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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$^{o}_{1/2, 3/2}$ 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.

In this work, we report a list of 91 strong Th ii spectral lines in the visible wavelength region that could be used as cosmochronometers in future investigations to determine stellar ages from thorium radioactive decay. This list was established on the basis of a pseudo-relativistic Hartree–Fock model including core-polarization corrections (HFR+CPOL) allowing us to compute the corresponding radiative decay parameters, the latter being found to be in good overall agreement with the most accurate experimental data when available. Besides this semi-empirical approach, the fully relativistic ab initio multiconfiguration Dirac–Hartree–Fock (MCDHF) method was attempted, showing large discrepancies with both the present HFR+CPOL and the most recent experimental oscillator strengths, although the calculated wavelengths from theoretical energy levels agreed with observed spectral line wavelengths within 2.4 per cent.

We modified the H$_{FS}$92 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$^{o}_{3/2}$ [Hull, R.; Brink, G. Phys. Rev. A 1970, 1, 685] and $^{2}$P$^{o}_{3/2}$ [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.

In previous work devoted to {\it ab initio} calculations of hyperfine structure constants in nitrogen and fluorine atoms, we observed sizeable relativistic effects, a priori unexpected for such light systems, that can even largely dominate over electron correlation. We observed that the atomic wave functions calculated in the Breit-Pauli approximation describe adequately the relevant atomic levels and hyperfine structures, even in cases for which a small relativistic $LS$-term mixing becomes crucial. In the present work we identify new levels belonging to the spectroscopic terms $2p^4(^3\!P) 3d ~ \; ^{2,4}\!(P,D,F)$ of the fluorine atom, for which correlation effects on the hyperfine structures are small, but relativistic $LS$-term admixtures are decisive to correctly reproduce the experimental values. The Breit-Pauli analysis of the hyperfine matrix elements nails cases with large cancellation, either between $LS$ pairs for individual hyperfine operators, or between the orbital and the spin-dipole contributions. Multiconfiguration Dirac-Hartree-Fock calculations are performed to support the Breit-Pauli analysis.

The changes in the mean-square charge radius (relative to 209Bi), magnetic dipole, and electric quadrupole moments of 187,188,189,191Bi were measured using the in-source resonance-ionization spectroscopy technique at ISOLDE (CERN). A large staggering in radii was found in 187,188,189Big, manifested by a sharp radius increase for the ground state of 188Bi relative to the neighboring 187,189Big. A large isomer shift was also observed for 188Bim. Both effects happen at the same neutron number, N=105, where the shape staggering and a similar isomer shift were observed in the mercury isotopes. Experimental results are reproduced by mean-field calculations where the ground or isomeric states were identified by the blocked quasiparticle configuration compatible with the observed spin, parity, and magnetic moment. ispartof: Physical Review Letters vol:127 issue:9 ispartof: location:United States status: published

In the case of the one-electron Dirac equation with a point nucleus, the virial theorem (VT) states that the ratio of the kinetic energy to potential energy is exactly −1, a ratio that can be an independent test of the accuracy of a computed solution. This paper studies the virial theorem for subshells of equivalent electrons and their interactions in many-electron atoms. This shows that the linear scaling of the dilation is achieved through the balancing of the contributions to the potential of an electron from inner and outer regions that some Slater integrals impose conditions on a single subshell, but others impose conditions between subshells. The latter slows the rate of convergence of the self-consistent field process in which radial functions are updated one at a time. Several cases are considered. Results are also extended to the nonrelativistic case.

We report multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction calculations on the thallium (Tl) electron affinity, as well as on the excited energy levels arising from the ground configuration of ${\mathrm{Tl}}^{\ensuremath{-}}$. The results are compared with the available experimental values and further validated by extending the study to its homologous, lighter element, indium (In), belonging to group 13 (III.A) of the Periodic Table. The calculated electron affinities of In and Tl, 383.4 and 322.8 meV, agree with the latest measurements by within 1%. Three bound states ${}^{3}{P}_{0,1,2}$ are confirmed in the $5{s}^{2}5{p}^{2}$ configuration of ${\mathrm{In}}^{\ensuremath{-}}$, while only the ground state ${}^{3}{P}_{0}$ is bound in the $6{s}^{2}6{p}^{2}$ configuration of ${\mathrm{Tl}}^{\ensuremath{-}}$. The isotope shifts on the In and Tl electron affinities are also estimated. The E2 and M1 intraconfiguration radiative transition rates within $5{s}^{2}5{p}^{2} {}^{3}{P}_{0,1,2}$ of ${\mathrm{In}}^{\ensuremath{-}}$ are used to calculate the radiative lifetimes of the metastable ${}^{3}{P}_{1,2}$ levels.

