Atomic Structure Calculations Research Articles

CORONIUM IN THE LABORATORY: MEASURING THE Fe XIV GREEN CORONAL LINE BY LASER SPECTROSCOPY

The green coronal line at 530.3 nm was first observed during the total solar eclipse of 1869. Once identified as emitted by Fe XIV, it became clear that this highly charged ion was typical for the range of temperatures found in coronal plasmas, stellar winds, outflows, and accretion disks. Under these conditions of high ionization, the strongest transitions are in the X-ray, extreme ultraviolet, and ultraviolet wavelength range, with only few optical lines. For these so-called forbidden coronal lines, only scarce laboratory data is available, and even advanced atomic theory codes cannot yet predict their wavelengths with the accuracy required for precise absolute velocity determinations of such plasmas. Here we report on a study of the Fe XIV line, a key coronal transition of a highly charged ion, using laser spectroscopy in an electron beam ion trap, obtaining the first laboratory measurement of 530.2801(4) nm for its rest wavelength. The result enables the determination of absolute line shifts and line broadenings in hot turbulent plasmas and astrophysical environments, with an error bar of only 0.24 km s–1. In addition, our measurement provides a much-needed benchmark for advanced atomic structure calculations, which are fundamental for astronomy.

Quantum computing with defects

Abstract

A beamline for x-ray laser spectroscopy at the experimental storage ring at GSI

By combining an x-ray laser (XRL) with a heavy-ion storage ring, precision laser spectroscopy of the fine-structure splitting in heavy Li-like ions will be possible. An initial study has been performed to determine the feasibility of a first experiment at the experimental storage ring at GSI in Darmstadt, which also has great potential for the experiments planned for FAIR. We plan to perform a unique, direct and precise measurement of a fine-structure transition in a heavy Li-like ion. Such a measurement will test state-of-the-art atomic structure calculations in strong fields. This endeavour will require that the existing infrastructure is complemented by a dedicated beamline for the XRL. In this paper, we will discuss the details of this project and outline a proof-of-principle experiment.

Theoretical spectral analysis of extreme ultraviolet emissions from lanthanide atomic ions in plasmas

The extreme ultraviolet emission spectra have been studied theoretically for gadolinium (Gd) and neodymium (Nd) atomic ions in the large helical device at National Institute for Fusion Science, Japan. The spectra have been analyzed and compared with the presently carried out atomic structure calculations using a group of computer codes GRASP92 and RATIP. The complex spectra from the unresolved transition array are generated theoretically. The theory has simulated well the experimental spectra.

Higher-order resonant electronic recombination as a manifestation of configuration interaction

Theoretical and experimental investigations of higher-order electron–ion recombination resonances including inter-shell excitations are presented for L-shell ions of Kr with the aim of examining details of atomic structure calculations. The particular importance of electron–electron interaction and configuration mixing effects for these recombination processes enables their use for detailed tests of electron correlation effects. A test of the required level of considered mixing configurations is presented and further experiments involving higher-order recombination channels are motivated.

Notes on Critical Assessment of Theoretical Calculations of Atomic Structure and Transition Probabilities

Atomic structure and transition probabilities are fundamental physical data required in many fields of science and technology. Atomic physics codes are freely available to other community users to generate atomic data for their interest, but the quality of these data is rarely verified. This special issue addresses estimation of uncertainties in atomic structure and transition probability calculations, and discusses methods and strategies to assess and ensure the quality of theoretical atomic data.

Experimental determination of the nuclear magnetic octupole moment of137Ba+ion

We perform precision measurements on the $5{D}_{5/2}$ manifold hyperfine intervals of a single trapped ion, ${}^{137}$Ba${}^{+}$. rf spectroscopy is used to measure the hyperfine intervals to an accuracy of a few Hz. Our results provide a three orders of magnitude improvement in accuracy over previous work and also provide a 10-fold improvement in the value of ${g}_{J}$ for this level. These results complement our previous work on the 5${D}_{3/2}$ manifold of ${}^{137}$Ba${}^{+}$, providing an independent measurement of the nuclear octupole, and a consistency check on atomic structure calculations.

