Atomic Structure Calculations Research Articles

Comparative study of kilonova opacities for three elements of the sixth period (hafnium, osmium, and gold) from new atomic structure calculations in Hf I-IV, Os I-IV, and Au I-IV

Comparative study of kilonova opacities for three elements of the sixth period (hafnium, osmium, and gold) from new atomic structure calculations in Hf I-IV, Os I-IV, and Au I-IV

Investigation of optical spectroscopy in W13+ ions

This study presents the investigation of magnetic dipole transition lines of W13+ ions in the wavelength range of 200–700 nm at a low-energy electron beam ion trap. Seventeen lines emitted from W13+ ions have been observed with three being reported experimentally for the first time. The atomic structure calculation and spectra simulation of W13+ ions have been carried out using the multiconfiguration Dirac–Hartree–Fock method combined with the relativistic configuration interaction approach and the collisional–radiative model, respectively. The theoretical calculations are in reasonable agreement with the experimental observations, and most of the observed lines have been identified.

Targeted optimization in small-scale atomic structure calculations: application to Au I

The lack of reliable atomic data can be a severe limitation in astrophysical modelling, in particular of events such as kilonovae that require information on all neutron-capture elements across a wide range of ionization stages. Notably, the presence of non-orthonormalities between electron orbitals representing configurations that are close in energy can introduce significant inaccuracies in computed energies and transition probabilities. Here, we propose an explicit targeted optimization (TO) method that can effectively circumvent this concern while retaining an orthonormal orbital basis set. We illustrate this method within the framework of small-scale atomic structure models of Au I, using the Grasp2018 multiconfigurational Dirac–Hartree–Fock atomic structure code. By comparing to conventional optimization schemes we show how a TO approach improves the energy level positioning and ordering. TO also leads to better agreement with experimental data for the strongest E1 transitions. This illustrates how small-scale models can be significantly improved with minor computational costs if orbital non-orthonormalities are considered carefully. These results should prove useful to multi-element atomic structure calculations in, for example, astrophysical opacity applications involving neutron-capture elements.

Accurate and experimentally validated transition data for Si I and Si II

Aims. The aim of this study is to provide radiative data for neutral and singly ionised silicon, in particular for the first experimental oscillator strengths for near-infrared Si I lines. In addition, we aim to perform atomic structure calculations both for neutral and singly ionised silicon while including lines from highly excited levels. Methods. We performed large-scale atomic structure calculations with the relativistic multiconfiguration Dirac-Hartree-Fock method using the GRASP2K package to determine log(𝑔ƒ) values of Si I and Si II lines, taking into account valence-valence and core-valence electron correlation. In addition, we derived oscillator strengths of near-infrared Si I lines by combining the experimental branching fractions with radiative lifetimes from our calculations. The silicon plasma was obtained from a hollow cathode discharge lamp, and the intensity-calibrated high-resolution spectra between 1037 and 2655 nm were recorded by a Fourier transform spectrometer. Results. We provide an extensive set of accurate experimental and theoretical log(𝑔ƒ) values. For the first time, we derived 17 log(𝑔ƒ) values of Si I lines in the infrared from experimental measurements. We report data for 1500 Si I lines and 500 Si II lines. The experimental uncertainties of our ƒ-values vary between 5% for the strong lines and 25% for the weak lines. The theoretical log(𝑔ƒ) values for Si I lines in the range 161 nm to 6340 nm agree very well with the experimental values of this study and complete the missing transitions involving levels up to 3s23p7s (61 970 cm−1). In addition, we provide accurate calculated log(𝑔ƒ) values of Si II lines from the levels up to 3s27f (122 483 cm−1) in the range 81 nm to 7324 nm.

