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grasp is a software package in Fortran 95, adapted to run in parallel under MPI, for research in atomic physics. The basic premise is that, given a wave function, any observed atomic property can be computed. Thus, the first step is always to determine a wave function. Different properties challenge the accuracy of the wave function in different ways. This software is distributed under the MIT Licence.

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.

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.

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.

Computational atomic physics continues to play a crucial role in both increasing the understanding of fundamental physics (e.g., quantum electrodynamics and correlation) and producing atomic data for interpreting observations from large-scale research facilities ranging from fusion reactors to high-power laser systems, space-based telescopes and isotope separators. A number of different computational methods, each with their own strengths and weaknesses, is available to meet these tasks. Here, we review the relativistic multiconfiguration method as it applies to the General Relativistic Atomic Structure Package [grasp2018, C. Froese Fischer, G. Gaigalas, P. Jönsson, J. Bieroń, Comput. Phys. Commun. (2018). DOI: 10.1016/j.cpc.2018.10.032]. To illustrate the capacity of the package, examples of calculations of relevance for nuclear physics and astrophysics are presented.

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.

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.

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 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

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

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 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 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.

The hyperfine structures of Be-7,9(-) 2s2p(2) P-4(1/2,3/2,5/2) are investigated theoretically using the multiconfiguration Hartree-Fock and configuration interaction methods. The effects of the hyperfine mixing between the fine-structure J-levels are discussed. The feasibility of some atomic spectroscopy experiments, allowing determination of the Be-7 quadrupole moment from the observed hyperfine structure of the Be-7(-) negative ion and from the present electronic parameters, is investigated. The Be 2s2p P-3(o) electron affinity is monitored as a function of the orbital and configuration spaces to assess the reliability of the wavefunctions of the neutral atom and the negative ion. The theoretical value nicely converges towards the most recent theoretical and experimental results. (Less)

The present work deals with a set of problems in isotope shifts of neutral barium spectral lines. Some well-known transitions $(6{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}\ensuremath{-}6s6p{\phantom{\rule{0.16em}{0ex}}}^{1,3}{P}_{1}^{o}$ and $6{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}\ensuremath{-}6{p}^{2\phantom{\rule{0.16em}{0ex}}3}{P}_{0})$ are investigated. Values of the changes in the nuclear mean-square charge radius are deduced from the available experimental isotope shifts using our ab initio electronic factors. The three sets ${\ensuremath{\delta}{\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}}^{A,{A}^{\ensuremath{'}}}}$ obtained from these lines are consistent with each other. The combination of the available nuclear mean-square radii with our electronic factors for the $6s5d{\phantom{\rule{0.16em}{0ex}}}^{3}{D}_{1,2}\ensuremath{-}6s6p{\phantom{\rule{0.16em}{0ex}}}^{1}{P}_{1}^{o}$ transitions produces isotope shift values in conflict with the laser spectroscopy measurements of U. Dammalapati et al. [Eur. Phys. J. D 53, 1 (2009)].

The multi-configuration Dirac-Fock model is used to evaluate the magnetic dipole hyperfine interaction constants of the 3d4s(1D)4p 2Do3/2,5/2, 3d4s(3D)4p 4Fo9/2, 3d4s(1D)4p 2Fo5/2,7/2 and 3d2(1D)4s 2D3/2,5/2 levels of atomic scandium. The wavefunctions are obtained with the active space expansion method, where configuration state functions of a specific parity and J value are generated by substitutions from the reference configurations to an active set of orbitals. The active set is then increased in a systematic way, allowing the convergence of the expectation values to be monitored. The calculated magnetic dipole hyperfine interaction constants are compared with experimentally determined values. On the grounds of the level of agreement between experiment and theory, we confirm three of the hypothetical A-values, previously deduced from high-resolution Fourier transform spectroscopy.