Chemical effects of high‐resolution YbLγ4 emission spectra: a possible probe for chemical analysis

An ‘eccentric’ X‐ray emission, YbLγ4, was measured for Yb metal, Yb2O3, YbF3, β‐YbAlB4, YbNi3Al9, and YbNi3Ga9 with a resolution of ~0.9 eV. Peak splitting of the YbLγ4 line was observed in all the recorded spectra and was attributed to the two components originating from the LS coupling of the Yb5p hole, the Yb5p1/2 (LIOII: Lγ4′) and Yb5p3/2 components (LIOIII: Lγ4). The spectra were substantially different depending on the chemical environment of Yb. The position of the Lγ4 + Lγ4′ band shifts depending on the valence of Yb (v): ~4.4 eV from divalent to trivalent. The Lγ4 + Lγ4′ spectra of the mixed valence intermetallics, i.e. YbNi3Ga9 (v = 2.59) and β‐YbAlB4 (v = 2.75), were fairly well reproduced by averaging the spectra of divalent Yb and trivalent YbNi3Al9, which suggests the possibility of using the YbLγ4 emission for determining the valence of Yb intermetallics. In trivalent Yb compounds, the relative intensity of Lγ4 compared with that of Lγ4′, as well as the appearance of a high‐energy satellite, was found to be influenced by the ligands around the Yb ions. With the aid of preliminary atomic multiplet and band structure calculations, the differences in the valence band structure and resultant screening effects on the OII,III−1 states were determined to be the possible causes for the observed ligand dependence. © 2013 The Authors. X‐ray spectrometry published by John Wiley & Sons, Ltd.

Accelerating atomic orbital-based electronic structure calculation via pole expansion and selected inversion

We describe how to apply the recently developed pole expansion and selected inversion (PEXSI) technique to Kohn–Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating the charge density, the total energy, the Helmholtz free energy and the atomic forces (including both the Hellmann–Feynman force and the Pulay force) without using the eigenvalues and eigenvectors of the Kohn–Sham Hamiltonian. We also show how to update the chemical potential without using Kohn–Sham eigenvalues. The advantage of using PEXSI is that it has a computational complexity much lower than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEXSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEXSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEXSI are modest. This even makes it possible to perform Kohn–Sham DFT calculations for 10 000-atom nanotubes with a sequential implementation of the selected inversion algorithm. We also perform an accurate geometry optimization calculation on a truncated (8, 0) boron nitride nanotube system containing 1024 atoms. Numerical results indicate that the use of PEXSI does not lead to loss of the accuracy required in a practical DFT calculation.

Special Issue on Critical Assessment of Theoretical Calculations of Atomic Structure and Transition Probabilities

There exist several codes in the atomic physics community to generate atomic structure and transition probabilities freely and readily distributed to researchers outside atomic physics community, in plasma, astrophysical or nuclear physics communities. Users take these atomic physics codes to generate the necessary atomic data or modify the codes for their own applications. However, there has been very little effort to validate and verify the data sets generated by non-expert users. [...]

Uncertainties on Atomic Data

There have been long outstanding requests from the modeling community for uncertainty estimates on atomic data. This paper outlines a systematic approach from fundamental atomic structure and collisional calculations, through to well-known spectral diagnostic lines, correlating the uncertainties from each contributing process.

Time-dependent Monte Carlo calculations of recoil-in-vacuumg-factor data for122,126,130,132Te

A method for extracting nuclear $g$ factors from the attenuation coefficients ${G}_{k}$ ($k=2$,4) of $\ensuremath{\gamma}$-ray angular distributions or particle-$\ensuremath{\gamma}$ angular correlations measured with the recoil-in-vacuum (RIV) technique is presented. The method uses time-dependent Monte Carlo simulations for ${G}_{k}$ as a function of the $g$ factor for a given nuclear lifetime. It is based on atomic-structure calculations from first principles using the grasp2k code by J\"onsson et al. [Comput. Phys. Commun. 177, 597 (2007)]. The simulations are compared with results of RIV measurements for the first excited states (${2}_{1}^{+}$) in ${}^{122,126,130,132}$Te. The choice of the electronic configurations and the effect of the charge-state distributions on ${G}_{k}$ are discussed. New ${2}_{1}^{+}$ $g$-factor values are obtained. These are compared with nuclear-model calculations.