S stars are late-type giants that are transition objects between M-type stars and carbon stars on the asymptotic giant branch (AGB). They are classified into two types: intrinsic or extrinsic, based on the presence or absence of technetium (Tc). The Tc-rich or intrinsic S stars are thermally-pulsing (TP-)AGB stars internally producing s-process elements (including Tc) which are brought to their surface via the third dredge-up (TDU). Tc-poor or extrinsic S stars gained their s-process overabundances via accretion of s-process-rich material from an AGB companion which has since turned into a dim white dwarf. Our goal is to investigate the evolutionary status of Tc-rich S stars by locating them in a Hertzsprung-Russell (HR) diagram using the results of Gaia early Data Release 3 (EDR3). We combine the current sample of 13 Tc-rich stars with our previous studies of 10 Tc-rich stars to determine the observational onset of the TDU in the metallicity range [-0.7; 0]. We also compare our abundance determinations with dedicated AGB nucleosynthesis predictions. The stellar parameters are derived using an iterative tool which combines HERMES high-resolution spectra, accurate Gaia EDR3 parallaxes, stellar evolution models and tailored MARCS model atmospheres for S-type stars. Using these stellar parameters we determine the heavy-element abundances by line synthesis. In the HR diagram, the intrinsic S stars are located at higher luminosities than the predicted onset of the TDU. These findings are consistent with Tc-rich S stars being genuinely TP-AGB stars. The comparison of the derived s-process abundance profiles of our intrinsic S stars with the nucleosynthesis predictions provide an overall good agreement. Stars with highest [s/Fe] tend to have the highest C/O ratios., 22 pages, 10 figures, accepted for publication in Section 7. Stellar structure and evolution of Astronomy and Astrophysics (A&A)

Atomic properties of n = 3 states of the W 56 + - W 61 + ions are systematically investigated through two state-of-the-art methods, namely, the second-order many-body perturbation theory, and the multi-configuration Dirac–Hartree–Fock method combined with the relativistic configuration interaction approach. The contributions of valence-valence and core-valence electron correlations, the Breit interaction, the higher-order retardation correction beyond the Breit interaction through the transverse photon interaction, and the quantum electrodynamical corrections to the excitation energies are studied in detail. The excitation energies and wavelengths obtained with the two methods agree with each other within ≈ 0.01 %. The present results achieve spectroscopic accuracy and provide a benchmark test for various applications and other theoretical calculations of W 56 + - W 61 + ions. They will assist spectroscopists in their assignment and direct identification of observed lines in complex spectra.

Large-scale ab initio calculations of the electronic contribution to the electric quadrupole hyperfine constant B were performed for the 5s25p6s1,3Po1 excited states of neutral tin. To probe the sensitivity of B to different electron correlation effects, three sets of variational multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction calculations employing different strategies were carried out. In addition, a fourth set of calculations was based on the configuration interaction Dirac-Fock-Sturm theory. For the 5s25p6s 1Po1 state, the final value of B/Q=703(50) MHz/b differs by 0.4% from the one recently used by Yordanov et al. [Commun. Phys. 3, 107 (2020)] to extract the nuclear quadrupole moments Q for tin isotopes in the range 117−131Sn from collinear laser spectroscopy measurements. Efforts were made to provide a realistic theoretical uncertainty for the final B/Q value of the 5s25p6s 1Po1 state based on statistical principles and on correlation with the electronic contribution to the magnetic dipole hyperfine constant A.

Hyperfine spectra of $^\text{27-32}$Al ($Z=13$) have been measured at the ISOLDE-CERN facility via collinear laser spectroscopy using the $3s^23p\ ^2\text{P}^\text{o} _{3/2}\rightarrow 3s^24s\ ^2\text{S}_{1/2}$ atomic transition. For the first time, mean-square charge radii of radioactive aluminum isotopes have been determined alongside the previously unknown magnetic dipole moment of $^{29}$Al and electric quadrupole moments of $^{29,30}$Al. A potentially reduced charge radius at $N=19$ may suggest an effect of the $N=20$ shell closure, which is visible in the Al chain, contrary to other isotopic chains in the $sd$ shell. The experimental results are compared to theoretical calculations in the framework of the valence-space in-medium similarity renormalization group using multiple sets of two and three-nucleon forces from chiral effective field theory. While the trend of experimental magnetic dipole and electric quadrupole moments is well reproduced, the absolute values are underestimated by theory, consistent with earlier studies. Moreover, both the scale and trend of the charge radii appear to be very sensitive to the chosen interaction.