The multiconfiguration Hartree-Fock method is used to calculate wavefunctions in the infinite nuclear mass limit for the terms 2s 2S, 2p 2Po, 3s 2S, 3p 2Po, 3d 2D and 4s 2S of lithium-like ions (3≤Z≤8). Transition data, isotope shift parameters and hyperfine structure electronic contributions involving the six terms of the six ions are evaluated ab initio and compared with the most recent observations and other theoretical calculations when available. The isotopes 7,6Li I, 11,10,9,7Be II, 11,10B III, 14,13,12C IV, 15,14N V and 18,17,16O VI are considered in the analysis of the mass isotope shifts.

The present paper reports the {ital ab initio} evaluation of the electron affinity of oxygen, and the value of its isotope shift. The theoretical results are in good agreement with the recent electron affinity measurements for {sup 16}O and{sup 18}O by photodetachment microscopy, revealing an {open_quotes}anomalous{close_quotes} isotope shift. The theoretical fine structure of the negative ion 2p{sup 5}thinsp{sup 2}P{sub 1/2{minus}3/2}{sup o} is also in very good agreement with observation. {copyright} {ital 1999} {ital The American Physical Society}

The oscillator strengths of the Mg+ weak transitions 3s 2S1/2-4p 2Po3/2,1/2 at = 1239,1240 A are evaluated using the multiconfiguration Hartree-Fock approach combined with the orbital active set method and configuration-interaction calculations, taking the effect of triple and quadruple excitations into account. The effects of core and core-valence correlation using different optimization schemes are discussed in detail. Relativistic corrections are calculated within the Breit-Pauli approximation.

Results from systematic multiconfiguration Hartree-Fock calculations of isotope shifts and oscillator strengths are reported for the and transitions in the Be isoelectronic sequence (Z = 4-10). In addition values for the same properties as well as for the hyperfine interaction constants are presented for the - transitions in Mg I. Different models for electron correlation are used, and it is shown that valence and core-valence effects alone are not sufficient to obtain accurate values for the isotope shifts, but that also core-core effects need to be accounted for.

Multiconfiguration Breit–Pauli energy levels, lifetimes, and transition data are presented for the lithium sequence in the range Z ≤ 8. Included are all J -levels of the six lowest 2 L terms, namely those with configuration labels 1 s 2 2 s , 1 s 2 2 p , 1 s 2 3 s , 1 s 2 3 p , 1 s 2 3 d , and 1 s 2 4 s .

A comparison between the recent measurements [Musielok et al, Phys. Rev. A53, 3122 (1996)] of the relative oscillator strengths for all lines in the three multiplets comprising the 2p3s-2p3p transition array in NII, and theoretical configuration interaction calculations performed with the CIV3 code [Bell et al., Physica Scripta 52 240 (1995)] shows that, although the agreement between the experimental data and the theoretical results is good for allowed transitions, some unexpected deviations occur for the intersystem lines. In this work, we show that the previous theoretical work can be improved and some significant discrepancies with experiment eliminated by increasing the accuracy of the calculated energy difference between the 2p3s 3P1o and 1P1o states. This is achieved by the inclusion of additional orbitals and configurations together with adjustment of the diagonal matrix elements of the Hamiltonian. The new theoretical results for the transitions 2p3s 1,3PJo → 2p2 and 2p3p LSJ are compared with other theoretical work and with the experimental data.

The hyperfine structure constants for the 1s 22s 22p 3 -4 S o ground state in nitrogen and the 1s 22s 22p 33s 5 S o excited state in oxygen are calculated using the MCHF Atomic Structure Package. The single excitation picture is explored through the use of compact wave functions allowing radial non-orthogonalities. Electron correlation is described through numerical multiconfiguration Hartree-Fock calculations for configuration expansions obtained by allowing all single and double excitations from the reference configuration to an active set of orbitals. The latter is increased in a systematic way allowing the convergence of the hyperfine parameters to be studied. Three- and four-particle effects are shown to be important and are taken into account in a sequence of large configuration interaction calculations. The final results are in good agreement with experiment.

