Search Results (17)

Building on our previous multi-configuration Dirac–Hartree–Fock (MCDHF) computational strategies tailored for the hyperfine structure (HFS) of low-lying levels in one-valence electron Sr II and Ba II ions and in two-valence electrons in a Ba I atom, we successfully extend these methodologies along the alkaline-earth elements to the lighter Ca II and heavier Ra I–II ions. MCDHF-recommended HFS constants, along with their uncertainty estimates, are reported for the first time and critically discussed. Where applicable, the Bohr–Weisskopf correction is applied to the HFS constants, and its effects are analyzed. This is particularly valuable for cases where no measurement is available such as for the [Rn]${6d }^2{D}_{3/2,5/2}$ levels in ^223,225Ra II, for the [Rn]${7s6d }^3{D}_{1,2,3}$ and ¹$D_2$ levels in ²²³Ra I, for the [Rn]$7s{6d }^3{D}_{2,3}$ and ${}^{1}D_2$ levels in ²²³Ra I, and for the [Rn]$7s{7p }^3{P}_2^o$ level in ²²⁵Ra I. In all cases, our MCDHF values agree with the ones found in the literature within our error bars. For the ${}^{2}D_{5/2}$ levels in Ca II and Ra II, the discrepancies with the experiment observed in Sr II and Ba II for the HFS A constant are not seen. Full article

In this work, we implement the finite-field (FF) method for isotope shift (IS) calculations within the relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) framework of the GRASPG program package. The implementation is benchmarked using the ten lowest-lying fine-structure levels of B II by comparing FF results for the IS parameters with first-order perturbation theory (PT) results obtained using the RIS4 program. The relative deviations for the IS parameters are within 0.03%, and the computed transition isotope shifts agree with previous theoretical predictions and experimental measurements within the reported experimental uncertainties. Additional calculations for Ar XV further confirm the consistency between the FF and PT methods for heavier ions, and the resulting isotope shifts are consistent with the experimental values. This implementation therefore provides GRASPG with two equivalent and reliable approaches for isotope shift calculations. Full article

Osmium is an element of the Periodic Table with an atomic number Z equal to 76. In Tokamaks with divertors made of tungsten ($Z=74$), it is produced in the neutron-induced transmutation of the latter. Therefore one can expect that their sputtering may generate ionic impurities of all possible charge states in the fusion plasma. As a consequence, these could contribute to radiation losses in these controlled nuclear devices. The knowledge of radiative rates in all the spectra of osmium is thus important in this field. In this framework, a multiplatform approach has been used to determine the Os V radiative properties and estimate their accuracy. The transition probabilities have been computed for the 2677 electric dipole (E1) transitions falling in the spectral range from 400 Å to 12,000 Å. Three independent atomic structure models have been considered; one based on the fully relativistic ab initio multiconfiguration Dirac–Hartree–Fock (MCDHF) method and two based on the semi-empirical pseudo-relativistic Hartree–Fock (HFR) method. Full article

Using the Multiconfiguration Dirac–Hartree–Fock method as implemented in the General Relativistic Atomic Structure Package, the magnetic dipole and electric quadrupole hyperfine structure constants were determined for the ground and first excited levels of ^135,137Ba II isotopes, as well as for ¹³⁷Ba I and ⁸⁷Sr II, to assess the robustness of the developed model. This study builds upon and extends previous investigations by examining the levels involved in resonance lines, with the aim of resolving persistent discrepancies in the hyperfine structure of ¹³⁷Ba II and ⁸⁷Sr II. New code developments such as the use of natural orbitals, as well as the addition of polarization effects and Configuration State Function Generators, as implemented in GRASPG, were tested for these heavy elements. The developed strategy allowed us to achieve encouraging results that satisfactorily agree with experiments for all studied levels but ${}^{2}D_{5/2}$ in the ¹³⁷Ba II isotope. This disagreement was also observed in ¹³⁵Ba II isotope as well as in ⁸⁷Sr II. With two valence electrons, ¹³⁷Ba I is definitely more complex, requiring a multireference approach. Even with the latter, the theory–observation disagreement observed for the hyperfine structure of the low-lying levels remains large in comparison with the alkali-like systems. Possible ongoing developments to remediate this issue are discussed in the conclusions. Full article

Dielectronic recombination (DR) is widely recognized as a fundamental atomic process in many astrophysical and laboratory plasmas, where it plays a crucial role in determining ionization balance and level populations over a broad temperature range. Reliable DR resonance strengths and plasma rate coefficients for such plasma modeling can be computed using the Jena Atomic Calculator (JAC)—a relativistic code based on the multiconfiguration Dirac–Hartree–Fock (MCDHF) method. In this work, we investigate the DR of Li-like Ar¹⁵⁺ ions in their ground state (2s), focusing on resonances associated with the fine-structure core excitations $2s_{1/2}\to 2p_{1/2,3/2}$. The resulting fine-structure-resolved DR resonance strengths and plasma rate coefficients are in good agreement with recent high-resolution DR measurements of Ar¹⁵⁺ ions performed at the Main Cooler Storage Ring (CSRm) in Lanzhou, China. These results provide a stringent benchmark for JAC calculations and support their applicability in plasma modeling. Full article

