics of spin-polarized ion beams, based on the rotation of the linear polarization of recombination light. In the second scenario we show how the internal structure of ions beams with inhomogeneous intensity and spin patterns can be probed by the capture of Bessel electrons, carrying different values of angular momentum.

Theoretical study is presented for a spinor Bose-Einstein condensate, whose two components are coupled by copropagating Raman beams with different orbital angular momenta. The investigation is focused on the behavior of the ground state of this condensate, depending on the atom-light coupling strength. By analyzing the ground state, we have identified a number of quantum phases, which reflect the symmetries of the effective Hamiltonian and are characterized by the specific structure of the wave function. In addition to the well-known stripe, polarized, and zero-momentum phases, our results show that the system can support phases whose wave functions contain a complex vortex molecule. Such a molecule plays an important role in the continuous phase transitions of the system. The predicted behavior of vortex-molecule phases can be examined in cold-atom experiments using currently existing techniques.

We study the resonant two-photon ionization of neutral atoms by a combination of twisted and plane-wave light within a fully relativistic framework. In particular, the ionization of an isotropic ensemble of neutral sodium atoms ($Z=11$) from their ground $3{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ state via the $3{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}$ level is considered. We investigate in details the influence of the kinematic parameters of incoming twisted radiation on the photoelectron angular distribution and the circular dichroism. Moreover, we study the influence of the geometry of the process on these quantities. This is done by changing the propagation directions of the incoming twisted and plane-wave light. It is found that the dependence on the kinematic parameters of the twisted photon is the strongest if the plane-wave and twisted light beams are perpendicular to each other.

We demonstrate a widely applicable technique to absolutely calibrate the energy scale of x-ray spectra with experimentally well-known and accurately calculable transitions of highly charged ions, allowing us to measure the K-shell Rydberg spectrum of molecular O_{2} with 8 meV uncertainty. We reveal a systematic ∼450 meV shift from previous literature values, and settle an extraordinary discrepancy between astrophysical and laboratory measurements of neutral atomic oxygen, the latter being calibrated against the aforementioned O_{2} literature values. Because of the widespread use of such, now deprecated, references, our method impacts on many branches of x-ray absorption spectroscopy. Moreover, it potentially reduces absolute uncertainties there to below the meV level.

We report on laser spectroscopic measurements on Li$^+$ ions in the experimental storage ring ESR at the GSI Helmholtz Centre for Heavy Ion Research. Driving the $2s\,^3\!{S}_1\;(F=\frac{3}{2}) \,\leftrightarrow\,2p\,^3\!P_2\;(F=\frac{5}{2}) \leftrightarrow 2s\,^3\!{S}_1\;(F=\frac{5}{2})$ $\Lambda$-transition in $^7$Li$^+$ with two superimposed laser beams it was found that the use of circularly polarized light leads to a disappearance of the resonance structure in the fluorescence signal. This can be explained by optical pumping into a dark state of polarized ions. We present a detailed theoretical analysis of this process that supports the interpretation of optical pumping and demonstrates that the polarization induced by the laser light must then be at least partially maintained during the round trip of the ions in the storage ring. Such polarized ion beams in storage rings will provide opportunities for new experiments, especially on parity violation., Comment: 14 pages, 8 figures, new version with small adjustments, closest to final publication in PRAB

The process of the elastic scattering of photons on atoms, known as the Rayleigh scattering, is investigated. Expressing the scattering observables in terms of the electric and magnetic complex scattering amplitudes, we work over the scenarios for their independent benchmarking by experiments. In particular, the combination of the cross section and polarization transfer of initially linearly polarized light provides an opportunity for a complete experiment for any but fixed scattering angle. It allows us to deduce the modulus of the electric and magnetic amplitudes together with the phase difference individually. The findings are illustrated by the theoretical calculations of the scattering of 150 - 250 keV photons on lead atoms., Comment: 9 pages, 6 figures