Communications Physics 3(1), 107 (2020). doi:10.1038/s42005-020-0348-9, Published by Springer Nature, London

Hyperfine structure (HFS) measurements of neutron-rich iridium isotopes $^{196,197,198}\mathrm{Ir}$ ($Z=77,\phantom{\rule{0.16em}{0ex}}N=119$--121) were performed via in-gas-cell laser resonance ionization spectroscopy at the KEK Isotope Separation System. Magnetic dipole moments $\ensuremath{\mu}$ and isotope shifts were determined from the HFS spectra. The variation of mean-square charge radii and quadrupole deformation parameters of these isotopes were evaluated from the isotope shifts. The $\ensuremath{\mu}$ value of $^{197}\mathrm{Ir}$ agreed with a theoretical value based on the strong coupling model, and the Ir nucleus was interpreted as prolately deformed by the theoretical calculations. The $\ensuremath{\mu}$ values of $^{196,198}\mathrm{Ir}$ were also compared with semiempirical values calculated based on the strong coupling model. From the comparison, we can suggest the possible spin values of ${I}^{\ensuremath{\pi}}=1,{2}^{\ensuremath{-}}$ for $^{196}\mathrm{Ir}$ and ${I}^{\ensuremath{\pi}}={1}^{\ensuremath{-}}$ for $^{198}\mathrm{Ir}$.

Ab initio multiconfiguration Dirac–Hartree–Fock (MCDHF) calculations have been carried out in order to determine the isotope shift (IS) electronic parameters of transitions belonging to electric dipole (E1) transition arrays 5 s 2 5 p 3 − 5 s 2 5 p 2 6 s , 5 s 2 5 p 2 6 s − 5 s 2 5 p 2 6 p and 5 s 2 5 p 2 6 s − 5 s 2 5 p 2 7 p in neutral antimony, Sb I. In a correlation model limited to single and double excitations from the valence shells, these parameters, combined with the changes in mean-square nuclear charge radius δ⟨r2⟩123,121 compiled by Angeli and Marinova [3] produce isotope shifts values in good agreement with the most recent measurements by high-resolution emission and optogalvanic absorption spectroscopy of Sobolewski et al. [5] but not with the old measurements of Buchholz et al. [4] for 5 p 3 − 5 p 2 6 s . However, our analysis does not allow to reject the latter due to the large uncertainty affecting δ⟨r2⟩123,121, i.e. 0.072 ± 0.048 fm2 [3]. This shows the need of a more accurate determination of this nuclear parameter. Although improving excitation energies, the inclusion of core-valence correlation limited to one hole in the 4d core subshell destroyed the theory-experiment agreement on the IS parameters.

Using the multiconfiguration Dirac-Hartree-Fock and the relativistic configuration interaction methods, a consistent set of transition energies and radiative transition data for the lowest 546 (623, 701, 745) states of the $3p^4 3d$, $3s 3p^2 3d^2$, $3s 3p^3 4p$, $3s 3p^4$, $3s^2 3d^3$, $3s^2 3p^2 3d$, $3s^2 3p^2 4d$, $3s^2 3p^2 4s$, $3p^3 3d^2$, $3p^5$, $3s 3p 3d^3$, $3s 3p^3 3d$, $3s 3p^3 4s$, $3s^2 3p 3d^2$, %$3s^2 3p^2 4f$, $3s^2 3p^2 4p$, $3s^2 3p^3$ configurations in Mn~XI (Fe~XII, Co~XIII, Ni~XIV) is provided. The comparison between calculated excitation energies for the $n=4$ states and available experimental values for Fe XII indicate that the calculations are highly accurate, with uncertainties of only a few hundred cm$^{-1}$. Lines from these states are prominent in the soft X-rays. With the present calculations, several recent new identifications are confirmed. Other identifications involving $3p^2 4d$ levels in Fe~XII that were found questionable are discussed and a few new assignments are recommended. As some $n=4$ states of the other ions also show large discrepancies between experimental and calculated energies, we reassess their identification. The present study provides highly accurate atomic data for the $n=4$ states of P-like ions of astrophysical interest, for which experimental data are scarce.