K-shell X-Ray Emission from Lithium-like Nitrogen N v

We present laboratory measurements of n = 3 → n = 1 N v X-ray emission lines situated near 26 Å. The lines are excited by electron-impact collisions and are shown to reach a combined intensity of about a fifth of the combined strong N v 1s2s2p 2 P 1/2,3/2 → 1s 22s 2 S 1/2 resonance lines, commonly labeled q and r, at 29.4 Å. In addition, we present new experimental data for the wavelength of the blended q and r lines at 29.4 Å, as well as for that of the blended inner-shell-excited N v lines u and v at 30.0 Å. All of these collisional N v lines need to be included in astrophysical emission models in order to properly account for flux from N v in the soft X-ray region. The measured wavelengths provide benchmarks for testing atomic structure calculations and excellent agreement is found with our calculations using the many-body perturbation theory method. We provide a complete listing of the N v energy levels with valence electrons in the n = 2, 3, and 4 shells calculated with this approach. The experimental and theoretical data, thus, provide accurate rest-frame wavelengths needed for velocity determinations based on high-resolution absorption features in spectra of warm absorbers in active galactic nuclei and other astrophysical objects.

Line identification of extreme ultraviolet spectra from aluminum ions in EAST Tokamak plasmas

Extreme ultraviolet (EUV) spectra emitted from aluminum in the 5-340 Å wavelength range were observed in Experimental Advanced Superconducting Tokamak (EAST) discharges. Several spectral lines from aluminum ions with different degrees of ionization were successfully observed with sufficient spectral intensities and resolutions using three fast-time-response EUV spectrometers. The line identification uses three independent state-of-art computational codes for the atomic structure calculations, which provide the wavelengths and the collisional and radiative transition rate coefficients. These programs are hullac (Hebrew University—Lawrence Livermore Atomic Code), autostructure, and fac (Flexible Atomic Code). Using three different codes allows us to resolve some ambiguities in identifying certain spectral lines and assess the validity of the theoretical predictions.

Simulation of extreme ultraviolet radiation of laser induced discharge plasma

Extreme ultraviolet (EUV) light source is an important part of EUV lithography system in semiconductor manufacturing. The EUV light source requires that the 4p<sup>6</sup>4d<sup><i>n</i></sup>-4p<sup>5</sup>4d<sup><i>n</i>+1</sup> + 4d<sup><i>n</i>-1</sup>4f transitions of Sn<sup>8+~13+</sup> ions emit thousands of lines which form unresolved transition arrays near 13.5 nm. Laser-induced discharge plasma is one of the important technical means to excite target into an appropriate plasma condition. Laser-induced discharge plasma has a simple structure and a low cost. It also has important applications in mask inspection, microscopic imaging, and spectral metrology. In the design and production process, there are many factors that can influence the conversion efficiency, such as current, electrode shape, and laser power density. The simulation method is a convenient way to provide guidance for optimizing the parameters. In this paper, a completed radiation magneto-hydrodynamic model is used to explore the dynamic characteristics of laser-induced discharge plasma and its EUV radiation characteristics. To improve the accuracy, a more detailed global equation of state model, an atomic structure calculation model including relativistic effect and a collision radiation model are proposed simultaneously. The simulation reconstructs the discharge process effectively, which is divided into five stages in the first half cycle of current, including expansion of laser plasma, column formation of discharge plasma, diffusion of discharge plasma, contraction of discharge plasma, and re-diffusion of discharge plasma. It is revealed that the pinch effect during the current rising time exerts a significant influence on the generation of EUV radiation. The conversion efficiency of EUV radiation is still low under our existing conditions, and hopefully a higher rising rate of current can improve the conversion efficiency in the future work.

Algebraic Solution of Gaunt Coefficients via the Angular Momentum Ladder Operators

In this study, Gaunt coefficients, frequently encountered in quantum mechanical calculations of atomic and molecular structures, have been algebraically derived. Firstly, the Gaunt coefficient, equal to the integral over the solid angle of the product of three spherical harmonics, is written in terms of angular momentum ladder operators. Subsequently, raising or lowering operators are applied to spherical harmonics, and the obtained integrals are solved using the recurrence and orthogonality relations of spherical harmonics. As a result, algebraic expressions for Gaunt coefficients are obtained in terms of quantum numbers.

