Atomic Structure Calculations Research Articles

QEDMOD: Fortran program for calculating the model Lamb-shift operator

We present Fortran package QEDMOD for computing the model QED operator hQED that can be used to account for the Lamb shift in accurate atomic-structure calculations. The package routines calculate the matrix elements of hQED with the user-specified one-electron wave functions. The operator can be used to calculate Lamb shift in many-electron atomic systems with a typical accuracy of few percent, either by evaluating the matrix element of hQED with the many-electron wave function, or by adding hQED to the Dirac–Coulomb–Breit Hamiltonian. New version program summaryProgram Title: QEDMODProgram Files doi:http://dx.doi.org/10.17632/ct869v4gxn.1Licensing provisions: Apache License 2.0.Programming language: Fortran 77.Journal reference of previous version: Computer Physics Communications 189 (2015) 175-181, http://dx.doi.org/10.1016/j.cpc.2014.12.002.Does the new version supersede the previous version?: Yes.Nature of problem: Fortran code for computation of the model QED operator that approximates the Lamb shift in many-electron atoms.Solution method: The method of solution is based on the algorithm developed in Ref. [1].Reasons for the new version: Extension of the region of applicability; fixing of minor bugs.Summary of revisions: Region of supported nuclear charges is extended to Z∈[3,120]; a problem that appeared for the extended nuclear model for several selected values of Z is fixed. [1]V. M. Shabaev, I. I. Tupitsyn, and V. A. Yerokhin, Model operator approach to the Lamb shift calculations in relativistic many-electron atoms, Phys. Rev. A 88, 012513 (2013).

Fully relativistic atomic structure calculations for W XLIV for determination of plasma diagnostic terms

We report accurate calculations of W XLIV through application of multi-configuration Dirac–Fock wave functions. We have calculated the energies for the lowest 100 fine structure levels, transition wavelengths, radiative rates, oscillator strengths, and line strengths for electric (E1) and magnetic dipole (M1) transitions with the extended average level multi-configurational Dirac–Fock method in the General-Purpose Relativistic Atomic Structure Package (GRASP). We have taken into account the electron correlations, quantum electrodynamics (QED) and Breit corrections in our calculations. We have also performed parallel calculations with the flexible atomic code (FAC) to assess the accuracy of our calculations. This is a fully relativistic code that provides a variety of atomic parameters, and (generally) yields results for energy levels and radiative rates comparable to GRASP. Our calculated results match well with experimentally observed results that are obtained in ASDEX upgrade Tokamak. Additionally, we have also provided the line intensity ratios and electron density for W XLIV, which is useful and important in plasma diagnostics and modeling in future International Thermonuclear Experimental Reactor (ITER) experiments. We believe that our results would be beneficial in the areas of fusion plasma research and astrophysical investigations and applications.

Relativistic multireference coupled-cluster theory based on a B -spline basis: Application to atomic francium

In this paper, we report the relativistic Fock space multireference coupled-cluster method for atomic structure calculations. We use the no-pair Dirac-Coulomb-Breit Hamiltonian, together with a finite $B$-spline basis set to expand the large and small components of the Dirac wave function. Our method is applied to calculate ionization energies, reduced matrix elements, lifetimes, and polarizabilities for many states of atomic francium. To evaluate uncertainties of our results and investigate the role of electron correlation effects, we carry out calculations using approximated models at different levels. The quality of our calculations is assessed by comparing with available experimental results, showing a good agreement. In addition, the tune-out wavelengths of the ground state in the range of 340--800 nm, the magic wavelengths for the transition $7s\ensuremath{-}8s$ in the range of 800--1500 nm and the transition $7s\ensuremath{-}7p$ in the range of 600--1500 nm are determined by evaluating the dynamic polarizabilities of the $7s, 8s$, and $7p$ states for a linearly polarized light. These tune-out and magic wavelengths may be useful for laser cooling and trapping of the Fr atom, and for related high-precision trapping measurements.

