Atoms, Volume 10, Issue 4 (December 2022) – 60 articles

We present an experimental study on the double K-shell ionization of argon in single collisions with the Xe⁵⁴⁺ ion at 197 MeV/u. The X-ray spectra of multi-ionized argon are measured at the observation angles of 90° and 145° with respect to the projectile beam. The target K X-ray satellite and hypersatellite lines are analyzed with a fitting model and the cross-section ratio of double to single K-shell ionization is derived. The experimental results are compared to the relativistic time-dependent, two-center calculations, and a reasonable agreement is reached. Full article

In this work, we report a spectroscopy measurement of Ru${}^{21+}$ to Ru${}^{24+}$ ions in the optical region using a low energy electron beam ion trap. Twelve lines were observed. The multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods were used to calculate the atomic level energies and the transition rates. With the assistance of the theoretical results, eleven magnetic dipole lines were identified. The experimental results provide new reference data for further theoretical investigations of the complex ions. Full article

Considering light-mediated long-range interactions between cold atoms in a magneto-optical trap (MOT), we present numerical evidence of a nonequilibrium steady state (NESS) for sufficiently large number of atoms (>${10}^8$). This state manifests itself as the appearance of an anisotropic distribution of velocity when a MOT approaches the threshold beyond which self-oscillating instabilities occur. Our three-dimensional (3D) spatiotemporal model with nonlocal spatial dependencies stemming from the interatomic interactions has recently been compared successfully to predict different instability thresholds and regimes in experiments with rubidium atoms. The behavior of the NESS is studied as a function of the main MOT parameters, including its spatiotemporal characteristics. Full article

Heavy Ion Beam Probing (HIBP) diagnostic is a powerful tool for electric field studies in the hot dense plasma of modern-day toroidal magnetic confinement devices. On the TUMAN-3M tokamak, the HIBP have been used in regimes with improved plasma confinement to clear up the role of the radial electric field in the transition to good confinement regimes. Recently, a modernization of the TUMAN-3M HIBP diagnostics was performed, aiming to reconfigure it for a work with a reversed plasma current direction and improvement of the overall stability of the diagnostic. The results of the first measurements of the plasma potential in the co-NBI scenario are reported and discussed. Full article

X-rays produced during collisions between Highly Charged Ions (HCI) and sample surfaces can potentially be used to investigate the surface’s magnetic properties, taking advantage of the (partial) conservation of the spin of the electrons captured by the ion during the collision. We conducted studies to characterize the X-ray detection system and to determine, with a sub-degree accuracy, the incident angle between the incoming ions and the sample surfaces. A series of proof-of-principle experiments are presented involving an Ar¹⁷⁺ ion beam interacting with a nonmagnetic Si sample. The obtained X-ray spectra show a significant dependency in terms of X-ray yield and energy on the ion incidence angle. These findings will be used to guide future ion–magnetic surface studies. Full article

Highly charged ions in the plasma produced by high-power laser can radiate bright and short-pulse X-rays. Owing to the unresolved transition array (UTA) from the high-Z elements, laser produced plasma has been applied for developing X-ray sources. In particular, X-rays in the water-window (WW) region (2.3–4.4 nm) is utilized as the light source of the X-ray microscopy to observe living organisms under high contrast and resolution. In this work, WW X-rays radiated from a laser (1064 nm, 6.2 ns) produced Au-plasma has been studied. UTA spectrum in the WW range has been observed through a grazing incident spectrometer (GIS). Dependence of Au-ion charge state distribution on laser intensity has been experimentally investigated and evaluated by a transition probability data calculated by the flexible atomic code. The integrated soft X-ray emission has been observed through a pinhole camera with a 1.0-μm Ti-filter, combined with a 2-D plasma radiation scanning achieved by the GIS. An intense WW emission region 200-μm away from the target surface has been observed, which indicates a more effective area is possible to be utilized for a practical use. Full article