We are reinvestigating the hyperfine structure of sodium using a fully relativistic multiconfiguration approach. In the fully relativistic approach, the computational strategy somewhat differs from the original nonrelativistic counterpart used in J\"onsson et al. (Phys. Rev. A 53 (1996) 4021). Numerical instabilities force us to use a layer-by-layer approach that has some broad unexpected effects. Core correlation is found to be significant and therefore requires to be described in an adequate orbital basis. The natural-orbital basis provides an interesting alternative to the orbital basis from the layer-by-layer approach, allowing us to overcome some deficits of the latter, giving rise to magnetic dipole hyperfine structure constant values in excellent agreement with observations. Effort is made to assess the reliability of the natural-orbital bases and to illustrate their efficiency., Comment: 12 tables, 2 figures

Atomic properties of S-like W are evaluated through a state-of-the-art method, namely, the multi-configuration Dirac-Hartree-Fock (MCDHF) method combined with the relativistic configuration interaction (RCI) approach. The level energies, wavelengths, and transition parameters involving the 88 lowest levels of W$^{+58}$ (W LIX) are calculated. We discuss in detail the relative importance of the valence- and core-valence electron correlation effects, the Breit interaction, the higher order retardation correction beyond the Breit interaction through the transverse photon interaction, and the quantum electrodynamical (QED) corrections. The present level energies are highly accurate, with uncertainties close to what can be achieved from spectroscopy. As such, they provide benchmark tests for other theoretical calculations of S-like W and should assist the spectroscopists in their assignment/identification of observed lines in complex spectra.

Nuclear charge radii of 62−80Zn have been determined using collinear laser spectroscopy of bunched ion beams at CERN-ISOLDE. The subtle variations of observed charge radii, both within one isotope and along the full range of neutron numbers, are found to be well described in terms of the proton excitations across the Z=28 shell gap, as predicted by large-scale shell model calculations. It comprehensively explains the changes in isomer-to-ground state mean square charge radii of 69−79Zn, the inversion of the odd-even staggering around N=40 and the odd-even staggering systematics of the Zn charge radii. With two protons above Z=28, the observed charge radii of the Zn isotopic chain show a cumulative effect of different aspects of nuclear structure including single particle structure, shell closure, correlations and deformations near the proposed doubly magic nuclei, 68Ni and 78Ni., SCOPUS: ar.j, info:eu-repo/semantics/published

Atoms and ions of lanthanides have multiple opens shells along with an open $4{f}^{k}$ subshell. This paper studies the effect of electron correlation in such systems and how wave functions can be determined for the accurate prediction of atomic properties in the case of ${\mathrm{Ce}}^{2+}$ where $k=2$, using the multireference single- and double-excitation method. An efficient higher-order method is recommended for more reliable results.

Using the multiconfiguration Dirac–Hartree–Fock and the relativistic configuration interaction methods, a consistent set of transition energies and radiative transition data for the main states of the 2 s 2 2 p 4 , 2 s 2 p 5 , 2 p 6 , 2 s 2 2 p 3 3 s , 2 s 2 2 p 3 3 p , 2 s 2 2 p 3 3 d , 2 s 2 p 4 3 s , 2 s 2 p 4 3 p , and 2 s 2 p 4 3 d configurations in O-like Ions between Ar XI ( Z = 18 ) and Cr XVII ( Z = 24 ) is provided. Our data set is compared with the NIST compiled values and previous calculations. The data are accurate enough for identification and deblending of new emission lines from hot astrophysical and laboratory plasmas. The amount of data of high accuracy is significantly increased for the n = 3 states of several O-like ions, where experimental data are very scarce.

We present the theoretical calculations of the electronic isotope shift factors of the 5 d 7 6 s 2 4 F 9 / 2 → ( odd , J = 9 / 2 ) line at 247.587 nm, that were recently used to extract nuclear mean square radii and nuclear deformations of iridium isotopes [Mukai et al. (2020)]. The fully relativistic multiconfiguration Dirac-Hartree-Fock method and the relativistic configuration interaction method were used to perform the atomic structure calculations. Additional properties such as the sharing rule, Lande g factors or phase tracking were employed to ensure an adequate description of the targeted odd level.