Substitutional Ta-doping in Y2O3 semiconductor by sol-gel synthesis: experimental and theoretical studies

The Pechini sol-gel method has been employed for the synthesis of pure and (181Hf→)181Ta-doped Y2O3 nanopowders. We performed a structural characterization from the micro to the subnanoscopic scale by means of scanning electron microscopy, energy dispersive x-ray spectroscopy, x-ray diffraction, and time-differential perturbed γ–γ angular correlation (PAC) spectroscopy. The results show the formation of the cubic bixbyite structure after a thermal treatment at 1473 K. For the synthesized 181Ta-doped Y2O3, the PAC experiments demonstrate that the impurities are mainly located at both substitutional cationic sites of the bixbyite structure. The experimental investigation was complemented by performing first-principles electronic structure calculations for Ta atoms localized at the two cationic sites of the Y2O3 semiconductor structure, which allow the study of the structural and electronic modifications induced in the host system when the impurities are introduced. These calculations confirm that the measured electric-field gradients for the synthesized 181Ta-doped Y2O3 correspond to double-ionized impurities located at substitutional defect-free cationic sites of the bixbyite host structure and indicate the site occupancy preference for 181Hf(→181Ta) doping. The behaviour of the site preference of 181Ta impurities with temperature is also discussed. In addition to an extensive structural and electronic characterization of pure and Ta-doped Y2O3 semiconductor, our results demonstrate that the Pechini sol-gel process is an affordable and effective way to successfully synthesize these PAC substitutional doped samples.

Atomic structure calculations of He and Li-like Ti ions for interpreting astrophysical spectra

SynopsisWe are working on atomic structure calculations with main focus on the ions relevant to Astrophysics and upcoming fusion reactors like ITER. Main work comprises of first generating atomic data of ions by theoretical calculations by Grasp2k code and then use it for plasma diagnostic studies by identifying the relevant transitions.

M-X-ray emission in interaction of slow highly charged Xeq+ ions (q=26-40) with metallic foils

SynopsisEmission of M-X-rays in interaction of slow highly charged Xeq+ ions, delivered by electron beam ion source (EBIS), with metallic surfaces was studied. Measured M-X-ray spectra for different charge states give access to interpret both the dynamics of neutralization of highly charged ions at surfaces and relaxation processes of hollow atoms formed in this process. The measured spectra are interpreted in terms of the performed atomic structure calculations using the GRASP code.

Precise determination of the quadrupole transition matrix element ofCa+40via branching-fraction and lifetime measurements

We report the first experimental determination of the $4s \ ^{2}S_{1/2} $ $\leftrightarrow $ $3d \ ^{2}D_{5/2}$ quadrupole transition matrix element in $^{40}$Ca$^+$ by measuring the branching ratio of the $3d \ ^{2}D_{5/2} $ state decaying into the ground state $4s \ ^{2}S_{1/2} $ and the lifetime of the $3d \ ^{2}D_{5/2} $ state, using a technique of highly synchronized measurement sequence for laser control and highly efficient quantum state detection for quantum jumps. The measured branching ratio and improved lifetime are, respectively, 0.9992(80) and 1.1652(46) s, which yield the value of the quadrupole transition matrix element (in absolute value) 9.737(43)~$ea_{0}^{2}$ with the uncertainty at the level of 0.44\%. The measured quadrupole transition matrix element is in good agreement with the most precise many-body atomic structure calculations. Our method can be universally applied to measurements of transition matrix elements in single ions and atoms of similar structure.

English

The optical transition probabilities and hetero-association of caffeine with norfloxacin were obtained using UV-Vis spectroscopy in aqueous solution at room temperature (295K). The heter-association constant of norfloxacin-caffeine complexes (6.67×103 M-1) was obtained using Benesi-Hildebrand approach by linear curve fitting to the experimental data. In order to characterize the binding system of the compounds, the thermodynamic parameters were investigated using Vant’s Hoff equation at the temperature ranges (295 to 304K) with a change in enthalpy value (-1.277±0.103 kJ.mol-1.K-1). The values of change in the thermodynamic parameters indicated that the electrostatic forces play the major role in the binding reaction between the molecules of norfloxacin-caffeine complexes. In addition, the optical transition probabilities of norfloxacin were also calculated in the wavenumber regions from (20000 to 40000 cm-1) by using integrated absorption coefficient techniques. This study is very important for understanding the binding reaction in biological system, nature and strength of the transition, absorption spectral interpretation, and in providing stringent test of atomic and molecular structure calculations for theoretical work of the compounds. Key words: Norfloxacin, caffeine, hetero-association, optical transition, thermodynamics, UV-Vis spectroscopy.

