Few-electron Ions Research Articles

Precise measurements of electron <i>g</i> factors in bound states of few-electron ions

<sec>The electron <i>g</i> factor is an important fundamental structural parameter in atomic physics, as it reveals various mechanisms of interactions between electrons and external fields. Precise measurements of <i>g</i> factors of bound electrons in simple atomic and molecular systems provide an effective method for investigating the bound-state quantum electrodynamics (QED) theory. Especially in highly-charged heavy ions (HCIs), the strong electromagnetic interactions between the nuclei and inner-shell electrons provide unique opportunities to test QED under extremely strong fields. Accurate measurements of the <i>g</i> factors of the bound-state electrons are also important for determining nuclear effects, nuclear parameters and fundamental constants. The research on <i>g</i> factors of the bound-state electrons has become a frontier topic in fundamental physics. A Penning trap, which uses steady-state electromagnetic fields to confine charged particles, is utilized to precisely measure the <i>g</i> factor. This paper presents a comprehensive review of the experiments on <i>g</i> factors for few-electron simple systems in Penning traps, including experimental principles, experimental setups, measurement methods, and a summary of important research findings. The physical concept of the electron <i>g</i> factor and its historical research background are introduced. The electron <i>g</i> factor is considered as an effective probe to study higher-order QED effects. Through high-precision measurements of the free electron g factor, discrepancies between the fine-structure constants and other experimental results in atomic physics are identified. Notably, the <i>g</i> factor of the 1s electron in HCIs deviates significantly from the value for free electrons as the atomic number increases. Experimental principles, including the principle of the Penning trap and the principle of measuring the bound-state electron <i>g</i> factors are discussed. A double-trap experiment setup and related precision measurement techniques are also introduced.</sec><sec>This paper reviews several milestone experiments including (1) the stringent test of bound-state QED by precise measurement of bound-state electron <i>g</i> factor of a <sup>118</sup>Sn<sup>49+</sup> ion, (2) measurement of the <i>g</i> factors of lithium-like and boron-like ions and their applications, and (3) measurement of the <i>g</i>-factor isotope shift by using an advanced two-ion balance technique in the Penning trap, providing an insight into the QED effects in nuclear recoil. Finally, this paper summarizes the challenges currently faced in measuring the <i>g</i> factors of bound-state electrons in few-electron ion systems and provides the prospects for the future developments of this field.</sec>

A high-resolution asymmetric von Hamos spectrometer for low-energy X-ray spectroscopy at the CRYRING@ESR electron cooler

We present research program and project for high-resolution wavelength-dispersive spectrometer dedicated to low-energy X-ray spectroscopy at the electron cooler of the CRYRING@ESR storage ring, which is a part of the international Facility for Antiproton and Ion Research (FAIR) currently being built in Darmstadt. Due to the unique shape of the electorn-ion recombination X-ray source, resulting from the overlapping of the electron and ion beams in the electron cooler, the spectrometer can work in the specific asymmetric von Hamos (AvH) geometry. In order to completely eliminate the influence of Doppler effect on the measured X-ray energies, two asymmetric von Hamos spectrometers will be installed next to the dipole magnets on both sides of the electron cooler to detect blue/red (0°/180°) shifted X-rays, e.g. emitted in the radiative recombination (RR) process. The X-ray-tracing Monte-Carlo simulations show that the proposed AvH spectrometer will allow to determine with sub-meV precision, the low-energy X-rays (5–10 keV) emitted from stored bare or few-electron heavy ions interacting with cooling electrons. This experimental precision will enable accurate studies of the quantum electrodynamics (QED) effects in mid-Z H- and He-like ions.