Astronomical spectroscopy has recently expanded into the near-infrared (nIR) wavelength region, raising the demands on atomic transition data. The interpretation of the observed spectra largely relies on theoretical results, and progress towards the production of accurate theoretical data must continuously be made. Spectrum calculations that target multiple atomic states at the same time are by nomeans trivial. Further, numerous atomic systems involve Rydberg series,which are associated with additional difficulties. In this work, we demonstrate how the challenges in the computations of Rydberg series can be handled in large-scale multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) calculations. By paying special attention to the construction of the radial orbital basis that builds the atomic state functions, transition data that are weakly sensitive to the choice of gauge can be obtained. Additionally, we show that the Babushkin gauge should not always be considered as the preferred gauge, and that, in the computations of transition data involving Rydberg series, the Coulomb gauge could be more appropriate for the analysis of astrophysical spectra. To illustrate the above, results from computations of transitions involving Rydberg series in the astrophysically important C IV and C III ions are presented and analyzed., SCOPUS: ar.j, info:eu-repo/semantics/published

We use the multiconfiguration Dirac-Hartree-Fock (MCDHF) method combined with the relativistic configuration interaction (RCI) approach (GRASP2K) to provide a consistent set of transition energies and radiative transition data for the lower $n =3$ states in all Cl-like ions of astrophysical importance, from \ion{Cr}{8} to \ion{Zn}{14}. We also provide excitation energies calculated for \mbox{Fe X} using the many-body perturbation theory (MBPT, implemented within FAC). The comparison of the present MCDHF results with MBPT and with the available experimental energies indicates that the theoretical excitation energies are highly accurate, with uncertainties of only a few hundred cm$^{-1}$. Detailed comparisons for Fe~X and Ni~XII highlight discrepancies in the experimental energies found in the literature. Several new identifications are proposed.

The relativistic multiconfiguration Dirac-Hartree-Fock and the nonrelativistic multiconfiguration Hartree-Fock methods have been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants of zinc. The calculated electric field gradients for the $4s4p\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}^{o}$ and $4s4p\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}^{3}P_{2}^{o}$ states, together with experimental values of the electric quadrupole hyperfine structure constants, made it possible to extract a nuclear electric quadrupole moment $Q(^{67}\mathrm{Zn})=0.122(10)$ b. The error bar was evaluated in a quasistatistical approach---the calculations were carried out with 11 different methods, and then the error bar was estimated from the differences between the results obtained with those methods.

Multiconfiguration Hartree-Fock (MCHF) and multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations are performed for the 2p(5) P-2 degrees, 2p(4)(P-3)3s P-4, 2p(4)(P-3)3s P-2, and 2p(4)(P-3)3 p ...

Relativistic atomic structure calculations are carried out in alkaline-earth-metal ions using a semiempirical-core-potential approach. The systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals are defined by a Dirac-Hartree-Fock calculation using the grasp2k package. The valence electron is described by a Dirac-like Hamiltonian involving a core-polarization potential to simulate the core-valence electron correlation. The associated equation is solved with the Lagrange-mesh method, which is an approximate variational approach having the form of a mesh calculation because of the use of a Gauss quadrature to calculate matrix elements. Properties involving the low-lying metastable $^{2}D_{3/2,5/2}$ states of ${\mathrm{Ca}}^{+}, {\mathrm{Sr}}^{+}$, and ${\mathrm{Ba}}^{+}$ are studied, such as polarizabilities, one- and two-photon decay rates, and lifetimes. Good agreement is found with other theory and observation, which is promising for further applications in alkalilike systems.

A Comment on the Letter by Mendoza and Bautista [Phys. Rev. Lett. 118, 163002 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.163002].

The present work reports results from systematic multiconfiguration Dirac-Hartree-Fock calculations of electronic isotope shift factors for a set of transitions between low-lying states in neutral zinc. These electronic quantities together with observed isotope shifts between different pairs of isotopes provide the changes in mean-square charge radii of the atomic nuclei. Within this computational approach, different models for electron correlation are explored in a systematic way to determine a reliable computational strategy and to estimate theoretical error bars of the isotope shift factors., Comment: 11 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1610.09233, arXiv:1604.07594

Energy levels, hyperfine interaction constants, and Lande $g_J$-factors are reported for n=2 states in beryllium-, boron-, carbon-, and nitrogen-like ions from relativistic configuration interaction calculations. Valence, core-valence, and core-core correlation effects are taken into account through single and double-excitations from multireference expansions to increasing sets of active orbitals. A systematic comparison of the calculated hyperfine interaction constants is made with values from the available literature.