EUV spectral analysis of ns-laser produced bismuth plasmas at 8-17 nm.

Extreme ultraviolet (EUV) spectra from laser produced bismuth plasmas were recorded in the 8-17 nm spectral region using a Nd:YAG laser with a pulse length of 8 ns operating at a range of laser power densities. Due to the broad-band emission at 8-17 nm, bismuth plasmas show promise as sources of quasicontinuous radiation in the extreme ultraviolet. When varying the incident laser power density, ionic populations of Bi ions at different power densities were estimated by the collisional-radiative (CR) model for explanation of changes in the spectral profile. Comparison of experimental spectra with atomic structure calculations using the Hartree-Fock with configuration interaction (HFCI) code of Cowan was performed in order to identify most of the features in the spectra.

Opacity effects on soft X-ray spectra from highly charged lanthanide ions in laser-produced plasmas

We have observed soft X-ray spectra from highly charged ions of seven different lanthanide elements with atomic numbers ranging from 60 to 70 in laser-produced plasmas (LPPs) using CO2 and Nd:YAG laser systems, the wavelengths of which are 10.6μm and 1.064μm, respectively. The spectral feature drastically changes between the two types of LPPs due primarily to the difference in opacity. Narrowband quasicontinuum features arising from n=4–4 transitions, the centre wavelength of which systematically moves to shorter wavelength as the atomic number (Z) increases, are observed in the CO2 LPPs, accompanied by sharp peaks coinciding with the strongest resonance lines of Pd-like ions for lower Z elements. In contrast, the quasicontinuum bands are broader and smoother in the Nd:YAG LPPs, appearing with bands of n=4–5 transitions on the shorter wavelength side. The results are also discussed based on comparisons with atomic structure calculations for ions with outermost 4d and 4f subshells.

Constraints on exotic spin-dependent interactions between electrons from helium fine-structure spectroscopy

Agreement between theoretical calculations of atomic structure and spectroscopic measurements is used to constrain possible contribution of exotic spin-dependent interactions between electrons to the energy differences between states in helium-4. In particular, constraints on dipole-dipole interactions associated with the exchange of pseudoscalar bosons (such as axions or axion-like particles, ALPs) with masses $10^{-2}~{\rm eV} \lesssim m \lesssim 10^{4}~{\rm eV}$ are improved by a factor of $\sim 100$. The first atomic-scale constraints on several exotic velocity-dependent dipole-dipole interactions are established as well.

A Generalized Grid-Based Fast Multipole Method for Integrating Helmholtz Kernels.

A grid-based fast multipole method (GB-FMM) for optimizing three-dimensional (3D) numerical molecular orbitals in the bubbles and cube double basis has been developed and implemented. The present GB-FMM method is a generalization of our recently published GB-FMM approach for numerically calculating electrostatic potentials and two-electron interaction energies. The orbital optimization is performed by integrating the Helmholtz kernel in the double basis. The steep part of the functions in the vicinity of the nuclei is represented by one-center bubbles functions, whereas the remaining cube part is expanded on an equidistant 3D grid. The integration of the bubbles part is treated by using one-center expansions of the Helmholtz kernel in spherical harmonics multiplied with modified spherical Bessel functions of the first and second kind, analogously to the numerical inward and outward integration approach for calculating two-electron interaction potentials in atomic structure calculations. The expressions and algorithms for massively parallel calculations on general purpose graphics processing units (GPGPU) are described. The accuracy and the correctness of the implementation has been checked by performing Hartree-Fock self-consistent-field calculations (HF-SCF) on H2, H2O, and CO. Our calculations show that an accuracy of 10-4 to 10-7 Eh can be reached in HF-SCF calculations on general molecules.