High-order finite element method for atomic structure calculations

We introduce featom, an open source code that implements a high-order finite element solver for the radial Schrödinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or exponential, and the convergence can be systematically controlled by increasing the number and/or polynomial order of the finite element basis functions. The Dirac equation is solved using a squared Hamiltonian approach to eliminate spurious states. To address the slow convergence of the κ=±1 states due to divergent derivatives at the origin, we incorporate known asymptotic forms into the solutions. We achieve a high level of accuracy (10−8 Hartree) for total energies and eigenvalues of heavy atoms such as uranium in both Schrödinger and Dirac Kohn-Sham solutions. We provide detailed convergence studies and computational parameters required to attain commonly required accuracies. Finally, we compare our results with known analytic results as well as the results of other methods. In particular, we calculate benchmark results for atomic numbers (Z) from 1 to 92, verifying current benchmarks. We demonstrate significant speedup compared to the state-of-the-art shooting solver dftatom. An efficient, modular Fortran 2008 implementation, is provided under an open source, permissive license, including examples and tests, wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines. Program summaryProgram Title: featomCPC Library link to program files:https://doi.org/10.17632/962fzmm7f7.1Licensing provisions: MITProgramming language: Fortran with command-line interfacesNature of problem: Solution of the Schrödinger, Dirac, and Kohn–Sham equations of density functional theory for isolated atoms.Solution method: A high-order finite element method is used to assemble a generalized eigenproblem that is then solved for eigenvalues and orbitals. The Poisson equation is solved using the finite element method also. Self-consistent field equations are solved using Pulay mixing.Additional comments including restrictions and unusual features: Our solution methodology for the Dirac equation does not suffer from spurious states. We maintain high accuracy even for κ=±1 states. Unlike other methods, our approach is not limited to Coulombic or self-consistent potentials and can handle non-uniform meshes, including exponential meshes.Restrictions: Spherical symmetry.

Atomic structure calculations, and electron impact ionization cross-sections of W LXI

The present study provides a wide range of calculations of atomic structure data for the tungsten ion W LXI, that belongs to the silicon isoelectronic sequence. The fully relativistic Multi-configuration Dira-Hartree–Fock (MCDHF) method including configuration interaction (CI) is applied to the current ion. Calculated results of energy levels, oscillator strengths, and radiative rates of W LXI are presented. A set of two configuration state lists including the configurations of 3s23p2, 3s3p3, 3s23p3d, and 3p4 at different angular momenta (J) and parity (P) are considered in the configuration interaction calculations of level energies and oscillator strengths. To increase the accuracy of the results, the electronic correlations from higher orbitals, i.e., 7l orbitals are included in the calculations. Quantum electrodynamics effects such as vacuum polarization and self-energy are recalled in the CI calculations. Many more transitions in the soft x-ray region (between 20 and 200 angstroms) have been identified. The flexible atomic code package has been used to compute the electron impact ionization cross-sections of 3s23p2 3P0,1, 1D2 levels in silicon-like tungsten. The cross-sections of the transitions from the ground level in W LXI to the first levels in the 61st ionization of tungsten have been computed using FAC code. The total ionization cross-sections of the 3s23p2 at electron energy range from 5–35 keV are evaluated as well.

Quantum defect and Rydberg energy level calculations for 85Rb and 87Rb by Weakest Bound Electron Potential Model

The Weakest Bound Electron Potential Model (WBEPM) is an effective emerging method for atomic structure calculations that gives results compatible with the experimental observations. In this paper, we have done theoretical calculations of quantum defects and Rydberg energies of high-lying Rydberg energy levels for 85Rb and 87Rb of nS1/2 (n= 14 – 85, 87Rb), nP3/2 (n= 31 – 100, 85Rb), nD3/2 (n= 14 – 85, 87Rb) and nD5/2 (n= 14 – 85, 87Rb) series, through WBEPM. The spectral coefficients for each Rydberg energy level series are determined from Martin's formula and are used to calculate the quantum defects and energy values of the Rydberg energy levels. The obtained results are compared with the available experimental data and show a minimum deviation of the theoretically calculated values from the experimental data. For more insight into the results, values of the Rydberg energy levels and the quantum defects are plotted as a function of the principal quantum number, respectively.

Laser Plasma Characterization and Atomic Structure Calculations of Ti II

Laser Plasma Characterization and Atomic Structure Calculations of Ti II

Deep-Learning Approach for the Atomic Configuration Interaction Problem on Large Basis Sets.