We consider the implications of the recent measurement of the W-boson mass $M_W=\mathrm{80,433.5}\pm 9.4\mathrm{MeV}/{\mathrm{c}}^2$ for atomic parity violation experiments. We show that the change in $M_W$ shifts the Standard Model prediction for the ${}^{133}$Cs nuclear weak charge to $Q_W\left({}^{133}\mathrm{Cs}\right)=-73.11\left(1\right)$, i.e., by $8.5\sigma$ from its current value, and the proton weak charge by 2.7%. The shift in $Q_W\left({}^{133}\mathrm{Cs}\right)$ ameliorates the tension between existing determinations of its value and motivates more accurate atomic theory calculations, while the shift in $Q_W\left(p\right)$ inspires next-generation atomic parity violation experiments with hydrogen. Using our revised value for $Q_W\left({}^{133}\mathrm{Cs}\right)$, we also readjust constraints on parameters of physics beyond the Standard Model. Finally, we reexamine the running of the electroweak coupling for the new W boson mass. Full article

A multitude of weaker Fe IX lines have been predicted in the vicinity of the strong 171 Å line that dominates the spectra of many astrophysical and laboratory sources. Some of these weaker lines have only recently been identified in the laboratory, albeit some only tentatively. Here, we present measurements on the Livermore EBIT-I electron beam ion trap that span the region from 170.0 to 173.6 Å, which surrounds the 171 Å line. The measurements stepped through electron beam energy to determine the charge state of iron associated with each observed feature. Moreover, we have minimized the presence of oxygen in the trap, because oxygen lines obscured possible Fe IX lines in past measurements and prevented their identification. Our measurement confirms formerly tentative identifications and adds several new assignments. Full article

Pulsed gas injection in a plasma can affect many fundamentals, including electron heating and losses. The case of an asymmetric RF magnetron plasma with a pulsed argon injection is analyzed by optical emission spectroscopy of argon 2p-to-1s transitions coupled with collisional-radiative modeling. For a fully detailed population model of argon 2p levels accounting for direct and stepwise electron-impact excitation in optically thick conditions, a rapid decrease in the electron temperature, T_e, is observed during each gas injection with the sudden pressure rise. The opposite trend, with unrealistic T_e values before and after each pulse, is observed for analysis based on simple corona models, thus emphasizing the importance of stepwise excitation processes and radiation trapping. Time-resolved electron temperature variations are directly linked to the operating parameters of the pulsed gas injection, in particular the injection frequency. Based on the complete set of data, it is shown that the instantaneous electron temperature monotonously decreases with increasing pressure, with values consistent with those expected for plasmas in which charged species are produced by electron-impact ionization of ground state argon atoms and lost by diffusion and recombination on plasma reactor walls. Full article

The design and performances of a newly built electrostatic charge state analyzer constructed to act as a spectrometer for keV/u ions are reported. It consists of two ${90}^{\circ }$ curved electrodes enclosed by Matsuda electrodes. This setup was recently tested using Ar${}^{9+}$ and Ar${}^{12+}$ ion beams at an energy of 10 keV per charge unit. This spectrometer achieves a good separation of different charge states formed by electron capture processes during collisions between primary ions and the residual gas. Thanks to these first tests, we have identified up to three different background contributions on the detector that need to be reduced or suppressed. Full article

The rigorous two-center approach based on the dual-kinetically balanced finite-basis-set expansion is applied to one-electron, heteronuclear diatomic Bi-Au, U-Pb, and Cf-U quasimolecules. The obtained $1\sigma$ ground-state energies are compared with previous calculations, when possible. Upon analysis of three different placements of the coordinate system’s origin in the monopole approximation of the two-center potential: (1) in the middle, between the nuclei, (2) in the center of the heavy nucleus, and (3) in the center of the light nucleus, a substantial difference between the results is found. The leading contributions of one-electron quantum electrodynamics (self-energy and vacuum polarization) are evaluated within the monopole approximation as well. Full article

The two-center wave-packet convergent close-coupling method has been applied to model the processes of electron capture and ionisation in collisions of fully stripped neon and lithium ions with atomic hydrogen at projectile energies from 1 keV/u to 1 MeV/u. For the Ne${}^{10+}$ projectile, the resulting total electron-capture cross section lies between the two sets of experimental results available for system, which differ from each other significantly. For Li${}^{3+}$, our total electron-capture cross section agrees with the available experimental measurements by Shah et al. [J. Phys. B: At. Mol. Opt. Phys 11, L233 (1978)] and Seim et al. [J. Phys. B: At. Mol. Opt. Phys 14, 3475 (1981)], particularly at low and high energies. We also get good agreement with the existing theoretical works, particularly the atomic- and molecular-orbital close-coupling calculations. Our total ionisation cross section overestimates the experimental data by Shah et al. [J. Phys. B: At. Mol. Opt. Phys 15, 413 (1982)] at the peak, however we get good agreement with the other existing theoretical calculations at low and high energies. Full article