Energy levels, normal and specific mass shift parameters as well as electronic densities at the nucleus are reported for numerous states along the beryllium, boron, carbon, and nitrogen isoelectronic sequences. Combined with nuclear data, these electronic parameters can be used to determine values of level and transition isotope shifts. The calculation of the electronic parameters is done using first-order perturbation theory with relativistic configuration interaction wave functions that account for valence, core-valence and core-core correlation effects as zero-order functions. Results are compared with experimental and other theoretical values, when available., 56 pages, 1 figure, Atomic Data and Nuclear Data Tables (2014)

Uncertainties of calculated transition rates in LS-allowed electric dipole transitions in boron-like O IV and carbon-like Fe XXI are estimated using an approach in which differences in line strengths calculated in length and velocity gauges are utilized. Estimated uncertainties are compared and validated against several high-quality theoretical data sets in O IV, and implemented in large scale calculations in Fe XXI., SCOPUS: re.j, info:eu-repo/semantics/published

Collinear laser spectroscopy was performed on Zn (Z=30) isotopes at ISOLDE, CERN. The study of hyperfine spectra of nuclei across the Zn isotopic chain, N=33–49, allowed the measurement of nuclear spins for the ground and isomeric states in odd-A neutron-rich nuclei up to N=50. Exactly one long-lived (&, SCOPUS: ar.j, info:eu-repo/semantics/published

Atomic data, such as wavelengths, spectroscopic labels, broadening parameters and transition rates, are necessary for many applications, especially in plasma diagnostics, and for interpreting the spectra of distant astrophysical objects. The experiment with its limited resources is unlikely to ever be able to provide a complete dataset on any atomic system. Instead, the bulk of the data must be calculated. Based on fundamental principles and well-justified approximations, theoretical atomic physics derives and implements algorithms and computational procedures that yield the desired data. We review progress and recent developments in fully-relativistic multiconfiguration Dirac-Hartree-Fock methods and show how large-scale calculations can give transition energies of spectroscopic accuracy, i.e. with an accuracy comparable to the one obtained from observations, as well as transition rates with estimated uncertainties of a few percent for a broad range of ions. Finally, we discuss further developments and challenges., SCOPUS: re.j, info:eu-repo/semantics/published

The present work reports results from systematic multiconfiguration Dirac-Hartree-Fock calculations of electronic isotope shift factors for a set of transitions between low-lying states in neutral aluminium. These electronic quantities together with observed isotope shifts between different pairs of isotopes provide the changes in mean-square charge radii of the atomic nuclei. Two computational approaches are adopted for the estimation of the mass- and field shift factors. Within these approaches, different models for electron correlation are explored in a systematic way to determine a reliable computational strategy and estimate theoretical error bars of the isotope shift factors., 10 pages, 1 figure, accepted for publication in Phys. Rev. A. arXiv admin note: substantial text overlap with arXiv:1604.07594

Collinear laser spectroscopy on Cu58-75 isotopes was performed at the CERN-ISOLDE radioactive ion beam facility. In this paper we report on the isotope shifts obtained from these measurements. State-of-the-art atomic physics calculations have been undertaken in order to determine the changes in mean-square charge radii δ(r2)A,A′ from the observed isotope shifts. A local minimum is observed in these radii differences at N=40, providing evidence for a weak N=40 sub-shell effect. However, comparison of δ(r2)A,A′ with a droplet model prediction including static deformation deduced from the spectroscopic quadrupole moments, points to the persistence of correlations at N=40., SCOPUS: ar.j, info:eu-repo/semantics/published

We present a consistent set of calculated energies and E1, M1, E2, M2 radiative transition data for the main n = 3 levels from the 3s 23p 4, 3p 6, 3p6, 3s3p43d, 3s23p23d2, 3s3p5, 3s23p33d, and 3s3p33d2 configurations for S-like ions from Cr ix to Cu xiv. The fully relativistic multiconfiguration Dirac-Hartree-Fock method implemented in the GRASP2K code is used to perform the present calculations. The excitation energies of the lowest 47 levels from the ,and configurations, producing the strongest lines, are found to be in good agreement, reaching spectroscopic accuracy, with the latest experimental values for Fe xi evaluated by Del Zanna. Our energies can reliably be used to identify in astrophysical and laboratory spectra the levels in other S-like ions, which are mostly unknown. On the contrary, significant discrepancies with the 3s3p 43d levels were found, emphasizing the need for more detailed experimental studies. A few new tentative identifications are suggested. The benchmarks we present indicate that our consistent set of radiative data is accurate and can be used for spectral line modeling., SCOPUS: ar.j, info:eu-repo/semantics/published

Excitation energies and lifetimes for the 213 lowest states of the n = 3 high-lying states. This level of accuracy confirms that elaborate ab initio calculations can assist in the identification of ...