High-precision atomic structure calculations require accurate modeling of electronic correlations typically addressed via the configuration interaction (CI) problem on a multiconfiguration wave function expansion. The latter can easily become challenging or infeasibly large even for advanced supercomputers. Here, we develop a deep-learning approach which allows us to preselect the most relevant configurations out of large CI basis sets until the targeted energy precision is achieved. The large CI computation is thereby replaced by a series of smaller ones performed on an iteratively expanding basis subset managed by a neural network. While dense architectures as used in quantum chemistry fail, we show that a convolutional neural network naturally accounts for the physical structure of the basis set and allows for robust and accurate CI calculations. The method was benchmarked on basis sets of moderate size allowing for the direct CI calculation, and further demonstrated on prohibitively large sets where the direct computation is not possible.

Opacities of singly and doubly ionized neodymium and uranium for kilonova emission modeling

ABSTRACT Even though the electromagnetic counterpart AT2017gfo to the binary neutron star merger GW170817 is powered by the radioactive decay of r-process nuclei, only few tentative identifications of light r-process elements have been made so far. One of the major limitations for the identification of heavy nuclei is incomplete or missing atomic data. While substantial progress has been made on lanthanide atomic data over the last few years, for actinides there has been less emphasis, with the first complete set of opacity data only recently published. We perform atomic structure calculations of neodymium (Z = 60) as well as the corresponding actinide uranium (Z = 92). Using two different codes [flexible atomic code (fac) and hartree–fock-relativistic (hfr)] for the calculation of the atomic data, we investigate the accuracy of the calculated data (energy levels and electric dipole transitions) and their effect on kilonova opacities. For the fac calculations, we optimize the local central potential and the number of included configurations and use a dedicated calibration technique to improve the agreement between theoretical and available experimental atomic energy levels (AELs). For ions with vast amounts of experimental data available, the presented opacities agree quite well with previous estimations. On the other hand, the optimization and calibration method cannot be used for ions with only few available AELs. For these cases, where no experimental nor benchmarked calculations are available, a large spread in the opacities estimated from the atomic data obtained with the various atomic structure codes is observed. We find that the opacity of uranium is almost double the neodymium opacity.

4f photoabsorption in Pt+ to Pt4+

Detailed knowledge of the inner-shell atomic structure of lowly-ionised species is lacking for most elements along the sixth row of the periodic table, from hafnium to bismuth. This paper presents 4f-photoabsorption spectra of Pt+ to Pt4+ ions, recorded between 69 and 127 eV (9.8 nm and 18 nm) using the dual laser plasma method. Analysis of the spectra was supported by atomic structure calculations using the Cowan suite of codes, by relativistic time-dependent local-density approximation (RTDLDA) calculations, and by comparison along isoelectronic series, particularly with spectra of lowly-ionised gold plasmas. The RTDLDA calculations account for the influence of photoionisation and photoexcitation on the recorded spectra. The spectra show 4f 5d, 6d, and 7d transitions, broadened by autoionisation.

Atomic Electronic Structure Calculations with Hermite Interpolating Polynomials.

We have recently described the implementation of atomic electronic structure calculations within the finite element method with numerical radial basis functions of the form χμ(r) = r-1Bμ(r), where high-order Lagrange interpolating polynomials (LIPs) were used as the shape functions Bμ(r). In this work, we discuss how χμ(r) can be evaluated in a stable manner at small r and also revisit the choice of the shape functions Bμ(r). Three kinds of shape functions are considered: in addition to the continuous LIPs, we consider the analytical implementation of first-order Hermite interpolating polynomials (HIPs) that are continuous, as well as numerical implementations of n-th order ( continuous) HIPs that are expressed in terms of an underlying high-order LIP basis. Furnished with the new implementation, we demonstrate that the first-order HIPs are reliable even with large numbers of nodes and that they also work with nonuniform element grids, affording even better results in atomic electronic structure calculations than LIPs with the same total number of basis functions. We demonstrate that discontinuities can be observed in the spin-σ local kinetic energy τσ in small LIP basis sets, while HIP basis sets do not suffer from such issues; however, either set can be used to reach the complete basis set limit with smooth τσ. Moreover, we discuss the implications of HIPs on calculations with meta-GGA functionals with a number of recent meta-GGA functionals, and we find most Minnesota functionals to be ill-behaved. We also examine the potential usefulness of the explicit control over the derivative in HIPs for forming numerical atomic orbital basis sets, but we find that confining potentials are still likely a better option.

