Atoms, Volume 10, Issue 1 (March 2022) – 34 articles

Recent atom interferometry (AI) experiments involving Bose–Einstein condensates (BECs) have been conducted under extreme conditions of volume and interrogation time. Numerical solution of the rotating-frame Gross–Pitaevskii equation (RFGPE), which is the standard mean-field theory applied to these experiments, is impractical due to the excessive computation time and memory required. We present a variational model that provides approximate solutions of the RFGPE for a power-law potential on a practical time scale. This model is well-suited to the design and analysis of AI experiments involving BECs that are split and later recombined to form an interference pattern. We derive the equations of motion of the variational parameters for this model and illustrate how the model can be applied to the sequence of steps in a recent AI experiment where BECs were used to implement a dual-Sagnac atom interferometer rotation sensor. We use this model to investigate the impact of finite-size and interaction effects on the single-Sagnac-interferometer phase shift. Full article

Inelastic processes rate coefficients for low-energy Sr + H, Sr${}^{+}$ + H${}^{-}$, Sr${}^{+}$ + H, and Sr${}^{2+}$ + H${}^{-}$ collisions are calculated using the multichannel quantum model approach. A total of 31 scattering channels of SrH${}^{+}$ and 17 scattering channels of SrH are considered. The partial cross sections and the partial rate coefficients are hence calculated for 1202 partial processes in total. Using new quantum data for Sr ii + H i collisions, we updated the model atom of Sr ii and performed the non-local thermodynamic equilibrium (non-LTE) calculations. We provide the non-LTE abundance corrections for the Sr ii resonance lines in two grids of model atmospheres, which are applicable to very metal-poor ([Fe/H] $\le -2$) dwarfs and giants. Full article

The extraordinary performance offered by cold atom-based clocks and sensors has the opportunity to profoundly affect a range of applications, for example in gravity surveys, enabling long term monitoring applications through low drift measurements. While ground-based devices are already starting to enter the commercial market, significant improvements in robustness and reductions to size, weight, and power are required for such devices to be deployed by Unstaffed Aerial Vehicle systems (UAV). In this article, we realise the first step towards the deployment of cold atom based clocks and sensors on UAV’s by demonstrating an UAV portable magneto-optical trap system, the core package of cold atom based systems. This system is able to generate clouds of $2.1\pm 0.2\times {10}^7$ atoms, in a package of 370 mm × 350 mm × 100 mm, weighing 6.56 kg, consuming 80 W of power. Full article

This article presents a theoretical investigation of the differential, integrated, elastic, inelastic, total, momentum-transfer, and viscosity cross-sections, along with the total ionization cross-section, for elastically scattered electrons and positrons from a carbon dioxide (CO${}_2$) molecule in the incident energy range of 1 eV $\le E_i\le$ 1 MeV. In addition, for the first time, we report the spin polarization of e${}^{\pm }-$CO${}_2$ scattering systems. The independent atom model (IAM) with screening correction (IAMS) using a complex optical potential was employed to solve the Dirac relativistic equation in partial-wave analysis. The comparison of our results with the available experimental data and other theoretical predictions shows a reasonable agreement in the intermediate- and high-energy regions. Full article

We investigate the properties of a dilute gas of impurities embedded in an ultracold gas of bosons that forms a Bose–Einstein condensate (BEC). This work focuses mainly on the equation of state (EoS) of the impurity gas at zero temperature and the induced interaction between impurities mediated by the host bath. We use perturbative field-theory approaches, such as Hugenholtz–Pines formalism, in the weakly interacting regime. In turn, for strong interactions, we aim at non-perturbative techniques such as quantum–Monte Carlo (QMC) methods. Our findings agree with experimental observations for an ultra dilute gas of impurities, modeled in the framework of the single impurity problem; however, as the density of impurities increases, systematic deviations are displayed with respect to the one-body Bose polaron problem. Full article