Neutral beam injection is supposed to be the main source of high-energy particles, driving non-inductive current and generating primary neutrons in fusion neutron sources design based on tokamaks. Numerical simulation of high-energy particles’ thermalization in plasma and fusion neutron emission is calculated by novel dedicated software (NESTOR code). The neutral beam is reproduced statistically by up to 10⁹ injected particles. The beam efficiency and contribution to primary neutron generation is shown to be dependent on the injection energy, input current, and plasma temperature profile. A beam-driven plasma operation scenario, specific for FNS design, enables the fusion rate and neutron generation in plasma volume to be controlled by the beam parameters; the resultant primary neutron yield can be efficiently boosted in plasma maintained at a relatively low temperature when compared to ‘pure’ fusion reactors. NESTOR results are applicable to high-precision nuclear and power balance estimations, neutron power loads distribution among tokamak components, tritium generation in hybrid reactors, and for many other tasks critical for FNS design. Full article

Highly charged heavy ions at rest offer a wide spectrum of precision measurements. The GSI Helmholtzzentrum für Schwerionenforschung GmbH is able to deliver ions up to U${}^{92+}$. As the production of these heavy, highly charged ions requires high kinetic energies, it is necessary to decelerate these ions for ultimate precision. The broad energy distribution, which results from the deceleration in the HITRAP linear decelerator, needs to be reduced to allow for further transportation and experiments. The HITRAP cooling trap is designed to cool, i.e., reduce, this energy spread by utilizing electron cooling. The commissioning of this trap is done with Ar${}^{16+}$-ions from a local EBIT ion source. By analyzing the signal of stored ions after ejection, properties such as ion lifetime, charge exchange, and ion motions can be observed. Here, we provide an overview of the recent results of the commissioning process and discuss future experiments. Full article

The low-energy heavy ion storage ring CRYRING was transported from Stockholm to Darmstadt, modernized and reconfigured, and recommissioned as CRYRING@ESR. The machine is now in operation with all installations in service and is available as a user facility for experiments proposed through the SPARC collaboration. During the 2020–2022 period, we brought a number of experimental installations into service and used them to measure first data: the ultra-cold electron cooler for merged-beam electron–ion collisions, the gas jet target for atomic collisions, a next-generation microcalorimeter-based X-ray spectroscopy setup, and others. Ions can be injected either in low charge states from a local ion source through a 300 keV/u RFQ linac, or in high charge states from the GSI accelerator chain through ESR. This allows for very broad access to ions across the entire periodic table. CRYRING@ESR is able to de- or accelerate ions and cool and store beams of isotopically pure species in a desired charge state. While the analysis is still largely ongoing, the first experimental data already show that the machine reached its expected performance level, and our high expectations regarding achievable resolution in spectroscopy experiments have been fulfilled. With access to new classes of ions available through ESR injection and a new generation of experimental instrumentation, CRYRING@ESR is a unique facility for experiments with heavy, highly charged ions. Here, we will review our present setup and machine performance, discuss the data from our first commissioning experiments and briefly preview the upcoming new installations for the coming years. Full article

We present a theoretical investigation of the elastic Rayleigh scattering of X-rays by atomic targets. Special attention is paid to the question of how the polarization of the scattered photons is affected if the incident light is itself polarized. In particular, we found that the circular polarization of the incoming X-rays may lead to a remarkable modification of the linear polarization of the scattered photons. Based on this ’circular-to-linear-polarization-transfer’ and on the fact that the linear polarization of X-rays can be conveniently observed by solid-state Compton detectors, we argue that Rayleigh scattering may be used as a tool for circular polarimetry of hard X-rays. To illustrate our proposal, we performed detailed calculations of 145 and 500 keV circularly polarized photons scattered by lead atoms. Based on these calculations, we found that the photon scattering under large angles with respect to the incident beam direction is most favorable for the circular polarimetry of hard X-rays. In particular, for 500 keV photon energy and scattering angles around 70 deg we found a remarkable modification of the linear polarization of scattered light for the case when the incident radiation is circularly polarized. Full article