We theoretically investigate the influence of gravity on laser light in a hemispherical optical cavity, operating on Earth. The propagation of light in such a cavity is modeled by a Gaussian beam, affected by the Earth's gravitational field. On laboratory scale, this field is described by the spacetime of homogeneous gravity, known as Rindler spacetime. In that spacetime, the beam is bent downwards and acquires a height dependent phase shift. As a consequence the phase fronts of the laser light differ from those of a usual Gaussian beam. Assuming that the initial beam enters the cavity along its symmetry axis, these gravitational effects cause variations of the beam phase with every cavity round trip. Detailed calculations are performed to investigate how these phase variations depend on the beam parameters and the cavity setup. Moreover, we discuss the implications of our findings for cavity calibration techniques and cavity-based laser stabilization procedures., 10 pages, 6 figures

The total two-photon decay rate of hydrogenlike ions is studied using relativistic quantum electrodynamics. In particular, we analyze how finite nuclear size and QED vacuum polarization corrections affect the decay rate. To calculate these corrections, a finite basis set method based on $B$ splines is used for the generation of quasicomplete atomic spectra and, hence, of the relativistic Green's function. By making use of this $B$-spline approach, high precision calculations have been performed for the $2{s}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}+2\ensuremath{\gamma}$ and $2{p}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}+2\ensuremath{\gamma}$ decay of hydrogenlike ions along the entire isoelectronic sequence. The results of these calculations show that both QED and finite nuclear size effects are comparatively weak for the $2{s}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}+2\ensuremath{\gamma}$ transition. In contrast, they are much more pronounced for the $2{p}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}+2\ensuremath{\gamma}$ decay, where, for hydrogenlike uranium, the decay rate is reduced by 0.484% due to the finite nuclear size and enhanced by 0.239% if the vacuum polarization is taken into account.

We present a theoretical investigation of the radiative recombination of twisted electrons into bound states of initially bare ions. Special emphasis is placed on the magnetic sublevel population of the residual hydrogenlike ions under the assumption that emitted photons remain unobserved. We show that this sublevel population strongly depends on the position of an ion within the incident electron wave front. To better understand this position dependence, detailed calculations are presented for the electron capture into $1{s}_{1/2}$ and $2{p}_{3/2}$ ionic states. The results of the calculations show that the structured beams of hydrogenlike ions can be produced in collisions with Bessel electrons at ion storage rings. Having multiple-ring intensity profiles and complex spin patterns, these structured beams can become a valuable tool for future ion collision studies.

A theoretical study is performed for the excitation of a single atom localized in the center of twisted light modes. Here we present the explicit dependence of excitation rates on critical parameters, such as the polarization of light, its orbital angular momentum projection, and the orientation of its propagation axis with respect to the atomic quantization axis. The effect of a spatial spread of the atom is also considered in detail. The expressions for transition rates obtained in this work can be used for any atom of arbitrary electronic configuration. For definiteness we apply them to the specific case of the $^{2}S_{1/2}(F=0)\ensuremath{\rightarrow}^{2}F_{7/2}(F=3,M=0)$ electric octupole (E3) transition in ${^{171}\mathrm{Yb}}^{+}$ ion. Our analytical and numerical results are suitable for the analysis and planning of future experiments on the excitation of electric-dipole-forbidden transitions by twisted light modes in optical atomic clocks.