The one-dimensional Landau–Vlasov equation describing ultracold dilute bosonic gases in the mean-field collisionless regime under strong transverse confinement is analyzed using traditional methods of plasma physics. Time-independent, stationary solutions are found using a similar approach as for the Bernstein–Greene–Kruskal nonlinear plasma modes. Linear stationary waves similar to the Case–Van Kampen plasma normal modes are also shown to be available. The new bosonic solutions have no decaying or growth properties, in the same sense as the analog plasma solutions. The results are applied for real ultracold bosonic gases accessible in contemporary laboratory experiments. Full article

Recently, we reported a series of global minima whose structures consist of carbon rings decorated with heavier group 14 elements. Interestingly, these structures feature planar tetracoordinate carbons (ptCs) and result from the replacement of five or six protons (H⁺) from the cyclopentadienyl anion (C₅H₅⁻) or the pentalene dianion (C₈H₆²⁻) by three or four E²⁺ dications (E = Si–Pb), respectively. The silicon derivatives of these series are the Si₃C₅ and Si₄C₈ clusters. Here we show that ptC persists in some clusters with an equivalent number of C and Si atoms, i.e., Si₅C₅, Si₈C₈, and Si₉C₉. In all these species, the ptC is embedded in a pentagonal C₅ ring and participates in a three-center, two-electron (3c-2e) Si-ptC-Si σ-bond. Furthermore, these clusters are π-aromatic species according to chemical bonding analysis and magnetic criteria. Full article

Since its initial development in the 1970s by Phil Burke and his collaborators, the R-matrix theory and associated computer codes have become the method of choice for the calculation of accurate data for general electron–atom/ion/molecule collision and photoionization processes. The use of a non-orthogonal set of orbitals based on B-splines, now called the B-spline R-matrix (BSR) approach, was pioneered by Zatsarinny. It has considerably extended the flexibility of the approach and improved particularly the treatment of complex many-electron atomic and ionic targets, for which accurate data are needed in many modelling applications for processes involving low-temperature plasmas. Both the original R-matrix approach and the BSR method have been extended to the interaction of short, intense electromagnetic (EM) radiation with atoms and molecules. Here, we provide an overview of the theoretical tools that were required to facilitate the extension of the theory to the time domain. As an example of a practical application, we show results for two-photon ionization of argon by intense short-pulse extreme ultraviolet radiation. Full article

Electron-induced chemistry is relevant to many processes that occur when ionizing radiation interacts with matter. This includes radiation damage, curing of polymers, and nanofabrication processes but also the formation of complex molecules in molecular ices grown on dust particles in space. High-energy radiation liberates from such materials an abundance of secondary electrons of which most have energies below 20 eV. These electrons efficiently trigger reactions when they attach to molecules or induce electronic excitation and further ionization. This review focuses on the present state of insight regarding the mechanisms of reactions induced by electrons with energies between 0 and 20 eV that lead to formation of larger products in binary ice layers consisting of small molecules (H₂O, CO, CH₃OH, NH₃, CH₄, C₂H₄, CH₃CN, C₂H₆) or some derivatives thereof (C₂H₅NH₂ and (C₂H₅)₂NH, CH₂=CHCH₃). It summarizes our approach to identify products and quantify their amounts based on thermal desorption spectrometry (TDS) and electron-stimulated desorption (ESD) experiments performed in ultrahigh vacuum (UHV). The overview of the results demonstrates that, although the initial electron-molecule interaction is a non-thermal process, product formation from the resulting reactive species is often governed by subsequent reactions that follow well-known thermal and radical-driven mechanisms of organic chemistry. Full article