Sequential two-photon ionization is a process that is experimentally accessible due to the use of new free-electron laser sources for excitation. For the prototypical rare Ar gas atoms, a photoelectron spectrum (PES) corresponding to the second step of the sequential two-photon double ionization (2PDI${}^{\mathrm{II}}$) at a photon excitation energy of 65.3 eV was studied theoretically with a focus on the consequences of electron correlations in the considered process. The calculation predicts many intense lines at low photoelectron energies, which cannot be explained on the basis of a one-electron approximation. The processes that lead to the appearance of these lines include many-electron correlations, either in the first or second step of photoionization. A significant fraction of the intensity of the low-energy part of PES is associated with the Auger decay of the excited states formed at the second step of 2PDI. The shape of the low-energy part of the 2PDI${}^{\mathrm{II}}$ PES is expected to be dependent on both the energy of photon excitations and the flux of the exciting beam. Full article

In this work, we present high-accuracy spectroscopic properties, such as line strengths, transition probabilities and oscillator strengths for allowed transitions among $n{D}_{3/2,5/2},n^{\prime }{S}_{1/2}$ and $n^{\prime }{P}_{1/2,3/2}(n=4,n^{\prime }=5,6)$ states of Rb-isoelectronic Tc (Tc VII), Ru (Ru VIII) and Rh (Rh IX) ions for their applications in the analysis of astrophysical phenomena occurring inside celestial bodies containing Tc, Ru and Rh ions. Due to the scarcity of computational data of atomic properties of these transitions, as well as considerable discrepancies within the literature about these ions, the precise determination of these properties is necessary. For this purpose, we have implemented relativistic many-body perturbation theory (RMBPT) for evaluation of the wave functions of the considered states. For better accuracy, we have accounted for electron interactions through random phase approximation, Brückner orbitals and structural radiations of wave functions in our RMBPT method for further precise evaluation of electric dipole amplitudes. Combining these values of the observed wavelengths, the above transition properties and radiative lifetimes, a number of excited states of Tc VII, Ru VIII and Rh IX ions have been calculated. For further validation of our work, we have compared our results with the data already available in the literature. Full article

The wave-packet convergent close-coupling approach is used to calculate integrated target excitation and ionisation cross sections in bare beryllium-ion collisions with the $2\ell m$ states of atomic hydrogen (where n, ℓ and m are the principal, orbital angular momentum and magnetic quantum numbers, respectively). The calculations are performed at representative projectile energies between 10 keV/u to 1 MeV/u. The calculated cross sections for collisions with H($2s$) are compared with recent theoretical results. Generally, good agreement is observed for the n-partial excitation and total ionisation cross sections. However, a significant discrepancy is found for excitation into the dominant $n=3$ states at 100 keV/u, where the target excitation cross-section peaks. We also present the first calculations of the excitation and ionisation cross sections for Be${}^{4+}$ collisions with H($2p_0$) and H($2p_{\pm 1}$). Full article

The results of experimental and theoretical studies on electron-impact excitation of the $6s6p P_1^{°}{}_{ }{}^3\to 6s^2 S_0^{ }{}_1{}^{}$ (λ190.8 nm) and $6s7s S_0^{ }{}_1{}^{}\to 6s6p P_1^{°}{}_{ }{}^3$ (λ179.9 nm) intercombination transitions in the single-charged thallium ion are presented. The crossed-beams technique was used in combination with a spectroscopic method in the experiment. A distinct structure revealed in the cross-sections of both lines results from electron decay of atomic autoionizing states and radiative transitions from upper ionic levels. The dominant mechanism of the structure formation was the Coster–Kronig process. Relativistic distorted wave calculations were performed to obtain emission cross-sections for the above transitions. The absolute values of the cross-sections were found to be (0.25 ± 0.08) × 10⁻¹⁶ cm² (λ190.8 nm) and (0.10 ± 0.04) × 10⁻¹⁶ cm² (λ179.9 nm) at the electron energy of 100 eV. Full article