Scaling method for the pair-density-functional theory in combination with energy functionals satisfying the virial theorem: Checking the validity via atomic-structure calculations

We perform atomic-structure calculations for the neutral Ne, Mg, and Ar atoms on the basis of the recently proposed correction method (scaling method) for the pair-density (PD) -functional theory [Phys. Rev. A 84, 044502 (2011)]. The formal features of the scaling method are that the search region of PDs is substantially extended and that the resultant variationally best PD, which can be obtained without the heavy calculation tasks, satisfies the virial theorem rigorously. To enjoy the benefit of these features, we also develop the approximate form of the kinetic energy functional. It is shown by the atomic-structure calculations that the scaling method can improve well not only various energy functionals but also the spatial profiles of the electron density and exchange-correlation hole. Especially it is found that the scaling method makes preferential modifications to the energetically effective regions of the electron density and exchange-correlation hole. These results suggest that the scaling method efficiently puts the PD close to the correct ground-state PD.

Dftatom: A robust and general Schrödinger and Dirac solver for atomic structure calculations

A robust and general solver for the radial Schrödinger, Dirac, and Kohn–Sham equations is presented. The formulation admits general potentials and meshes: uniform, exponential, or other defined by nodal distribution and derivative functions. For a given mesh type, convergence can be controlled systematically by increasing the number of grid points. Radial integrations are carried out using a combination of asymptotic forms, Runge–Kutta, and implicit Adams methods. Eigenfunctions are determined by a combination of bisection and perturbation methods for robustness and speed. An outward Poisson integration is employed to increase accuracy in the core region, allowing absolute accuracies of 10−8 Hartree to be attained for total energies of heavy atoms such as uranium. Detailed convergence studies are presented and computational parameters are provided to achieve accuracies commonly required in practice. Comparisons to analytic and current-benchmark density-functional results for atomic number Z=1–92 are presented, verifying and providing a refinement to current benchmarks. An efficient, modular Fortran 95 implementation, dftatom, is provided as open source, including examples, tests, and wrappers for interface to other languages; wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines. Program summaryProgram title:dftatomCatalogue identifier: AEPA_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPA_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: MIT licenseNo. of lines in distributed program, including test data, etc.: 14122No. of bytes in distributed program, including test data, etc.: 157453Distribution format: tar.gzProgramming language: Fortran 95 with interfaces to Python and C.Computer: Any computer with a Fortran 95 compiler.Operating system: Any OS with a Fortran 95 compiler.RAM: 500 MBClassification: 2.1.External routines: Numpy (http://www.numpy.org/) and Cython (http://cython.org/)Nature of problem:Solution of the Schrödinger, Dirac, and Kohn–Sham equations of Density Functional Theory for isolated atoms.Solution method:Radial integrations are carried out using a combination of asymptotic forms, Runge–Kutta, and implicit Adams methods. Eigenfunctions are determined by a combination of bisection and perturbation methods. An outward Poisson integration is employed to increase accuracy in the core region. Self-consistent field equations are solved by adaptive linear mixing.Restrictions:Spherical symmetryUnusual features:Radial integrators work for general potentials and meshes. No restriction to Coulombic or self-consistent potentials; no restriction to uniform or exponential meshes. Outward Poisson integration. Fallback to bisection for robustness.Running time:For uranium, non-relativistic density functional calculation execution time is around 0.6 s for 10−6 a.u. accuracy in total energy on an Intel Core i7 1.46 GHz processor.

Towards a precise measurement of atomic parity violation in a single Ra + ion

A single trapped Ra + (Z = 88) ion provides a very promising route towards a most precise measurement of Atomic Parity Violation (APV), since APV effects grow faster than Z 3. This experiment promises the best determination of the electroweak coupling constant at the lowest accessible energies. Such a measurement provides a sensitive test of the Standard Model in particle physics. At the present stage of the experiment, we focus on trapping and laser cooling stable Ba + ions as a precursor for radioactive Ra + . Online laser spectroscopy of the isotopes 209 − 214Ra + in a linear Paul trap has provided information on transition wavelengths, fine and hyperfine structures and excited state lifetimes as test of atomic structure calculations. Additionaly, a single trapped Ra + ion could function as a very stable clock.