Electron-impact excitation of atoms or ions with the screened Coulomb potential

This paper reports the development of a novel distorted wave approach based on the relativistic configuration interaction theory for calculating atomic structures, radiative properties, and collision dynamics of atoms or ions under external confinement. Due to its physical interpretations, the Hulthén potential, valid for many important areas (widely plasma environments) in physics and chemistry, such as atomic physics, solid-state physics, nuclear physics, particle physics, and astrophysics, is used to include the effect of plasma background. The Breit interaction and quantum electromagnetic dynamics effects are perturbatively included in the multi-electron Hamiltonian. Wave functions of bound and continuous states are obtained, which are analyzed by means of the Dirac equations. Interparticle interactions in the scattering matrix element of the system are described by the screened Coulomb interactions. As a test desk, the present approach is applied to the calculation of atomic structures and collision dynamics of an exemplary He-like S14+ ion embedded in a plasma. The energy eigenvalues, transition probabilities, and excitation cross sections are analyzed in detail in terms of the screening parameter. The results of the verification cases are compared to references from the literature, which show a good agreement. The present study not only opens up an opportunity to provide a simple and effective way for understanding the plasma shielding models for many-electron systems but also has important implications for a wide range of applications in astrophysics and laboratory plasma experiments.

Electric-quadrupole transition-rate measurement of a highly charged ion in an electron-beam ion trap using pulsed laser excitation from a metastable state

We present the lifetime measurement of the ${(4{d}_{3/2}^{\ensuremath{-}1}5s)}_{J=2}$ state in Pd-like ${\mathrm{I}}^{7+}$, which predominantly decays to the $(4{d}^{10}{)}_{J=0}$ ground state by an electric-quadrupole transition modified by strong spin-orbit mixing. We measure this microsecond-order lifetime in an electron-beam ion trap using pulsed laser excitation from a metastable state which is continuously populated by electron collisions. The measured lifetime provides a new benchmark for relativistic atomic structure calculations with $d$-state electrons.

Measurement of the electric quadrupole amplitude in atomic thallium transition using electromagnetically induced transparency

We report on a measurement of the transition amplitude ratio χ of an electric quadrupole () to a magnetic dipole () of the transition in atomic thallium. We utilized the electromagnetically induced transparency mechanism and the sideband-bridging technique to resolve the isotopic transitions and their hyperfine manifold. Our measurement gave for 205Tl, and for 203Tl, which was measured for the first time. Our results provide a reference point for the theoretical calculation of atomic structures, and new input for the long dispute on the atomic thallium parity non-conservation measurements.

Hyperfine-structure-resolved laser spectroscopy of many-electron highly charged ions

Hyperfine structures of highly charged ions (HCIs) are favourable spectroscopic targets for exploring fundamental physics along with nuclear properties. Recent proposals of HCI atomic clocks highlight their importance, especially for many-electron HCIs, and they have been theoretically investigated by refining atomic-structure calculations. However, developments in hyperfine spectroscopy of many-electron HCIs have not proceeded due to experimental difficulty. Here, we demonstrate hyperfine-structure-resolved laser spectroscopy of HCIs in an electron beam ion trap plasma, employing the magnetic-dipole transition in the 4d95s state of 127I7+. Ion-state manipulation by controlled electron collisions in the well-defined laboratory plasma enables laser-induced fluorescence spectroscopy of trapped HCIs. The observed spectrum of evaporatively cooled ions under low magnetic fields shows characteristic features reflecting the hyperfine structures. The present demonstration using combined optical and plasma approaches provides a benchmark for state-of-the-art atomic calculations of hyperfine structures in many-electron HCIs, and offers possibilities for a variety of unexploited experiments.