The Fock expansion, which describes the properties of two-electron atoms near the nucleus, is studied. The angular Fock coefficients ${\psi }_{k,p}(\alpha ,\theta )$ with the maximum possible value of subscript p are calculated on examples of the coefficients with $5\le k\le 10$. The presented technique makes it possible to calculate such angular coefficients for any arbitrarily large k. The mentioned coefficients being leading in the logarithmic power series representing the Fock expansion, they may be indispensable for the development of simple methods for calculating the helium-like electronic structure. The theoretical results obtained are verified by other suitable methods. The Wolfram Mathematica is used extensively. Full article

In this study, the variants of structures are considered for fission fragments of the 235U nucleus caused by thermal neutrons, depending on differences in the initial configuration of proton, neutron and alpha particle compositions, according to a symmetrical model developed for the atomic nucleus. The proposed model is based on the principles of spatial symmetry and the analysis of the binding energy of the nucleus, taking into account the quark structure of nucleons. For the first time, the number of alpha particles in the composition of the 235U nucleus is considered to be 44 and the total number of connections between nucleons is 292. The work compares the binding energy of fragments of the atomic nucleus 235U, which have the same number of protons and neutrons in their composition, but a different number of alpha particles. The results obtained are the basis for an experimental study on the energy characteristics of various fission options of the 235U+n reaction, which is of interest for improving the efficiency of nuclear power sources. Full article

The analysis of geological samples that have several chemically diffused zones which formed under certain physico-chemical condition is difficult to achieve. The quantitative estimations of the minerals in such samples are tedious. The present work demonstrates the application of LIBS for qualitative and quantitative analyses of a quartz-fluorite composite which was procured from an amygdaloidal basalt from Deccan Traps, India. The presence of weak emission lines of F in the spectral range of 200–900 nm makes it challenging to quantify the fluorine. This study has addressed a promising alternative to quantify the fluorine using electronic bands of CaF molecules observed in the Laser-induced Breakdown Spectroscopy (LIBS) spectrum. In addition to this spectroscopic technique, the authors also have used Photoacoustic Spectroscopy (PAS) and UV-VIS spectroscopy technique to obtain molecular information from the geological sample. Principal Component Analysis (PCA) was applied to a truncated spectral region of the CaF molecule, and it showed 99% variance. Further, the obtained results with these spectroscopic techniques were compared with the results that were obtained from X-ray diffraction and Electron Probe Micro Analyzer, and they show good agreement. Thus, the LIBS technique can be promising for in situ profile section (varies from few microns to centimeters size) studies without the sample’s destruction using the point detection capability of LIBS. Full article

We modified the Hfs92 code of the GRASP package in order to describe the magnetic octupole hyperfine interaction. To illustrate the utility of the modified code, we carried out state-of-the-art calculations of the electronic factors of the magnetic octupole hyperfine interaction constants for levels in the ground configuration of the Bi atom. The nuclear magnetic octupole moment of the ${}^{209}$Bi isotope was extracted by combining old measurements of the hyperfine structures of $6p^3{}^4{S}_{3/2}^o$ [Hull, R.; Brink, G. Phys. Rev. A 1970, 1, 685] and ${}^2{P}_{3/2}^o$ [Landman, D.A.; Lurio, A. Phys. Rev. A 1970, 1, 1330] using the atomic-beam magnetic-resonance technique with our theoretical electronic factors. The present extracted octupole moment was consistent with all the available values but the one obtained in the single-particle nuclear shell model approximation. This observation supports the previous finding that nuclear many-body effects, such as the core polarization, significantly contribute to the nuclear magnetic octupole moment in the case of ${}^{209}$Bi. Full article

In this study, comprehensive calculations of energies, hyperfine structure constants, Landé $g_J$ factors and isotope shifts have been performed for the lowest 71 states of Na-like Ar${}^{7+}$, Kr${}^{25+}$ and Xe${}^{43+}$ ions. Radiative parameters viz., wavelengths, transition rates, oscillator strengths and lifetimes are estimated for the electric dipole E1 transitions among these levels. The states under consideration include $1s^{2}2s^{2}2p^{6}nl$ for n = 3–9, l = 0–6, and the fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) method integrated in the latest version of the general-purpose relativistic atomic structure package (GRASP2018) is used for the calculations. The additional corrections, such as the Breit interaction and quantum electrodynamics effects are included in the relativistic configuration interaction calculations, and their effects on energies and other parameters are analysed. We examined the impact of including the core–core and core–valence correlations on level energies. Furthermore, to inspect the reliability of our MCDHF results, we performed another set of calculations using the many-body perturbation theory built into the Flexible Atomic Code (FAC). Moreover, we estimated the uncertainties in the computed lifetimes and transition parameters and assigned their accuracy class. A thorough comparison between the two obtained calculations and with the previous theoretical and experimental results, wherever available, is carried out and a good agreement is observed. Full article