The first nuclear excited state in ${}^{229}$Th possesses the lowest excitation energy of all currently known nuclear levels. The energy difference between the ground- and first-excited (isomeric) state (denoted with ${}^{229\mathrm{m}}$Th) amounts only to ≈8.2 eV (≈151.2 nm), which results in several interesting consequences: Since the excitation energy is in the same energy range as the binding energy of valence electrons, the lifetime of ${}^{229\mathrm{m}}$Th is strongly influenced by the electronic structure of the Th atom or ion. Furthermore, it is possible to potentially excite the isomeric state in ${}^{229}$Th with laser radiation, which led to the proposal of a nuclear clock that could be used to search for new physics beyond the standard model. In this article, we will focus on recent technical developments in our group that will help to better understand the decay mechanisms of ${}^{229\mathrm{m}}$Th, focusing primarily on measuring the radiative lifetime of the isomeric state. Full article

Double photoionization events provide a direct evaluation of electron correlation. The recent focus on few-electron targets continues to reveal the consequences of electron correlation for targets that possess several electrons. We consider the double photoionization of the $2p^2$ valence electrons of atomic carbon and focus on the first energetically accessible final-state symmetries that originate from coupling the active electrons in ${}^{3}P$ configurations, which are doubly ionized by a single photon. Comparison of this process in carbon with neon provides an analogous case for the resulting final-state symmetries within the framework where the ejected electrons are influenced by the remaining bound electrons in a frozen-core approximation. Choosing this symmetry allows for comparison with previous theoretical results for total and energy sharing cross-sections of carbon. Fully differential cross-sections for both carbon and neon are also compared. Full article

The convergent close-coupling (CCC) method was initially developed to describe electron scattering on atomic hydrogen and the hydrogenic ions such as He${}^{+}$. The latter allows implementation of double photoionization (DPI) of the helium atom. For more complex single valence-electron atomic and ionic targets, the direct and exchange interaction with the inner electron core needs to be taken into account. For this purpose, the Hartree-Fock (HF) computer codes developed in the group of Miron Amusia have been adapted. In this brief review article, we demonstrate the utility of the HF technique by examples of electron scattering on Li and the DPI of the H${}^{-}$ and Li${}^{-}$ ions. We also discuss that modern-day computer infrastructure allows the associated CCC code, and others, to be readily run directly via the Atomic, Molecular and Optical Science Gateway. Full article

We present the first results obtained from the S${}^3$ Low-Energy Branch, the gas cell setup at SPIRAL2-GANIL, which will be installed behind the S${}^3$ spectrometer for atomic and nuclear spectroscopy studies of exotic nuclei. The installation is currently being commissioned offline, with the aim to establish optimum conditions for the operation of the radio frequency quadrupole ion guides, mass separation and ion bunching, providing high-efficiency and low-energy spatial spread for the isotopes of interest. Transmission and mass-resolving power measurements are presented for the different components of the S${}^3$-LEB setup. In addition, a single-longitudinal-mode, injection-locked, pumped pulsed-titanium–sapphire laser system has been recently implemented and is used for the first proof-of-principle measurements in an offline laser laboratory. Laser spectroscopy measurements of erbium, which is the commissioning case of the S${}^3$ spectrometer, are presented using the $4f^{12}6s^2$${}^3{H}_6\to 4f^{12}{(}^{3}H)6s6p$ optical transition. Full article

In this work, we direct our attention to the study of the effect of a nonuniform and strong magnetic field on the quantum properties of ions in plasma. We have assumed that the strong magnetic field is a sum of two magnetic fields: one, the most intense, has a toroidal geometry, whereas the other of less intensity (about the third of the first) is poloidal. Regarding the quantum properties, we have focused our attention on obtaining the corresponding eigenenergy of n hydrogen-like ion in this nonuniform magnetic field. Using the obtained eigenenergy, we investigated the spectral line shape (Lyman-alpha) of three types of ions: He${}^{+}$, C${}^{5+}$, and Ar${}^{17+}$ for different magnetic field magnitudes. In this study, we considered only Doppler and electronic Stark broadening of the spectral line shapes. Full article

We present a comprehensive discussion of the ground-state properties of dilute D-dimensional Bose gas interacting with a few static impurities. Assuming the short-ranged character of the boson-impurity interaction, we calculated the energy of three- and two-dimensional Bose systems with one and two impurities immersed. Full article