Hyperfine-induced effects on linear polarization following electron-impact excitation of heliumlike Tl79+ ions with nuclear spin

A most general density-matrix formalism is presented to investigate linear polarization of characteristic lines following electron-impact excitation of atoms or ions with arbitrary nuclear spin, which can account for depolarization of energy levels and multipole mixing of radiation fields. It is then applied to the linear polarization of the line radiated from heliumlike ions with nuclear spin . As an example, detailed calculations are performed for Tl79+ ions using the multi-configurational Dirac-Fock method and relativistic distorted-wave theory. It is found that the effect of the hyperfine interaction on the linear polarization depends dominantly on impact electron energy. For low impact energies close to the excitation threshold, the hyperfine interaction results in an enhancement of the linear polarization, especially for those photons emitted perpendicularly to the impact electron beam. In contrast, such a hyperfine-induced effect diminishes quickly with increasing impact energy and vanishes at medium and high energies, which is very different from the results for the case of radiative electron capture (Surzhykov et al 2013 Phys. Rev. A 87 052507). The present study is experimentally accessible at both electron-beam ion traps and ion storage rings and, thus, accurate polarization measurements at low energies can be utilized to probe the hyperfine interaction in highly charged few-electron ions.

Radioactive decays of stored highly charged ions

Decay properties known in neutral atoms can be altered significantly if all or most bound electrons are removed. Straightforwardly, in fully-ionised nuclei, the decay channels involving electrons are simply disabled. Also decay modes, that are hindered or completely blocked in neutral atoms, may, respectively, become dominant or open up in highly charged ions. Few-electron ions are by themselves clean systems with well-defined quantum numbers, in which the interactions within the remaining electrons can either be excluded or treated precisely, thereby allowing for investigations of the influence of atomic shell on nuclear decay properties. Violent stellar environments characterised by high temperatures and densities lead to high ionisation degrees of nuclides involved in nucleosynthesis processes. In spite of the rich motivation for studying radioactive decays of highly charged ions, intensive measurements became possible only after heavy-ion storage rings coupled to radioactive-ion beam facilities became available. Presented here is a compact review of the relevant experimental techniques and experiments.

Proof-of-Principle Experiment for Testing Strong-Field Quantum Electrodynamics with Exotic Atoms: High Precision X-Ray Spectroscopy of Muonic Neon.

To test bound-state quantum electrodynamics (BSQED) in the strong-field regime, we have performed high precision x-ray spectroscopy of the 5g-4f and 5f- 4d transitions (BSQED contribution of 2.4 and 5.2eV, respectively) of muonic neon atoms in the low-pressure gas phase without bound electrons. Muonic atoms have been recently proposed as an alternative to few-electron high-Z ions for BSQED tests by focusing on circular Rydberg states where nuclear contributions are negligibly small. We determined the 5g_{9/2}- 4f_{7/2} transition energy to be 6297.08±0.04(stat)±0.13(syst) eV using superconducting transition-edge sensor microcalorimeters (5.2-5.5eV FWHM resolution), which agrees well with the most advanced BSQED theoretical prediction of 6297.26eV.

Multipole mixing effects on the angular distribution and polarization of dielectronic hypersatellite lines from highly charged helium-like ions

The angular distribution and the degree of linear polarization of the dielectronic hypersatellite lines of highly charged helium-like ions are studied by using the multiconfiguration Dirac-Fock method and density matrix theory with a focus on the multipole mixing effects. Detailed calculations have been carried out for the emission of characteristic X-rays from the (2s2p)P1,23 and P11 resonant states decay to the (1s2s)S13 state following the KLL dielectronic recombination of initial hydrogen-like ions with atomic nuclear charge from Z=22 to Z=100. It is shown that the mixing of electric dipole (E1) and magnetic quadrupole (M2) radiations significantly alters the angular distribution and the degree of linear polarization, in which the shifts are dependent on the resonant capture states and the atomic nuclear charges. The E1+M2 mixing has opposite effects for the (2s2p)P23 and (2s2p)P11 resonant states, except for the (2s2p)P11 resonance of the heavy ions with Z≳90, where the profile of angular distribution is reversed by strong mixing effects due to the contribution of the M2 term and its interference with the E1 radiative channel. The results should be of particular interest to the diagnosis of anisotropic plasmas and the test of fundamental physics in few-electron heavy ions.