Observation of the nuclear magnetic octupole moment of173Yb from precise measurements of the hyperfine structure in the3P2state

We measure hyperfine structure in the metastable ${{}^{3}P}_{2}$ state of ${}^{173}$Yb and extract the nuclear magnetic octupole moment. We populate the state using dipole-allowed transitions through the ${{}^{3}P}_{1}$ and ${{}^{3}S}_{1}$ states. We measure frequencies of hyperfine transitions of the ${{}^{3}P}_{2}\ensuremath{\rightarrow}{{}^{3}S}_{1}$ line at 770 nm using a Rb-stabilized ring cavity resonator with a precision of 200 kHz. Second-order corrections due to perturbations from the nearby ${{}^{3}P}_{1}$ and ${{}^{1}P}_{1}$ states are below 30 kHz. We obtain the hyperfine coefficients as $A=\ensuremath{-}742.11(2)$ MHz and $B=1339.2(2)$ MHz, which represent a two orders-of-magnitude improvement in precision, and $C=0.54(2)$ MHz. From atomic structure calculations, we obtain the nuclear moments quadrupole $Q=2.46(12)$ b and octupole $\ensuremath{\Omega}=\ensuremath{-}34.4(21)$ $\mathrm{b}\ifmmode\times\else\texttimes\fi{}{\ensuremath{\mu}}_{N}$.

Self-energy screening approximations in multi-electron atoms

Atomic structure calculations have reached levels of accuracy which require evaluation of many-electron QED contributions. Since exact analytic solutions do not exist, a number of heuristics have been used to approximate the screening of additional electrons. Herein we present an implementation for the widely used GRASP atomic-structure code based on Welton's concept of the electron self-energy. We show that this implementation provides far superior agreement compared with a range of other theoretical predictions, and that the discrepancy between the present implementation and that previously used is of comparable magnitude to other sources of error in high-accuracy atomic calculations. This improvement is essential for ongoing studies of complex atomic systems.

Measurement of a Wavelength of Light for Which the Energy Shift for an Atom Vanishes

Light at a magic-zero wavelength causes a zero energy shift for an atom. We measured the longest magic-zero wavelength for ground state potassium atoms to be λ(zero)=768.9712(15) nm, and we show how this measurement provides an improved experimental benchmark for atomic structure calculations. This λ(zero) measurement determines the ratio of the potassium atom D1 and D2 line strengths with record precision. It also demonstrates a new application for atom interferometry, and we discuss how decoherence will fundamentally limit future measurements of magic-zero wavelengths.

XUV spectra of laser-produced zirconium plasmas

XUV spectra of laser-produced zirconium plasmas in the 20 to 65 Å wavelength range, where 3d–4p and 3d–4f transitions dominate the observed emission, were studied experimentally and theoretically. Atomic structure calculations were performed with the Cowan and flexible atomic codes. Spectator satellite transitions, especially 3dn-14s–3dn-24s4f, where the 4s electron acts as a ‘real’ spectator, in Mn-, Fe-, Co-, Ni- and Cu-like ions have been found to play an important role. The resulting emission causes arrays resulting from 3dn–3dn4f transitions to broaden and must be included in spectral simulations in order to reproduce the overall spectral profile.

Fine structure transitions in Fe XIV

Results are reported for Fe XIV energy levels and transitions obtained from the ab initio relativistic Breit–Pauli R-matrix (BPRM) method. BPRM method developed under the Iron Project is capable of calculating very large number of fine structure energy levels and corresponding transitions. However, unlike in the atomic structure calculations, where levels are identified spectroscopically based on the leading percentage contributions of configurations, BPRM is incapable of such identification of the levels and hence the transitions. The main reason for it is that the percentage contributions can not be determined exactly from the large number of channels in the R-matrix space. The present report describes an identification method that uses considerations of quantum defects of channels, contributions of channel from outer regions, Hund’s rule, and angular momenta algebra for addition and completeness of fine structure components. The present calculations are carried out using a close coupling wave function expansion that included 26 core excitations from configurations 2s22p63s2, 2s22p63s3p,2s22p63p2,2s22p63s3d, and 2s22p63p3d. A total of 1002 fine structure levels with n⩽10, l⩽9, and 0.5⩽J⩽9.5 with even and odd parities and the corresponding 130,520 electric dipole allowed (E1) fine structure transitions, a most complete set for astrophysical modelings of spectral analysis and opacities, is presented. Large number of new energy levels are found and identified. The energies agree very well, mostly in less than 1% with the highest being 1.9%, with the 68 observed fine structure levels. While the high lying levels may have some uncertainty, an overall accuracy of energy levels should be within 10%. BPRM transitions have been benchmarked with the existing most accurate calculated transition probabilities with very good agreement for most cases. Based on the accuracy of the method and comparisons, most of the transitions can be rated with A (⩽10%) to C (⩽30%).