The electronic redistribution of an ion or atom induced by a sudden recoil of the nucleus occurring during the emission or capture of a neutral particle is theoretically investigated. For one-electron systems, analytical expressions are derived for the electronic transition probabilities to bound and continuum states. The quality of a B-spline basis set approach is evaluated from a detailed comparison with the analytical results. This numerical approach is then used to study the dynamics of two-electron systems (neutral He and ) using correlated wavefunctions for both the target and daughter ions. The total transition probabilities to discrete states, autoionizing states and direct single- and double-ionization probabilities are calculated from the pseudospectra. Sum rules for transition probabilities involving an initial bound state and a complete final series are discussed.

Results from systematic multiconfiguration Hartree - Fock studies of the - transitions in the Be-like sequence in the range of Z = 4 - 10 are reported for valence and core-valence models of correlation. The inclusion of core - valence correlation was essential for obtaining good agreement for the fine-structure splitting. The most accurate transition rates are in good agreement with the rates predicted from a semi-empirical analysis of experimental data.

The hyperfine interaction constants of the 2p(4)(P-3)3p D-2(3/2,5/2)o, D-4(1/2-7/2)o, and P-4(1/2-5/2)o levels in neutral fluorine are investigated theoretically. Large-scale calculations are carried out using the multiconfiguration Hartree-Fock (MCHF) and Dirac-Hartree-Fock (MCDHF) methods. In the framework of the MCHF approach, the relativistic effects are taken into account in the Breit-Pauli approximation using nonrelativistic orbitals. In the fully relativistic approach, the orbitals are optimized using the Dirac-Coulomb Hamiltonian with correlation models inspired by the nonrelativistic calculations. Higher-order excitations are captured through multireference configuration interaction calculations including the Breit interaction. In a third (intermediate) approach, the Dirac-Coulomb-Breit Hamiltonian matrix is diagonalized in a relativistic configuration space built with nonrelativistic MCHF radial functions converted into Dirac spinors using the Pauli approximation. The magnetic dipole hyperfine-structure constants calculated with the three relativistic models are consistent and reveal unexpectedly large effects of relativity for 2D(5/2)(o), P-4(3/2)o, and P-4(5/2)o. The agreement with the few available experimental values is satisfactory. The strong J dependence of relativistic corrections on the hyperfine constants is investigated through the detailed analysis of the orbital, spin-dipole, and contact relative contributions calculated with the nonrelativistic magnetic dipole operator.

The oscillator strength of the resonance transition - in neutral beryllium is evaluated using two independent codes: CIV3 and MCHF. Two separate approaches are executed using the code CIV3, which uses a common set of orbitals, the inclusion of valence, core - valence and core - core correlation being approached in different ways. In the MCHF scheme, the wavefunctions of the two states are optimized independently. The convergence of the MCHF results with respect to the addition of orbital functions is considered in some detail. This convergence, together with the results of the CIV3 calculations, lead us to recommend a value of 1.375 for the oscillator strength, with an estimated uncertainty of less than 0.5%. This agrees closely with other recent extensive calculations but is 2.5% higher than the value derived from beam-foil experiments.

Results from systematic multiconfiguration Hartree - Fock calculations of transition probabilities, isotope shifts and hyperfine structures of the - and - transitions in B I, the - transitions in C II and the - transition in C I are reported. Higher-order correlation effects beyond the pair-correlation approximation are shown to be important for the transition probabilities, and are included in large configuration interaction calculations. For all the transitions except one, the agreement between the length and velocity forms of the weighted oscillator strength is better than 0.4%. The present results are believed to be substantially more accurate than those of other theories.