Radiative Recombination Plasma Rate Coefficients for Multiply Charged Ions

Radiative recombination (RR) plasma rate coefficients are often applied to estimate electron densities and temperatures under quite different plasma conditions. Despite their frequent use, however, these rate coefficients are available only for selected (few-electron) ions and isoelectronic sequences, mainly because of the computational efforts required. To overcome this limitation, we report here a (relativistic) cascade model which helps compute fine-structure and shell-resolved as well as total RR plasma rate coefficients for many, if not most, elements of the periodic table. This model is based on Jac, the Jena Atomic Calculator, and supports studies on how the electron is captured in selected levels of the recombined ion, a relativistic (Maxwellian) electron distribution, or how the multipoles beyond the electric-dipole field in the electron-photon interaction affect the RR rate coefficients and, hence, the ionization and recombination dynamics of hot plasma. As a demonstration of this model, we compute, compare, and discuss different RR plasma rate coefficients for initially helium-like ions, with an emphasis especially on Fe24+ ions.

Testing standard-model extensions with isotope shifts in few-electron ions

When collecting spectroscopic data on at least four isotopes, nonlinearities in the King plot are a possible sign of physics beyond the standard model. In this work, an improved approach to the search for hypothetical new interactions with isotope-shift spectroscopy of few-electron ions is presented. Careful account is taken of the small nuclear corrections to the energy levels and the gyromagnetic factors, which cause deviations from King linearity within the standard model and are hence a possible source of confusion. In this approach, the experimental King nonlinearity is not compared to the vanishing prediction of the standard model at the leading order, but to the calculated full standard model contribution to King nonlinearity. This makes searching for beyond-the-standard-model physics with King linearity analysis possible in a high-precision experimental regime, avoiding confusion. The bounds which can be set on beyond-the-standard-model parameters remain limited by the uncertainties on the small standard model nuclear corrections which cause King nonlinearity. Direct comparison between theory and experiment on a single pair of isotopes is advocated as a more suitable approach for few-electron ions.

Power spectrum of relativistic heliumlike ions strongly coupled to two coherent light fields

Resonance fluorescence occurs when an atom is irradiated by a continuous monochromatic field. We analyze a ladder-type heliumlike highly charged ion, strongly coupled to two coherent light fields. The independent-particle approximation, where electron–electron correlations are neglected, works very well for few-electron ions when the nuclear charge Z is greater than 50. In order to treat heliumlike systems, one decomposes the corresponding matrix elements into hydrogenlike matrix elements using the independent-particle approximation. To calculate the hydrogenlike matrix elements, we consider that energy states are described fully relativistically.

Hyperfine-induced effects on the Kα1 angular distribution following electron-impact excitation of heliumlike spin- 1/2 Tl79+ ions

Angular distribution of the $K{\ensuremath{\alpha}}_{1}$ $(1s2p\phantom{\rule{0.16em}{0ex}}^{1,3}P_{1,2}\ensuremath{\rightarrow}1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0})$ emission line following electron-impact excitation of heliumlike spin-1/2 ${\mathrm{Tl}}^{79+}$ ions is studied within the framework of the density-matrix theory and the relativistic distorted-wave theory. In particular, we aim to explore how a (nonzero) nuclear magnetic dipole moment ${\ensuremath{\mu}}_{I}$ affects the $K{\ensuremath{\alpha}}_{1}$ angular distribution due to the hyperfine interactions. To this end, detailed calculations are performed for selected spin-1/2 $_{81}^{A}\mathrm{Tl}^{79+}$ ($A=187$, 205, and 207) ions with large ${\ensuremath{\mu}}_{I}$. It is found that the hyperfine-induced effects on the $K{\ensuremath{\alpha}}_{1}$ angular distribution depend strongly on the impact electron energy. When compared with the case of zero-spin ${\mathrm{Tl}}^{79+}$ ions, the $K{\ensuremath{\alpha}}_{1}$ angular distribution becomes much more anisotropic for low impact energies, whereas this anisotropy decreases quickly at intermediate and high impact energies. Such a behavior is in sharp contrast to the results for the fine-structure-resolved $1s2p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}\ensuremath{\rightarrow}1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$ component [Phys. Rev. A 102, 042813 (2020)]. Therefore, accurate $K{\ensuremath{\alpha}}_{1}$ angular measurements at low impact electron energies could be employed as a sensitive tool to probe the hyperfine interaction in highly charged few-electron ions.