Hyperfine Structure and Isotope Shifts in Dy II

Using fast-ion-beam laser-fluorescence spectroscopy (FIBLAS), we have measured the hyperfine structure (hfs) of 14 levels and an additional four transitions in Dy II and the isotope shifts (IS) of 12 transitions in the wavelength range of 422–460 nm. These are the first precision measurements of this kind in Dy II. Along with hfs and IS, new undocumented transitions were discovered within 3 GHz of the targeted transitions. These atomic data are essential for astrophysical studies of chemical abundances, allowing correction for saturation and the effects of blended lines. Lanthanide abundances are important in diffusion modeling of stellar interiors, and in the mechanisms and history of nucleosynthesis in the universe. Hfs and IS also play an important role in the classification of energy levels, and provide a benchmark for theoretical atomic structure calculations.

Laser spectroscopy studies on nobelium

Laser spectroscopy of the heaviest elements provides high-precision data on their atomic and nuclear properties. For example, atomic level energies and ionization potentials allow us to probe the influence of relativistic effects on their atomic structure and to benchmark state-of-the-art atomic structure calculations. In addition, it offers an alternative route to determine nuclear properties like spins, magnetic moments and quadrupole moments in a nuclear model-independent way. Recently, a sensitive method based on resonant laser ionization has been applied to nobelium isotopes around N = 152 at GSI Darmstadt. In pioneering experiments, several atomic states have been identified extending the reach of laser spectroscopy beyond fermium. In this contribution, the main achievements and future perspectives are briefly summarized.

Unexpectedly large difference of the electron density at the nucleus in the $$ 4p\, ^2{\mathrm {P}}_{{1}/{2},{3}/{2}}$$ 4 p 2 P 1 / 2 , 3 / 2 fine-structure doublet of Ca $$^+$$ +

We measured the isotope shift in the $^2$S$_{1/2}$-$^2$P$_{3/2}$ (D2) transition in singly-ionized calcium ions using photon recoil spectroscopy. The high accuracy of the technique enables us to resolve the difference between the isotope shifts of this transition to the previously measured isotopic shifts of the $^2$S$_{1/2}$-$^2$P$_{1/2}$ (D1) line. This so-called splitting isotope shift is extracted and exhibits a clear signature of field shift contributions. From the data we were able to extract the small difference of the field shift coefficient and mass shifts between the two transitions with high accuracy. This J-dependence is of relativistic origin and can be used to benchmark atomic structure calculations. As a first step, we use several ab initio atomic structure calculation methods to provide more accurate values for the field shift constants and their ratio. Remarkably, the high-accuracy value for the ratio of the field shift constants extracted from the experimental data is larger than all available theoretical predictions.

English

The self-association, optical transition probabilities, and hetero-association with chlorogenic acid of nicotinamide were obtained from UV-Vis spectroscopy in aqueous solution at room temperature (293K). The dimerization constant of nicotinamide ( ) was obtained using dimer model by nonlinear curve fitting technique. The hetero-association constant in the system of molecules of nicotinamide with chlorogenic acid were obtained in aqueous solution using a Benesi-Hildebrand equation. In order to characterize the binding system of the dimerization reactions for the self and hetero-association of the compound, the thermodynamic parameters were investigated using Vant’s Hoff equation at the temperature range (293 to 299K). As a result, the change of enthalpy obtained for the self and hetero-association is and respectively. The values of change in the thermodynamic parameters indicated that the hydrophobic interaction and electrostatic forces subsequently plays the major role in the binding reaction between the molecules of nicotinamide and its complexes with chlorogenic acid, respectively. In addition, the optical transition probabilities of nicotinamide were also calculated in the wavenumber regions by using integrated absorption coefficient techniques. Finally, the results of this study are very important for understanding the binding reaction in biological system, nature and strength of the transition in molecular interaction, absorption spectral interpretation, and in providing stringent test of atomic and molecular structure calculations in theoretical work of the compounds. Key words: Nicotinamide, chlorogenic acid, self-association, hetero-association, optical transition probabilities, thermodynamic properties, UV-Vis spectroscopy.