The detection of gravitational waves and electromagnetic signals from the neutron star merger GW170817 has provided evidence that these astrophysical events are sites where the r-process nucleosynthesis operates. The electromagnetic signal, commonly known as kilonova, is powered by the radioactive decay of freshly synthesized nuclei. However, its luminosity, colour and spectra depend on the atomic opacities of the produced elements. In particular, opacities of lanthanides and actinides elements, due to their large density of bound–bound transitions, are fundamental. The current work focuses on atomic structure calculations for lanthanide and actinide ions, which are important in kilonovae modelling of ejecta spectra. Calculations for Nd III and U III, two representative rare-earth ions, were achieved. Our aim is to provide valuable insights for future opacity calculations for all heavy elements. We noticed that the opacity of U III is about an order of magnitude greater than the opacity of Nd III due to a higher density of levels in the case of the actinide. Full article

We study electron impact excitation of dipole allowed transitions in the extreme ultraviolet range—8–55 nm—for the germanium isoelectronic sequence Te²⁰⁺–Cd¹⁶⁺. The fine structure transitions between the ground state having configuration 4s²4p² and the excited states with configurations 4s4p³ and 4s²4p4d are considered for these ions. We employ the relativistic distorted wave method to calculate the excitation cross sections in the incident electron energy range from the excitation threshold to 5000 eV. To obtain the required ionic bound state wavefunctions we have used the multi-configuration Dirac-Fock method with correlations within the n = 5 complexes as well as performed relativistic configuration interaction calculations to include the quantum electrodynamic effects. The accuracy of these wavefunctions is established by comparing our calculated wavelengths and oscillator strengths of the considered transitions with the previously reported measurements and other available theoretical results. We also provide the fitting parameters of the calculated cross sections and the excitation rate coefficients for their direct applications in plasma modeling. Full article

We present in this review our recent theoretical studies on atomic processes subject to the plasma environment including the $\alpha$ and $\beta$ emissions and the ground state photoabsorption of the one- and two-electron atoms and ions. By carefully examining the spatial and temporal criteria of the Debye–Hückel (DH) approximation based on the classical Maxwell–Boltzmann statistics, we were able to represent the plasma effect with a Debye–Hückel screening potential $V_{DH}$ in terms of the Debye length D, which is linked to the ratio between the plasma density N and its temperature $kT$. Our theoretical data generated with $V_{DH}$ from the detailed non-relativistic and relativistic multiconfiguration atomic structure calculations compare well with the limited measured results from the most recent experiments. Starting from the quasi-hydrogenic picture, we were able to show qualitatively that the energy shifts of the emission lines could be expressed in terms of a general expression as a function of a modified parameter, i.e., the reduced Debye length $\lambda$. The close agreement between theory and experiment from our study may help to facilitate the plasma diagnostics to determine the electron density and the temperature of the outside plasma. Full article

We generalize Schrödinger’s factorization method for Hydrogen from the conventional separation into angular and radial coordinates to a Cartesian-based factorization. Unique to this approach is the fact that the Hamiltonian is represented as a sum over factorizations in terms of coupled operators that depend on the coordinates and momenta in each Cartesian direction. We determine the eigenstates and energies, the wavefunctions in both coordinate and momentum space, and we also illustrate how this technique can be employed to develop the conventional confluent hypergeometric equation approach. The methodology developed here could potentially be employed for other Hamiltonians that can be represented as the sum over coupled Schrödinger factorizations. Full article

A fully differential cross section for single ionization of helium induced by 1 MeV proton impact is calculated using the parabolic convoluted quasi-Sturmian (CQS) method. In the framework of this approach the transition amplitude is extracted directly from the asymptotic behavior of the solution of an inhomogeneous Schrödinger equation for the Coulomb three-body system $(e^{-},{\mathrm{H}\mathrm{e}}^{+},p^{+})$. The driven equation is solved numerically by expanding in convolutions of quasi-Sturmians for the two-body proton-He⁺ and electron-He⁺ systems. It is found, at least in the high energy limit, that the calculated cross sections within the proposed CQS method converge quickly as the number of terms in the expansions is increased, and are in reasonable agreement with experimental data and other theoretical results. Full article