The hyperfine constants of the levels 2p 2 ( 3P)3s 4P J, 2p 2 ( 3P)3p 4P o J and 2p 2 ( 3P)3p 4D o J, deduced by Jennerich et al. [Eur. Phys. J. D 40, 81 (2006)] from the observed hyperfine structures of the transitions 2p 2 ( 3P)3s 4P J→ 2p 2 ( 3P)3p 4P o J and 2p 2 ( 3P)3s 4P J→ 2p 2 ( 3P)3p 4D o J recorded by saturation spectroscopy in the near-infrared, strongly disagree with the ab initio values of Jönsson et al. [J. Phys. B: At. Mol. Opt. Phys. 43, 115006 (2010)]. We propose a new interpretation of the recorded weak spectral lines. If the latter are indeed reinterpreted as crossover signals, a new set of experimental hyperfine constants is deduced, in very good agreement with the ab initio predictions. © 2010 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg., SCOPUS: ar.j, info:eu-repo/semantics/published

Relativistic dipolar to hexadecapolar polarizabilities of the ground state and some excited states of hydrogenic atoms are calculated by using numerically exact energies and wave functions obtained from the Dirac equation with the Lagrange-mesh method. This approach is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. The partial polarizabilities conserving the absolute value of the quantum number κ are also numerically exact with small numbers of mesh points. The ones where, SCOPUS: ar.j, info:eu-repo/semantics/published

The present work reports results from systematic multiconfiguration Dirac-Hartree-Fock calculations of isotope shifts for several well-known transitions in neutral magnesium. Relativistic normal and specific mass shift factors as well as the electronic probability density at the origin are calculated. Combining these electronic quantities with available nuclear data, energy and transition level shifts are determined for the Mg26-Mg24 pair of isotopes. Different models for electron correlation are adopted. It is shown that, although valence and core-valence models provide accurate values for the isotope shifts, the inclusion of core-core excitations in the computational strategy significantly improves the accuracy of the transition energies and normal mass shift factors., SCOPUS: ar.j, info:eu-repo/semantics/published