Using two independent theoretical methods based on the pseudo-relativistic Hartree–Fock (HFR) and the fully relativistic Multiconfigurational Dirac–Hartree–Fock (MCDHF) approaches, we computed the radiative parameters (transition probabilities and oscillator strengths) corresponding to the spectrum of quadruply ionized lutetium (Lu V). The agreement observed between both sets of results allowed us to deduce the radiative rates for a large amount of transitions in order to calculate the contribution of this ion to the opacity of kilonovae in their early phases, i.e., for T = 25,000 K. The results obtained were compared to previous data computed for other quadruply ionized lanthanide atoms, namely La V, Ce V, Pr V, Nd V and Pm V, in order to highlight the main contributors to the opacity among these ions under kilonovae conditions where the V^th spectra are predominant. Full article

A program library for computing pure spin-angular coefficients for any one- and scalar two-particle operators is presented. The method used is based on the combination of the second quantization and quasi-spin techniques with the angular momentum theory and the method of irreducible tensorial sets. A relativistic approach is assumed. This program library is integrated in the General Relativistic Atomic Structure Package but it can be implemented in other program packages, too. Full article

A recombination plasma soft X-ray laser that is associated with Li-like Aluminum ion Al¹⁰⁺ 3d-4f transition (wavelength: 15.47 nm) was investigated to increase the gain coefficient. By optimizing the time interval of the 16-pulse train, higher-density plasma with a low temperature could be generated, and thus, we obtained the gain coefficient of 9.84 cm⁻¹ at the pump laser pulse energy which was as low as 3 J. To further enhance the X-ray laser output energy, the single resonator which was installed by using a Mo/Si multilayer mirror that has a high reflectivity of 0.45 at 15.5 nm, and the X-ray spectrum after the double pass in the lasing medium was measured. As a result, the output intensity was increased to be 1.5 times higher than t=when it was compared with those that were conducted with no X-ray mirror. Full article

Following the work of Giulio Racah and others from the 1940s onward, the rotational symmetry of atoms and ions, e.g., the conservation of angular momentum, has been utilized in order to efficiently predict atomic behavior, from their level structure to the interaction with external fields, and up to the angular distribution and polarization of either emitted or scattered photons and electrons, while this rotational symmetry becomes apparent first of all in the block-diagonal structure of the Hamiltonian matrix, it also suggests a straight and consequent use of symmetry-adapted interaction amplitudes in expressing the observables of most atomic properties and processes. We here emphasize and discuss how atomic structure theory benefits from exploiting this symmetry, especially if open-shell atoms and ions in different charge states need to be combined with electrons in the continuum. By making use of symmetry-adapted amplitudes, a large number of excitation, ionization, recombination or even cascade processes can be formulated rather independently of the atomic shell structure and in a language close to the formal theory. The consequent use of these amplitudes in existing codes such as Grasp will therefore qualify them to deal with the recently emerging demands for developing general-purpose tools for atomic computations. Full article

Closed analytical formulas are derived for the differential and total cross sections of the non-relativistic photoelectric effect in the three main classes of few-electron atomic systems: (a) neutral atoms and positively charged atomic ions which contain more than one bound electron, (b) negatively charged atomic ions, and (c) one-electron atoms and ions. Our procedure developed in this study is a combination of QED methods and results of the density functional theory obtained for atoms and ions. In all these systems the photoelectric effect is considered as photodetachment of the outer-most electron and our analysis is based on the results of density functional theory obtained for the electron density (radial) distribution in these atomic systems. Analytical formulas (similar to ours) for the differential and total cross sections of photoelectric effect for atomic systems from classes (a) and (b) contribute to our understanding of these systems and have not appeared in the literature, to the best of our knowledge. Full article