Van der Waals interactions, primarily attractive van der Waals interactions, have been studied over one and half centuries. However, repulsive van der Waals interactions are less widely studied than attractive van der Waals interactions. In this article, we focus on repulsive van der Waals interactions. Van der Waals interactions are dipole–dipole interactions. In this article, we study the van der Waals interactions between multiple dipoles. Specifically, we focus on two-dimensional six-body van der Waals interactions. This study has many potential applications. For example, the result may be applied to physics, chemistry, chemical engineering, and other fields of sciences and engineering, such as breaking molecules. Full article

The two-center basis generator method is used to obtain cross sections for excitation, capture, and ionization in Li${}^{3+}$, C${}^{3+}$, and O${}^{3+}$ collisions with ground-state hydrogen at projectile energies from 1 to 100 keV/u. The interaction of the C${}^{3+}$ and O${}^{3+}$ projectiles with the active electron is represented by a model potential. Comparisons of cross sections with previously reported data show an overall good agreement, while discrepancies in capture for C${}^{3+}$ collisions at low energies are noted. The present results show that excitation and ionization are similar across the three collision systems, which indicates that these cross sections are mostly dependent on the net charge of the projectile only. The situation is different for the capture channel. Full article

Photoionization or photodetachment is an important process. It has applications in solar- and astrophysics. In addition to accurate wave function of the target, accurate continuum functions are required. There are various approaches, like exchange approximation, method of polarized orbitals, close-coupling approximation, R-matrix formulation, exterior complex scaling, the recent hybrid theory, etc., to calculate scattering functions. We describe some of them used in calculations of photodetachment or photoabsorption cross sections of ions and atoms. Comparisons of cross sections obtained using different approaches for the ejected electron are given. Furthermore, recombination rate coefficients are also important in solar- and astrophysics and they have been calculated at various electron temperatures using the Maxwell velocity distribution function. Approaches based on the method of polarized orbitals do not provide any resonance structure of photoabsorption cross sections, in spite of the fact that accurate results have been obtained away from the resonance region and in the resonance region by calculating continuum functions to calculate resonance widths using phase shifts in the Breit–Wigner formula for calculating resonance parameters. Accurate resonance parameters in the elastic cross sections have been obtained using the hybrid theory and they compare well with those obtained using the Feshbach formulation. We conclude that accurate results for photoabsorption cross sections can be obtained using the hybrid theory. Full article

The ClF molecule belongs to an interhalogen family and is important in laser physics and condensed phase molecular dynamics. The elastic and excitation scattering cross sections are obtained in a fixed nuclei approximation using the UKRmol+ codes based on R-matrix formalism. The scattering calculations were performed in the static-exchange (SE), static-exchange-plus-polarisation (SEP), and close-coupling (CC) models. Three CC models with different target states were employed, namely, the 1-state, 5-states, and 12-states. In the CC model, the target states were represented by configuration interaction (CI) wavefunctions. A good agreement of dipole and quadrupole moments of the ground state was obtained with the experimental values, which indicates a good representation of the target modelling. The study predicted the existence of a shape resonance in the SE, SEP, and 5-states CC models. This resonance vanished in the 12-states CC model. The excitation cross sections from ground to the lowest two excited states were also reported. The elastic differential and momentum transfer cross sections were obtained in the 12-states CC models. The contribution of long-range interactions to elastic scattering was included via Born closure approach. The quantities like collision frequencies and rate coefficients were also presented over a wide range of electron temperatures. The ionization cross sections were computed using the binary-encounter-Bethe (BEB) model. The results were reported in $C_{2v}$ point group representation. Full article