An MCHF atomic-structure package is presented based on dynamic memory allocation, sparse matrix methods, and a recently developed angular library. It is meant for large-scale calculations in a basis of orthogonal orbitals for groups of LS terms of arbitrary parity. For Breit–Pauli calculations, all operators—spin–orbit, spin–other orbit, spin–spin, and orbit–orbit—may be included. For transition probabilities the orbitals of the initial and final state need not be orthogonal. A bi-orthogonal transformation is used for the evaluation of matrix elements in such cases. In addition to transition rates of all types, isotope shifts and hyperfine constants can be computed as well as g J factors. New version summary Title of program: atsp 2K Version number: 1.00 Catalogue identifier: ADLY_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADLY_v2_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer: Pentium III 500 MHz Installations: Vanderbilt University, Nashville, TN 37235, USA Operating systems under which the present version has been tested: Red Hat 8 Programming language used in the present version: FORTRAN 90 Memory required to execute with typical data: 256 Mbytes words No. of bits in a word: 32 Supplementary material: User manuals for the program atsp 2k and for the Spin-Angular library are available No. of lines in distributed program, including test data, etc.: 209 992 No. of bytes in distributed package, including test data, etc.: 1 740 883 Distribution format: tar.gz CPC Program Library subprograms used: none Does the new version supersede the previous version?: Yes Nature of physical problem: This program determines energy levels and associated wave functions for states of atoms and ions in the MCHF ( LS ) or Breit–Pauli ( LSJ ) approximation. Given the wave function, various atomic properties can be computed such as electric (E k ) and magnetic (M k ) multipole radiative transition probabilities ( k max = 10 ) between LS or LSJ states, isotope shift constants, hyperfine parameters, and g J factors. Method of solution: The new version of the program closely follows the design and structure of the previous one [C. Froese Fischer, Comput. Phys. Comm. 128 (2000) 635], except that a simultaneous optimization scheme has been introduced. This program uses the angular methodology of [G. Gaigalas, Lithuanian J. Phys. 41 (2000) 39] and has been extended to include partially filled f -subshells in wavefunction expansions but assumes all orbitals are orthonormal. The bi-orthogonal transformation method is used to deal with the non-orthogonality of orbitals between initial and final states of an electromagnetic radiative transition. Reasons for new version: The previous version of the MCHF atomic structure package [C. Froese Fischer, Comput. Phys. Comm. 128 (2000) 635] was intended for small calculations, ideal for someone not familiar with the code, producing extensive print-out of intermediate results. The codes for the calculation of spin-angular coefficients were often not the most efficient and could only treat configurations with open f -subshells containing at most two electrons or an almost filled shell with one hole. The present version is designed for large-scale computation using algorithms for angular integration that have been shown to be faster, and include the case of arbitrarily filled f -shells. In addition, the MCHF program has been modified to include optimization on an energy functional that is a weighted average of energy functionals for expansions of wavefunctions for different LS terms or parity, thus facilitating Breit–Pauli calculations for complex atomic systems and for computing targets in collision calculations. Summary of revisions: Programs have been modified to take advantage of the newly developed angular library [G. Gaigalas, Lithuanian J. Phys. 41 (2000) 39], extended to arbitrarily filled f -shells. New programs have been developed for simultaneous optimization and for the efficient calculation of atomic spectra and transition rates for an iso-electronic sequence. All applications now take advantage of dynamic memory allocation and sparse matrix methods. Restrictions on the complexity of the problem: All orbitals in a wave function expansion are assumed to be orthonormal. Configuration states are restricted to at most eight (8) subshells in addition to the closed shells common to all configuration states. The maximum size is limited by the available memory and disk space. Typical running time: Included with the code are scripts for calculating E2 and M1 transitions between levels of 3 s 2 3 p 2 for Si and P + . This calculation has two stages: LS and LSJ . The calculation of the former required 21 minutes for the LS calculation and 36.5 minutes for the Breit–Pauli configuration interaction calculation that determines the mixing of the terms. Unusual features of the program: The programming style is essentially F77 with extensions for the POINTER data type and associated memory allocation. These have been available on workstations for more than a decade but their implementations are compiler dependent. The present serial code has been installed and tested extensively using both the Portland Group, pgf90, compiler and the IBM SP2, xlf90, compiler. The former is compatible also with the Intel Fortran90 compiler. The MPI codes are included for completeness though testing has not been as extensive. Additional comments: Parallel versions (MPI) of the following programs are included in the distribution. Use of these is optional but can speed up the angular integration processing. Serial Parallel nonh nonh_mpi mchf mchf_mpi bp_ang, bp_mat, bp_eiv bp_ang_mpi, bp_mat_ang, bp_eiv_mpi biotr_ang, biotr_tr biotr_ang_mpi, biotr_tr_mpi

Ab initio multiconfiguration calculations are performed for the oscillator strengths of the A = 4238, 4262 and 4297 A Tc i resonance lines of astrophysical interest. Electron correlation is treated through multiconfiguration expansions built from elaborate correlation models, while relativistic effects are introduced in the perturbation Breit-Pauli approximation or in the multiconfiguration Dirac-Fock-Breit variational approach. The calculated gf-values are sensitively lower (30 per cent) than the values obtained with the pseudo-relativistic Hartree-Fock wavefunctions calculated from a parametric analysis of Tc I by Palmeri & Wyart. The inclusion of a core-polarization potential in the latter approach confirms the present ab initio results when different ionic cores are used for the different transition arrays. The strong lines of Tc I are revisited adopting this model, giving rise to a systematic reduction in the oscillator strength scale due to core polarization. The astrophysical implications are discussed.

The study of the isotope shift in the electron affinity is interesting for probing correlation effects. Experiments that allow this property to be measured are rare, being difficult to realize, while accurate calculations remain a challenge for atomic theory. The present work focuses on the theoretical estimation of the isotope shift in the electron affinity of Be (2s2p 3Po), using correlated electronic wavefunctions obtained from multiconfiguration Hartree–Fock and configuration interaction variational calculations. The reliability of the correlation models is assessed from a comparison between the observed and theoretical electron affinities, and between theoretical isotope shift values for the 2s2p 3Po 2s2 1S transition of neutral beryllium. The sign and the magnitude of the difference between the mass polarization term expectation values obtained for the neutral atom and the negative ion are such that the resulting isotope shift in the electron affinity is 'anomalous', corresponding to a smaller electron affinity for the heavier isotope.