Results from large-scale multiconfiguration Hartree-Fock (MCHF) and configuration-interaction (CI) calculations of the transition probability and hyperfine structures in the sodium 3{ital s}{sup 2}{ital S}{minus}3{ital p}{sup 2}{ital P} resonance transition are presented. In the calculations the orbital sets of the initial and final state wave functions were not restricted to be the same, but were optimized independently. The evaluation of the transition matrix elements was done using a technique where the two orbital sets are transformed so as to become biorthonormal, in which case standard Racah algebra can be used. Three-particle effects were taken into account in the CI calculations and were found to be important for the hyperfine structures, but less important for the transition probability. The calculated transition probability is in perfect agreement with the most recent experimental values, thus resolving the long-standing disagreement between theory and experiment. Also the 3{ital s}{sup 2}{ital S}{sub 1/2} and 3{ital p}{sup 2}{ital P}{sub 1/2,3/2} hyperfine interaction constants are in very good agreement with available experimental values. {copyright} {ital 1996 The American Physical Society.}

Extensive configuration-interaction calculations have been performed to obtain oscillator strengths for the resonance line of the ions of the beryllium isoelectronic sequence up to nuclear charge Z = 12. Valence, core-valence and core-core correlation effects are taken into account and relativistic effects are incorporated using the Breit-Pauli scheme. The present results are believed to be accurate to better than 1%.

The spectrum of scandium was recorded in the infrared region using a high resolution Fourier transform spectrometer and a hollow-cathode discharge. Hyperfine structures of the lines connecting the 3d24s and 3d4s4p level systems of Sc45 I were observed between 4000 and 5000 cm−1. The structures were not completely resolved but the individual line contributions to the complex profiles were simulated using the 3d24s 4FJ hyperfine structure constants previously measured with a high precision by laser techniques. We investigate the possibility of extracting the hyperfine constants of the 3d4s4p levels from a least-squares fit of the line profiles, assuming a Doppler lineshape and theoretical relative intensities. New results are presented for 12 levels.

The progress achieved over the last few years in variational Multiconfiguration Hartree-Fock and Configuration Interaction calculations is reviewed. The high level of accuracy which can be reached in the ab initio calculation of atomic properties of light systems is illustrated through the results of calculations of isotope shifts, hyperfine structures and transition probabilities. The active space method and associated restricted active space methods allowing systematic calculations from which the accuracy of the studied property can be estimated will be discussed. We exemplify quality checks through results in small systems for which spectroscopic accuracy is often required. For transition probabilities, recent progress derived from new algorithm developments allowing independent optimization of the states is emphasized.

Today, the electron affinity is experimentally well known for most of the elements and is a useful guideline for developing ab initio computational methods. However, the measurements of isotope shifts on the electron affinity are limited by both resolution and sensitivity. In this context, theory eventually contributes to the knowledge and understanding of atomic structures, even though correlation plays a dominant role in negative ions properties and, particularly, in the calculation of the specific mass shift contribution. The present study solves the longstanding discrepancy between calculated and measured specific mass shifts on the electron affinity of chlorine (Phys. Rev. A 51 (1995) 231), Comment: 18 pages, 2 figures, 7 tables

The isotope effects in Si$^-$ bound levels are studied using the multi-configuration Hartree-Fock ab initio approach. Large scale calculations are carried out for the $3p^3\ ^4S^o,\, ^2D^o$ and $^2P^o$ multiplets of Si$^-$ and the $3p^2\ ^3P$ multiplet of Si. We predict an anomalous isotope shift on the electron affinity, dominated by the specific mass shift, with a value of $IS(^e\!\!A)= -0.66(6)$ m$^{-1}$ for the ($30-28$) isotope pair. We also report hyperfine structure parameters for the studied multiplets. Finally, we provide the values of level electric field gradients at the nucleus that could be of interest in a study of the metastable silicon isotopes. Relativistic corrections are estimated using non-relativistic orbitals in the Breit-Pauli and fully relativistic frameworks., Comment: 9 pages, 11 tables (accepted in PRA)