Reflectance anisotropy spectroscopy of the Si(111)−(5×2)Au surface

Hybrid DFT calculations of atomic structure, electronic band structure, and reflectance anisotropy (RA) are used to correlate atomic and electronic structures and optical transitions of eight structures for the $\mathrm{Si}(111)\text{\ensuremath{-}}(5\ifmmode\times\else\texttimes\fi{}2)\mathrm{Au}$ phase with Au coverage and Si adatom site occupancy. The structure recently proposed by Kwon and Kang (KK) [S. G. Kwon and M. H. Kang, Phys. Rev. Lett. 113, 086101 (2014)] and strongly supported by surface x-ray diffraction [T. Shirasawa et al., Phys. Rev. Lett. 113, 165501 (2014)] is found to be the most stable in the Au coverage range from 0.6 to 0.8 ML. The band structure of the Si adatom covered $(5\ifmmode\times\else\texttimes\fi{}4)$ surface has a surface state whose dispersion and position agree very well with the prominent ${S}_{1}$ surface state observed in angle-resolved photoemission experiment. Reflectance anisotropy spectra in the energy range 0.5 to 5 eV for the eight surface structures show variations with Au and Si adatom coverage which can be explained in terms of filling of this surface state. The best agreement between predicted and measured RA spectra, which are sensitive to both Au atom and Si adatom coverage, is found for coverages from 0.7 to 0.75 ML Au, when the surface has regions where Si adatoms are absent and where there are sufficient adatoms to cause surface-state band filling, in equal parts. Surface formation energy calculations favor a coverage of 0.7-ML Au. The structures of the $(5\ifmmode\times\else\texttimes\fi{}2)$ KK and $(6\ifmmode\times\else\texttimes\fi{}6)\mathrm{Au}$ phases on the Si(111) surface are compared and it is shown that the repeat unit of the KK phase also occurs in the $(6\ifmmode\times\else\texttimes\fi{}6)$ structure.

Atomic structure calculations and study of EUV and SXR spectral lines in Cu-like ions

In the present work, we provide a most extensive and detailed study of highly ionized Cu-like ions and diagnose extreme ultraviolet (EUV) and soft X-ray (SXR) transitions with N-shell electron excitation to M-shell and higher shells. We have determined energy levels and lifetimes for lowest 27 fine-structure levels by adopting multiconfiguration Dirac–Fock (MCDF) with the inclusion of quantum electrodynamics (QED) as well as Breit corrections as a first-order perturbation theory. We have also reported complete radiative data for strong electric dipole transitions within lowest 27 levels. We have compared our calculated results with theoretically calculated and experimentally measured results available in the literature, to measure the credibility and genuineness of our results, and achieve good agreement. Further, because of insufficiency of adequate and complete atomic data for higher levels of highly ionized Cu-like ions in the literature, we have performed other equivalent parallel calculations by implementing fully relativistic distorted wave flexible atomic code (FAC) to ensure the accuracy of our results. Additionally, we have also presented transition wavelengths of Nα transitions of high-Z Cu-like ions by using Moseley’s law. We believe that the large amount of atomic data presented in this paper may be useful in fusion and astrophysical plasma and in several applications, especially in lithography and cell biology.

Atomic structure calculations and study of line intensity ratio for Kr XXIV

In this work, we provide a detailed and elaborate theoretical study of atomic data along with plasma parameters for Kr XXIV. We have computed energy levels, lifetimes, and wave-function compositions for the lowest 148 fine-structure levels by implementing the multi-configuration Dirac–Fock method with the addition of quantum electrodynamics as well as Breit corrections. We have also given the radiative data among 148 levels for electric dipole (E1) transition, which lie in the extreme ultraviolet range. We have compared our calculated results with NIST and other theoretical results available in the literature and attain a good agreement. Because of the unavailability of sufficient and complete data for higher excited levels for Kr XXIV in the literature, a similar calculation has also been compiled using fully relativistic flexible atomic code (FAC) to access the credibility and integrity of our results. On the other hand, we have also presented the line intensity ratio and plasma parameters for optically thin plasma, which are not published anywhere in the literature, and we believe that our presented results may be advantageous in plasma modeling and astrophysical and fusion plasma research applications.

Atomic Structure Calculations for Neutral Oxygen

Energy levels and oscillator strengths for neutral oxygen have been calculated using the Cowan (CW), SUPERSTRUCTURE (SS), and AUTOSTRUCTURE (AS) atomic structure codes. The results obtained with these atomic codes have been compared with MCHF calculations and experimental values from the National Institute of Standards and Technology (NIST) database.