We theoretically study the nonadiabatic relaxation dynamics of low-lying singlet excited-states of semisaturated planar tetracoordinated carbon molecule, C${}_7$H${}_4$. This molecule possesses a stable C${}_{2\mathrm{v}}$ ground-state equilibrium geometry. The three low-lying singlet states, S${}_1$, S${}_2$ and S${}_3$, lie in the energy gap of about 1.2 eV. The potential energy surfaces constructed within the quadratic vibronic coupling formalism reveal multiple conical intersections in the Franck-Condon region. Upon photoexcitation to S${}_3$, the wavepacket decays rapidly to lower states via these conical intersections. We also observe the wavepacket transfer to S${}_3$ during the initial wavepacket evolution on lower states, suggesting the nonadiabatic behavior of photoexcited planar C${}_7$H${}_4$. Full article

Open f-shell elements still constitute a great challenge for atomic theory owing to their (very) rich fine-structure and strong correlations among the valence-shell electrons. For these medium and heavy elements, many atomic properties are sensitive to the correlated motion of electrons and, hence, require large-scale computations in order to deal consistently with all relativistic, correlation and rearrangement contributions to the electron density. Often, different concepts and notations need to be combined for just classifying the low-lying level structure of these elements. With Jac, the Jena Atomic Calculator, we here provide a toolbox that helps to explore and deal with such elements with open d- and f-shell structures. Based on Dirac’s equation, Jac is suitable for almost all atoms and ions across the periodic table. As an example, we demonstrate how reasonably accurate computations can be performed for the low-lying level structure, transition probabilities and lifetimes for Th${}^{2+}$ ions with a $5f6d$ ground configuration. Other, and more complex, shell structures are supported as well, though often for a trade-off between the size and accuracy of the computations. Owing to its simple use, however, Jac supports both quick estimates and detailed case studies on open d- or f-shell elements. Full article

Pressure shifts inside an atomic beam are among the more theoretically challenging effects in high-precision measurements of atomic transitions. A crucial element in their theoretical analysis is the understanding of long-range interatomic interactions inside the beam. For excited reference states, the presence of quasi-degenerate states leads to additional challenges, due to the necessity to diagonalize large matrices in the quasi-degenerate hyperfine manifolds. Here, we focus on the interactions of hydrogen atoms in reference states composed of an excited $nD$ state (atom A), and in the metastable $2S$ state (atom B). We devote special attention to the cases $n=3$ and $n=8$. For $n=3$, the main effect is generated by quasi-degenerate virtual P states from both atoms A and B and leads to experimentally relevant second-order long-range (van-der-Waals) interactions proportional to the sixth inverse power of the interatomic distance. For $n=8$, in addition to virtual states with two states of P symmetry, one needs to take into account combined virtual P and F states from atoms A and B. The numerical value of the so-called $C_6$ coefficients multiplying the interaction energy was found to grow with the principal quantum number of the reference D state; it was found to be of the order of ${10}^{11}$ in atomic units. The result allows for the calculation of the pressure shift inside atomic beams while driving transitions to $nD$ states. Full article

The excitation cross-sections of the nS states of atomic hydrogen, n = 2 to 6, by electron impact on the ground state of atomic hydrogen were calculated using the variational polarized-orbital method at various incident electron energies in the range 10 to 122 eV. Converged excitation cross-sections were obtained using sixteen partial waves (L = 0 to 15). Excitation cross-sections to 2S state, calculated earlier, were calculated at higher energies than before. Results obtained using the hybrid theory (variational polarized orbital method) are compared to those obtained using other approaches such as the Born–Oppenheimer, close-coupling, R-matrix, and complex-exterior scaling methods using only the spherical symmetric wave functions. Phase shifts and elastic cross-sections are given at various energies and angular momenta. Excitation rate coefficients were calculated at various electron temperatures, which are required for plasma diagnostics in solar and astrophysics to infer plasma parameters. Excitation cross-sections are compared with those obtained by positron impact excitation. Full article