As known from Einstein's theory of general relativity, the propagation of light in the presence of a massive object is affected by gravity. In this work, we discuss whether the effect of gravitational light bending can be observed in Earth-based experiments, using high-finesse optical cavities. In order to do this, we theoretically investigate the dynamics of electromagnetic waves in the spacetime of a homogeneous gravitational field and give an analytical expression for the resulting modifications to Gaussian beam propagation. This theoretical framework is used to calculate the intensity profile at the output of a Fabry-P\'erot cavity and to estimate the imprints of Earth's gravity on the cavity output signal. In particular, we found that gravity causes an asymmetry of the output intensity profile. Based on that, we discuss a measurement scheme, that could be realized in facilities like the GEO600 gravitational wave detector and the AEI 10 m detector prototype., Comment: 7 pages, 5 figures, 1 table

Physical review letters 124(22), 225001 (1-7) (2020). doi:10.1103/PhysRevLett.124.225001, For more than 40 years, most astrophysical observations and laboratory studies of two key soft x-ray diagnostic $2p$−$3d$ transitions, $3C$ and $3D$, in Fe XVII ions found oscillator strength ratios $f(3C)$/$f(3D)$ disagreeing with theory, but uncertainties had precluded definitive statements on this much studied conundrum. Here, we resonantly excite these lines using synchrotron radiation at PETRA III, and reach, at a millionfold lower photon intensities, a 10 times higher spectral resolution, and 3 times smaller uncertainty than earlier work. Our final result of $f(3C)$/$f(3D)$=3.09(8)(6) supports many of the earlier clean astrophysical and laboratory observations, while departing by five sigmas from our own newest large-scale ab initio calculations, and excluding all proposed explanations, including those invoking nonlinear effects and population transfers., Published by APS, College Park, Md.

The Gamma Factory initiative proposes to develop novel research tools at CERN by producing, accelerating and storing highly relativistic, partially stripped ion beams in the SPS and LHC storage rings. By exciting the electronic degrees of freedom of the stored ions with lasers, high-energy narrow-band photon beams will be produced by properly collimating the secondary radiation that is peaked in the direction of ions' propagation. Their intensities, up to $10^{17}$ photons per second, will be several orders of magnitude higher than those of the presently operating light sources in the particularly interesting $\gamma$--ray energy domain reaching up to 400 MeV. This article reviews opportunities that may be afforded by utilizing the primary beams for spectroscopy of partially stripped ions circulating in the storage ring, as well as the atomic-physics opportunities afforded by the use of the secondary high-energy photon beams. The Gamma Factory will enable ground breaking experiments in spectroscopy and novel ways of testing fundamental symmetries of nature., Comment: 15 pages, 3 figures

International audience; The Gamma Factory (GF) initiative proposes to use partially stripped ion (PSI) beams as drivers of a new type of high-intensity and high-energy (0.1–400 MeV) photon source. As part of the ongoing Physics Beyond Collider studies, initial beam tests were carried out in 2017 and 2018 at the SPS and LHC with partially stripped xenon and lead beams. This contribution discusses the results of these tests and the preparations for the next GF R&D step: the proof-of-principle experiment at the SPS to study interaction of PSI beams with the laser light

Acta physica Polonica / B / Proceedings supplement 13(4), 645 (2020). doi:10.5506/APhysPolBSupp.13.645, Published by Inst. of Physics, Jagellonian Univ., Cracow

Annalen der Physik OF, 2100285 (2022). doi:10.1002/andp.202100285, For photon energies from several 10 keV up to a few MeV Compton polarimetry is an indispensable tool to gain insight into subtle details of fundamental atomic radiative processes. Within the SPARC collaboration several segmented semiconductor detectors are developed that are well suited for application as efficient Compton polarimeters. In this report, these recent developments are reviewed and it is discussed how Compton polarimetry can be employed at the upcoming Gamma Factory., Published by Barth, Leipzig

We investigate the dielectronic recombination (DR) of an electron and a highly-charged ion with non-zero nuclear spin. We assume that the incident electron is captured into doubly-excited 1 s 2 κ κ ′ J = 0 , 1 , 2 levels of Be-like ions just above of its autoionization threshold. The angular distribution of the subsequent radiative emission is investigated especially for its dependence upon the nuclear spin and the nuclear magnetic moment. While the hyperfine and even the fine-structure of the ions cannot be resolved in typical DR experiments, we found the photon angular distribution, following the decay of the 1 s 2 2 p 3 / 2 ns J = 1 , 2 DR resonance very sensitive to the nuclear parameters.