We present excitation energies, transition wavelengths, electric dipole (E1) transition rates, oscillator strengths, line strengths, and lifetimes for the 86 lowest states up to and including $1{\mathrm{s}}^{2}2{\mathrm{s}}^{2}7\mathrm{f}$ in N iii, the 125 lowest states up to and including $1{\mathrm{s}}^{2}2\mathrm{s}7\mathrm{f}$ in N iv, and the 53 lowest states up to $1{\mathrm{s}}^{2}8\mathrm{g}$ in N v using the multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods. The computed results are then compared with data from the Atomic Spectra Database of the National Institute of Standards and Technology (NIST-ASD), experimental results, and other theoretical studies. For all levels in N iii – v, the root mean square energy differences from the NIST values are 130, 103, and 6 cm⁻¹, respectively. Compared to previous multiconfiguration Hartree–Fock and the Breit–Pauli (MCHF-BP) calculations, 89.3%, 98.5%, and 100% of the $log\left(gf\right)$ values for N iii – v agree within 5%, respectively. Full article

In this work, we present a new set of transition probabilities for experimentally classified spectral lines in the Os VI spectrum. To do this, two independent computational approaches based on the pseudo-relativistic Hartree–Fock, including core polarization effects (HFR+CPOL) and fully relativistic Multiconfiguration Dirac–Hartree–Fock (MCDHF) methods, were used, with the detailed comparison of the results obtained with these two approaches allowing us to estimate the quality of the calculated radiative parameters. These atomic data, corresponding to 367 lines of five-times ionized osmium between 438.720 and 1486.275 Å, are expected to be useful for the analysis of the spectra emitted by fusion plasmas in which osmium could appear as a result of transmutation by the neutron bombardment of tungsten used as component of the reactor wall, such as the ITER divertor. Full article

The latest published version of GRASP (General-purpose Relativistic Atomic Structure Package), i.e., GRASP2018, retains a few suboptimal subroutines/algorithms, which reflect the limited memory and file storage of computers available in the 1980s. Here we show how the efficiency of the relativistic self-consistent-field (SCF) procedure of the multiconfiguration-Dirac–Hartree–Fock (MCDHF) method and the relativistic configuration-interaction (RCI) calculations can be improved significantly. Compared with the original GRASP codes, the present modified version reduces the CPU times by factors of a few tens or more. The MPI performances for all the original and modified codes are carefully analyzed. Except for diagonalization, all computational processes show good MPI scaling. Full article

In multiconfiguration Dirac–Hartree–Fock (MCDHF) calculations, there is a strong coupling between the localization of the orbital set and the configuration state function (CSF) expansion used to determine it. Furthermore, it is well known that an orbital set resulting from calculations, including CSFs describing core–core correlation and other effects, which aims to lower the weighted energies of a number of targeted states as much as possible, may be inadequate for building CSFs that account for correlation effects that are energetically unimportant but decisive for computed properties, e.g., hyperfine structures or transition rates. This inadequacy can be traced in irregular or oscillating convergence patterns of the computed properties as functions of the increasing orbital set. In order to alleviate the above problems, we propose a procedure in which the orbital set is obtained by merging several separately optimized, and mutually non-orthogonal, orbital sets. This computational strategy preserves the advantages of capturing electron correlation on the total energy through the variational MCDHF method and allows to target efficiently the correlation effects on the considered property. The orbital sets that are merged are successively orthogonalized against each other to retain orthonormality. The merged orbital set is used to build CSFs that efficiently lower the energy and also adequately account for the correlation effects that are important for the property. We apply the procedure to compute the hyperfine structure constants for the $1s^{2}2s{}^2{S}_{1/2}$ and $1s^{2}2p{}^2{P}_{1/2,3/2}^o$ states in ${}^7$Li and show that it leads to considerably improved convergence patterns with respect to the increasing orbital set compared to standard calculations based on a single orbital set, energy-optimized in the variational procedure. The perspectives of the new procedure are discussed in a broader context in the summary. Full article

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

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

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

Variational methods are used extensively in the calculation of transition rates for numerous lines in a spectrum. In the GRASP code, solutions of the multiconfiguration Dirac–Hartree–Fock (MCDHF) equations that optimize the orbitals are represented by numerical values on a grid using finite differences for integration and differentiation. The numerical accuracy and efficiency of existing procedures are evaluated and some modifications proposed with heavy elements in mind. Full article

Charlotte Froese Fischer has been at the forefront of research in atomic structure theory for over 60 years. She has developed many of the methods currently used by researchers and has written associated computer programs which have been published and hence made accessible to the research community. Throughout her career, she has consistently encouraged and mentored young scientists, enabling them to embark on independent careers of their own. This article provides an overview of the methods and codes she has developed, some large-scale calculations she has undertaken, and some insight into the impact she has had on young scientists, and the leadership she continues to show as she reaches her 90th birthday. Full article

Calculated radiative transition probabilities and oscillator strengths are reported for 392 lines of neutral lanthanum (La I) atom in the spectral range from the near ultraviolet to the mid infrared. They were obtained using two different theoretical methods based on the pseudo-relativistic Hartree–Fock (HFR) and the fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) approaches, both including the most important intravalence and core-valence electron correlations. The quality of these radiative parameters was assessed through detailed comparisons between the results obtained using different physical models and between our theoretical results and the experimental data, where available. Of the total number of La I lines listed in the present work, about 60% have gf- and gA-values determined for the first time. Full article