No lines have been observed for transitions between the doublet and quartet levels of B i. Consequently, energy levels based on observation for the latter are obtained through extrapolation of wavelengths along the isoelectronic sequence for the $2{s}^{2}2p$ ${\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}^{o}$ -- $2s2{p}^{2}$ ${\phantom{\rule{0.16em}{0ex}}}^{4}{P}_{5/2}$ transition. In this paper, accurate theoretical excitation energies from a partitioned-correlation-function-interaction (PCFI) method are reported for B i that include both relativistic effects in the Breit-Pauli approximation and a finite mass correction. Results are compared with extrapolated values from observed data. For B i our estimate of the excitation energy 28 959 $\ifmmode\pm\else\textpm\fi{}$ 5 cm${}^{\ensuremath{-}1}$ is in better agreement with the values obtained by Edl\'en et al. (1969) than those reported by Kramida and Ryabtsev (2007). Our method is validated by applying the same procedure to the separation of these levels in C ii.

A new isotope shift program, part of the MCHF atomic structure package, has recently been written. The program calculates the isotope shift of an atomic level from multiconfiguration Hartree-Fock (MCHF) or configuration interaction (CI) wavefunctions and is specially designed to be used with very large CI expansions, for which angular data cannot be stored on disk. To explore the capacity of the program, large-scale isotope shift calculations have been performed for the 1s22s 2S and 1s22p 2P levels in C IV and for the 1s22s22p2 1S, 1s22s22p3s 1p, 1s22s22p2 3P and 1s22s2p3 5S levels in C I. From the isotope shifts of these levels the 14C-12C isotope shifts were calculated for the 1s22s 2S-1s22p 2P transition in C IV and for the 1s22s22p2 1S-1s22s22p3s 1P and 1s22s22p2 3P-1s22s2p3 5S transitions in C I. The calculated transition isotope shifts are in very good agreement with experimental values, available for the C I transitions. As a check on the overall quality of the wavefunctions, the hyperfine structure interaction constants were calculated for the levels in C IV.

High resolution profiles of neutral vanadium lines have been recorded in the infrared region (1800-9000 cm-1) by Fourier transform spectroscopy. 106 transitions showing resolved or partially resolved hyperfine profiles have been analysed. An investigation of these structures has allowed the deduction of magnetic dipole constants for 101 levels. For 69 levels the results obtained are new. The results of the present work have been compared with the few data previously published in the literature and they are generally in good agreement.

Multiconfiguration wave function expansions combined with configuration interaction methods are a method of choice for complex atoms where atomic state functions are expanded in a basis of configuration state functions. Combined with a variational method such as the multiconfiguration Hartree-Fock (MCHF) or multiconfiguration Dirac-Hartree-Fock (MCDHF), the associated set of radial functions can be optimized for the levels of interest. The present review updates the variational MCHF theory to include MCDHF, describes the multireference single and double process for generating expansions and the systematic procedure of a computational scheme for monitoring convergence. It focuses on the calculations of energies and wave functions from which other atomic properties can be predicted such as transition rates, hyperfine structures and isotope shifts, for example.

We calculated the magnetic dipole hyperfine interaction constants and the electric field gradients of $2p^53p~^2[3/2]_2$ and $2p^53s~^2[3/2]^o_2$ levels of Ne I by using the multiconfiguration Dirac-Hartree-Fock method. The electronic factors contributing to the isotope shifts were also estimated for the $\lambda = 614.5$ nm transition connecting these two states. Electron correlation and relativistic effects including the Breit interaction were investigated in details. Combining with recent measurements, we extracted the nuclear quadrupole moment values for $^{20}$Ne and $^{23}$Ne with a smaller uncertainty than the current available data. Isotope shifts in the $2p^53p~^2[3/2]_2 - 2p^53s~^2[3/2]^o_2$ transition based on the present calculated field- and mass-shift parameters are in good agreement with the experimental values. However, the field shifts in this transition are two or three orders of magnitude smaller than the mass shifts, making rather difficult to deduce changes in nuclear charge mean square radii. According to our theoretical predictions, we suggest to use instead transitions connecting levels arising from the $2p^53s$ configuration to the ground state, for which the normal mass shift and specific mass shift contributions counteract each other, producing relatively small mass shifts that are only one order of magnitude larger than relatively large field shifts, especially for the $2p^53s~^2[1/2]^o_1 - 2p^6~^1S_0$ transition.