Radiative and photon-exchange corrections to new-physics contributions to energy levels in few-electron ions

The influence of hypothetical new interactions beyond the Standard Model on atomic spectra has attracted recent interest. In the present work, interelectronic photon-exchange corrections and radiative quantum electrodynamic corrections to the hypothetical contribution to the energy levels of few-electron ions from a new interaction are calculated. The $1s$, $2s$ and $2p_{1/2}$ ground states of H-like, Li-like and B-like ions are considered, as motivated by proposals to use isotope shift spectroscopy of few-electron ions in order to set stringent constraints on hypothetical new interactions. It is shown that, for light Li-like and B-like ions, photon-exchange corrections are comparable to or even larger, by up to several orders of magnitude, than the leading one-electron contribution from the new interaction, when the latter is mediated by heavy bosons.

Short-time emission of higher-angular-momentum photons by atomic transitions

The short-time regime of spontaneous light emission by few-electron ions is examined in detail, with a specific emphasis on the angular momentum of the emitted light. It is found that, in general, photons carrying a higher angular momentum are emitted with important probabilities, at short times, in transitions that are not of the electric dipole type. The probability of emission of such photons is found to be parametrically non-negligible in this time regime, and even numerically dominant for some cases. It is also found that, in all time regimes, the emission of electric 2 n+1-pole fields is typically numerically dominant over the emission of magnetic 2 n -pole fields by many orders of magnitude. These results refine and deepen our understanding of the emission of angular momentum-carrying light by simple atomic systems.

Calculations of Electron Loss to Continuum in Collisions of Li- and Be-Like Uranium Ions with Nitrogen Targets

Doubly differential cross sections for projectile ionization in fast collisions of few-electron uranium ions with the nitrogen target are calculated within the first order of the relativistic perturbation theory. A comparison with the recent measurements of the energy distribution of forward-emitted electrons is made and good agreement is found.

Observation of strong two-electron–one-photon transitions in few-electron ions

We resonantly excite the $K$ series of O$^{5+}$ and O$^{6+}$ up to principal quantum number $n=11$ with monochromatic x rays, producing $K$-shell holes, and observe their relaxation by soft-x-ray emission. Some photoabsorption resonances of O$^{5+}$ reveal strong two-electron--one-photon (TEOP) transitions. We find that for the $[(1s\,2s)_1\,5p_{3/2}]_{3/2;1/2}$ states, TEOP relaxation is by far stronger than the radiative decay and competes with the usually much faster Auger decay path. This enhanced TEOP decay arises from a strong correlation with the near-degenerate upper states $[(1s\,2p_{3/2})_1\,4s]_{3/2;1/2}$ of a Li-like satellite blend of the He-like $K\alpha$ transition. Even in three-electron systems, TEOP transitions can play a dominant role, and the present results should guide further research on the ubiquitous and abundant many-electron ions where electronic energy degeneracies are far more common and configuration mixing is stronger.

Fifth-force search with the bound-electron g factor

The use of high-precision measurements of the g factor of few-electron ions and its isotope shifts is put forward as a probe for physics beyond the Standard Model. The contribution of a hypothetical fifth fundamental force to the g factor is calculated for the ground state of H-like, Li-like and B-like ions, and employed to derive bounds on the parameters of that force. The weighted difference and especially the isotope shift of g factors are used in order to increase the experimental sensitivity to the new physics contribution. It is found that, combining measurements from four different isotopes of H-like, Li-like and B-like calcium ions at accuracy levels projected to be accessible in the near future, experimental results compatible with King planarity would constrain the new physics coupling constant more than one order of magnitude further than the best current atomic data and theory.