We propose an improvement of the basis for the solution of the stationary two-centre Dirac equation in Cassini coordinates using the finite-basis-set method presented in our earlier article [J. Phys. B 43, 235207 (2010)]. For the calculations in the above article, we constructed the basis for approximating the energy eigenfunctions by using smooth piecewise defined polynomials, called B-splines. In the present article, we report that an analysis of the employed representation of the Dirac matrices shows that the above approximation is not efficient using B-splines only. Therefore, we include basis functions which are defined using functions with step-like behavior instead of B-splines. Thereby, we achieve a significant increase of accuracy of results.

We present a theoretical study of bound-free electron-positron pair production in the interaction of $\ensuremath{\gamma}$ rays with bare ions. Special attention is paid to the longitudinal polarization of both the emitted positrons and the produced hydrogenlike ions. To evaluate this polarization we employed exact solutions of the relativistic Dirac equation and treat the electron-photon coupling within the framework of first-order perturbation theory. Detailed calculations have been performed for both low- and high-$Z$ ions and for a wide range of photon energies. The results of these calculations suggest that bound-free pair production can be a source of strongly polarized positrons and ions.

A theoretical analysis is presented for the excitation of single many-electron atoms and ions by twisted (or vortex) light. Special emphasis is put on excitations that can proceed via several electric and magnetic multipole channels. We argue that the relative strength of these multipoles is very sensitive to the topological charge and kinematic parameters of the incident light and can be strongly modified with respect to the plane-wave case. Most remarkably, the modification of multipole transitions by twisted radiation can be described by means of a geometrical factor. This factor is independent of the shell structure of a particular target atom and just reflects the properties of the light beam as well as the position of an atom with respect to the vortex axis. An analytical expression for the geometrical factor is derived for Bessel photons and for a realistic experimental situation in which the position of an atom is not well determined. To illustrate the use of the geometrical factor for the analysis of (future) measurements, detailed calculations are presented for the $3s3p \, ^3P_1 \to 3s 3p \, ^1P_1$ excitation in neutral Mg., Comment: 8 pages, 4 figures

Violation of linearity of the King plot is investigated for a chain of partially stripped argon isotopes. The nonlinearity originates within the Standard Model from subtle contributions to the isotope shifts from next-to-leading order effects, which have never been systematically studied so far. In light atoms these nonlinear effects are dominated by the quadratic nuclear recoil ($\propto 1/M^2$ where $M$ is the nuclear mass). Large-scale relativistic calculations of the linear and quadratic mass shift and the field shift are performed for the $2P$ fine-structure transitions in Be-like, B-like, and C-like argon ions. Nonlinearities of the King plots from 5 to 30 kHz are found, which is four orders of magnitude larger than previous estimates in comparable systems. Accurate calculations of these effects are vital for identification of possible nonlinearities originating from physics beyond the Standard Model.

The authors investigate relativistic corrections to the energy levels of an electron confined in a Penning trap. The Earth's gravitational field induces small changes to transition frequencies that may become relevant for future measurements of the electron's magnetic moment.

Using resonant two-step laser excitation of trapped $^{232}{\mathrm{Th}}^{+}$ ions, we observe 166 previously unknown energy levels of even parity within the energy range from 7.8 to 9.8 eV and angular momenta from $J=1/2$ to $7/2$. We also classify the high-lying levels observed in our earlier experiments by the total angular momentum and perform multiconfiguration Dirac-Fock calculations to compare their results with the observed level density. The observed levels can be relevant for the excitation or decay of the $^{229m}\mathrm{Th}$ isomeric nuclear state which lies in this energy range. The high density of electronic levels promises a strongly enhanced electronic bridge excitation of the isomer in $^{229}{\mathrm{Th}}^{+}$.