In the framework of the multiconfiguration Dirac-Hartree-Fock method, we investigate the transition properties of four excited states in the 2p(5)3s configuration of neutral neon. The electron correlation effects are taken into account systematically by using the active space approach. The effect of higher-order correlation on fine structures is shown. We also study the influence of the Breit interaction and find that it reduces the oscillator strength of the P-3(1)o-S-1(0) transition by 17%. It turns out that the inclusion of the Breit interaction is essential even for such a light atomic system. Our ab initio calculated line strengths, oscillator strengths, and transition rates are compared with other theoretical values and experimental measurements. Good agreement is found except for the P-3(2)o-S-1(0) M2 transition for which discrepancies of around 15% between theories and experiments remain. In addition, the impact of hyperfine interactions on the lifetimes of the P-3(0)o and P-3(2)o metastable states is investigated for the Ne-21 isotope (I = 3/2). We find that hyperfine interactions reduce the lifetimes drastically. For the P-3(0)o state the lifetime is decreased by a factor of 630. (Less)

The Dirac kinetic energy (DKE) form of the normal mass shift operator $$\left( {\tfrac{{m_e }} {M}\sum\nolimits_{i = 1}^N {T_i } } \right)$$ , which is an approximation of the $$\left( {\tfrac{1} {{2M}}\sum\nolimits_{i = 1}^N {P_i^2 } } \right)$$ operator built on the relativistic electron momenta, is widely used in relativistic atomic structure calculations. In the present paper, we illustrate the progressive breakdown of the Dirac kinetic energy form relatively to the momentum form when increasing the nuclear charge along the lithium isoelectronic sequence. Both forms are incorrect in the relativistic case but the DKE operator provides expectation values that are closer to the results obtained with the more complete relativistic recoil operator.

1/2,3/2 transitions along the lithium isoelectronic sequence. Based on the multiconfiguration Dirac-Hartree-Fock method, the electron correlation and the Breit interaction are taken into account systematically. The analysis of the isotope shifts for these two transitions along the isoelectronic sequence demonstrates the importance and competition between the mass shifts and the field shifts.

The atomic d shell is explored from the perspective of the quark model of the atom. In this scheme, all the states are generated by four statistically independent fictitious particles (the quarks), each with angular momentum 3/2, augmented by two parity labels. The detailed quark expansions are given for the two 2D terms of d3, and the results are compared to the classic analysis of Condon and Shortley (1935). Matrix elements of single-electron tensor operators and of the Coulomb interaction are calculated in the quark scheme, and the connection to the conventional approach is made. The diagonal sum method of Slater is applied to the quark states and extensions to many-electron operators are discussed. The correspondence between the quark model and the traditional method implies relations between various n-j symbols, and this is illustrated by two special cases.

We investigate the stability of homonuclear diatomic molecules from ${\mathrm{H}}_{2}$ up to ${\mathrm{C}}_{2}$ and of the finite chains ${\mathrm{H}}_{\mathit{n}}$ (n\ensuremath{\le}5) and ${\mathrm{He}}_{\mathit{n}}$ (n\ensuremath{\le}4) immersed in very intense magnetic fields (B\ensuremath{\approxeq}${10}^{8}$ T). The atomic and molecular total energies are calculated within the one-dimensional Hartree-Fock approximation, using a Lagrange basis set associated with a Cartesian mesh. The stability of the molecules decreases beyond ${\mathrm{Li}}_{2}$ although all the studied molecules are found stable. The energy per atom of H and He finite chains stabilizes already for the small chain sizes that we have investigated.