Few-electron atomic ions in non-relativistic QED: The ground state

Following detailed analysis of relativistic, QED and mass corrections for helium-like and lithium-like ions with static nuclei for Z≤20 the domain of applicability of Non-Relativistic QED (NRQED) is localized for ground state energy. It is demonstrated that for both helium-like and lithium-like ions with Z≤20 the finite nuclear mass effects do not change 4–5 significant digits (s.d.), and the leading relativistic and QED effects leave unchanged 3–4 s.d. in the ground state energy. It is shown that the non-relativistic ground state energy can be interpolated with accuracy not less than 13 s.d. for Z≤12, and not less than 12 s.d. for Z≤50 for helium-like as well as for Z≤20 for lithium-like ions by a compact meromorphic function in variable λ=Z−ZB (here ZB is the 2nd critical charge (Turbiner et al., 2016)), P9(λ)∕Q5(λ). It is found that both the Majorana formula – a second degree polynomial in Z with two free parameters – and a fourth degree polynomial in λ (a generalization of the Majorana formula) reproduce the ground state energy of the helium-like and lithium-like ions for Z≤20 in the domain of applicability of NRQED, thus, at least, 3 s.d. It is noted that ≳99.9% of the ground state energy is given by the variational energy for properly optimized trial function of the form of (anti)-symmetrized product of three (six) screened Coulomb orbitals for two-(three) electron system with 3 (7) free parameters for Z≤20, respectively. It may imply that these trial functions are, in fact, exact wavefunctions in non-relativistic QED, thus, the NRQED effective potential can be derived. It is shown that the sum of relativistic and QED effects in leading approximation - 3 s.d. - for both 2 and 3 electron systems is interpolated by 4th degree polynomial in Z for Z≤20.

Asymptotic and interpolation series for the Coulomb three-body systems with unit charges

Accurate mass-interpolation and mass-asymptotic formulas are derived for one- and two-center three-body ions with unit charges. The derived formulas are applied to predict accurate numerical values of the total energies of the ground (bound) $1^{1}S(L = 0)-$states in one-center atomic ions $X^{+} e^{-} e^{-}$ and analogous ground (bound) $1 s \sigma-$states in the two-center, quasi-adiabatic (or quasi-molecular) $X^{+} X^{+} e^{-}$ ions. We also discuss a few problems which currently remain unsolved for the $Q^{-1}$ expansions constructed for the ground (bound) states in few-electron atoms and ions.

Phase-matched extreme-ultraviolet frequency-comb generation

Laser-driven high-order harmonic generation1,2 provides spatially3 and temporally4 coherent tabletop sources of broadband extreme-ultraviolet (XUV) light. These sources typically operate at low repetition rates, frep ≲ 100 kHz, where phase-matched HHG is readily achieved5,6. However, many applications demand the improved counting statistics or frequency-comb precision afforded by high repetition rates, frep > 10 MHz. Unfortunately, at such high frep, phase matching is prevented by steady-state plasma accumulated in the generation volume7–11, strongly limiting the XUV average power. Here, we use high-temperature gas mixtures as the generation medium to increase the gas translational velocity, thereby reducing the steady-state plasma in the laser focus. This allows phase-matched XUV emission inside a femtosecond enhancement cavity at frep = 77 MHz, enabling a record generated power of ~ 2 mW in a single harmonic order. This power scaling opens up many demanding applications, including XUV frequency-comb spectroscopy12,13 of few-electron atoms and ions for precision tests of fundamental physical laws and constants14–20. Using high-temperature gas mixtures as the generation medium to increase the translational velocity of Xe atoms through the focus of a femtosecond enhancement cavity, phase-matched extreme-ultraviolet emission at a repetition rate of 77 MHz and with an average power of ~ 2 mW in a single harmonic order is achieved.

Bremsstrahlung from few-electron ions

We have developed the new approach which can be used for accurate evaluations of the bremsstrahlung cross-sections in the case of few-electron atoms and ions. Our approach is based on the explicit formula for the electron density distribution in such systems. We derive the closed analytical formula for the matrix elements which are needed for highly accurate computations of atomic form-factors of two-electron atoms and ions. Multiple bremsstrahlung from few-electron ions is considered. We also discuss the energy loss due to bremsstrahlung in a plasma which contains multi-charged ions and free electrons. Bremsstrahlung from a high-temperature plasma is considered as well as its role in the high-temperature burn-up of deuterium plasma.

Higher-order perturbative relativistic calculations for few-electron atoms and ions

An effective computational method is developed for electronic-structure calculations in few-electron atoms and ions on the basis of the Dirac-Coulomb-Breit Hamiltonian. The recursive formulation of the perturbation theory provides an efficient access to the higher-order contributions of the interelectronic interaction. Application of the presented approach to the binding energies of lithiumlike and boronlike systems is demonstrated. The results obtained are in agreement with the large-scale configuration interaction Dirac-Fock-Sturm method and other all-order calculations.