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 682841 “ASTRUm”). This work is supported by the Helmholtz International Center for FAIR (HIC for FAIR), by the Bundesministerium fur Bildung und Forschung (BMBF) (05P15RFFAA, 05P15RGFAA), by the Science and Technology Facilities Council (STFC) UK (ST/L005824/1, ST/M001652/1, ST/M006085), by the Helmholtz-CAS Joint Research Group (HCJRG-108), and by the Helmholtz-OCPC Postdoctoral Program (GSI08). C. L. W. acknowledges support by the European Research Council (Grant Agreement ERC-2015-StG No. 677497 “DoRES”). S. D. gratefully acknowledges the support provided by the Alexander von Humboldt Foundation and the Jordanian Scientific Research Support Fund under Grant No. Bas/2/4/2014. S. Yu. T. acknowledges the support by the DAAD through Mendeleev Grant, SPbU(28999675). C. L. and J. G. thank the ExtreMe Matter Institute EMMI at GSI, Darmstadt, and JINA-CEE (NSF Grant No. PHY-1430152) for support in the framework of the EMMI/JINA-CEE Workshop “NARRS” during which this work was discussed.

We investigate the process of nuclear excitation via a two-photon electron transition (NETP) for the case of the doubly charged thorium. The theory of the NETP process was originally devised for heavy-helium-like ions. In this work, we study this process in the nuclear clock isotope $^{229}\mathrm{Th}$ in the $2+$ charge state. For this purpose we employ a combination of configuration interaction and many-body perturbation theory to calculate the probability of NETP in resonance approximation. The experimental scenario we propose for the excitation of the low-lying isomeric state in $^{229}\mathrm{Th}$ is a circular process starting with a two-step pumping stage followed by NETP. The ideal intermediate steps in this process depends on the supposed energy $\ensuremath{\hbar}{\ensuremath{\omega}}_{N}$ of the nuclear isomeric state. For each of these energies, the best initial state for NETP is calculated. Special focus is put on the most recent experimental results for $\ensuremath{\hbar}{\ensuremath{\omega}}_{N}$.

The rest-frame transition frequencies of the $6s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}$ (${D}_{1}$) and $6s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}$ (${D}_{2}$) lines in the stable isotopes of ${\mathrm{Ba}}^{+}$ were measured with an accuracy better than $200\phantom{\rule{4pt}{0ex}}\mathrm{kHz}$ through (quasi)simultaneous collinear and anticollinear laser spectroscopy, leading to an improvement in the accuracy of the isotope shifts by more than an order of magnitude compared to previous data. The ratio of the field-shift constants in the ${D}_{1}$, ${D}_{2}$ fine-structure doublet has been determined to $f=1.0186(9)$ through a King plot analysis. These collinear laser spectroscopy measurements have reached an accuracy comparable to ion-trap measurements on allowed dipole transitions. Our result provides an accurate benchmark for atomic many-body calculations and is compared to pure Dirac-Hartree-Fock calculations and to elaborate multiconfigurational Dirac-Fock calculations. The influence of correlation effects and the Breit interaction on the isotope shift in ${\mathrm{Ba}}^{+}$ are discussed.

We publish three Roadmaps on photonic, electronic and atomic collision physics in order to celebrate the 60th anniversary of the ICPEAC conference. Roadmap III focusses on heavy particles: with zero to relativistic speeds. Modern theoretical and experimental approaches provide detailed insight into the wide range of many-body interactions involving projectiles and targets of varying complexity ranging from simple atoms, through molecules and clusters, complex biomolecules and nanoparticles to surfaces and crystals. These developments have been driven by technological progress and future developments will expand the horizon of the systems that can be studied. This Roadmap aims at looking back along the road, explaining the evolution of the field, and looking forward, collecting nineteen contributions from leading scientists in the field., Journal of Physics B: Atomic, Molecular and Optical Physics, 52 (17), ISSN:1361-6455, ISSN:0368-3508, ISSN:0953-4075, ISSN:0022-3700