arXiv subjects

Michel Godefroid

Publications and source records attributed to Michel Godefroid.

At least 19 recordsLinked to original sources

arXiv2026

Atomic data benchmarked by Large-scale Multiconfiguration Dirac-Hartree-Fock Calculations for Beryllium

The multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) methods are used to provide excitation energies, radiative transition data, lifetimes, Lande g-factors, hyperfine interaction constants and isotope shift parameters for the 99 lowest levels of configurations 1s^22snl (n <= 7) + 1s^22p^2 in beryllium. Compared with available experimental excitation energies, the average difference with the standard deviation is 7.08 +/- 1.14cm^-1 (0.011% +/- 0.003%), which demonstrates the excellent theory-observation agreement. The uncertainties of the transition rates are estimated based on two independent methods. The present MCDHF/RCI oscillator strengths and those obtained from the explicitly correlated Gaussian (ECG) method all agree within 2%, except for four transitions affected by strong cancellation effects. For lifetimes, hyperfine splittings and isotope shifts, the present MCDHF/RCI results show good agreement with the few available experimental values, supporting the reliability of our predictions for many states lacking experimental measurements. These comprehensive results can be used in line identification and diagnostics of astrophysical plasmas.

physics.atom-ph↗

arXiv2025

Atomic determination of the nuclear quadrupole moment $\mathrm{Q}(^{209}{\rm Bi})$ using the multi-configuration Dirac-Hartree-Fock method

The multiconfiguration Dirac-Hartree-Fock method implemented in the Grasp2018 package was employed to calculate the magnetic dipole hyperfine interaction constants and electric field gradients of levels in the ground configuration of the neutral bismuth atom. Combining the calculated electric field gradient of the ground state with the measured electric quadrupole hyperfine interaction constant, we extracted the nuclear quadrupole moment for the $^{209}$Bi isotope, $\mathrm{Q}(^{209}\textbf{Bi}) = -422(22)$~mb. This value, together with other results obtained from atomic- and molecular-structure calculations, created the ``world average" nuclear quadrupole moment of this isotope, $\mathrm{Q}(^{209}\textbf{Bi}) = -420(17)$~mb.

physics.atom-ph↗

arXiv2024

Kilonova ejecta opacity inferred from new large-scale HFR atomic calculations in all elements between Ca (Z = 20) and Lr (Z = 103)

In the context of kilonova (KN) modeling, the present work focusses on large-scale atomic data and opacity computations for all heavy elements from Ca to Lr, with a special effort on lanthanides and actinides, for a grid of typical KN ejecta conditions between one day and one week after the merger (corresponding to the LTE photosphere phase of the KN ejecta). In order to do so, we used the pseudo-relativistic Hartree-Fock (HFR) method, in which the choice of the interaction configuration model is of crucial importance. In this paper, HFR atomic data and opacities for all elements between Ca (Z = 20) and Lr (Z = 103) are presented, with a special focus on lanthanides and actinides. Besides, we also discuss the contribution of every single element to the total KN ejecta opacity for a given neutron star merger model, depending on their Planck mean opacities and elemental abundances. An important result is that lanthanides are found to not be the dominant sources of opacity, at least on average. The impact on KN light curves of considering such atomic-physics based opacity data instead of typical crude approximation formulae is also evaluated. In addition, the importance of taking the ejecta composition into account directly in the expansion opacity determination (instead of estimating single-element opacities) is highlighted. A database containing all the relevant atomic data and opacity tables has also been created and published online along with this work.

astro-ph.HE↗

arXiv2024

Graspg -- An extension to Grasp2018 based on Configuration State Function Generators

The Graspg program package is an extension of Grasp2018 [Comput. Phys. Commun. 237 (2019) 184-187] based on configuration state function generators (CSFGs). The generators keep spin-angular integrations at a minimum and reduce substantially the execution time and the memory requirements for large-scale multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (CI) atomic structure calculations. The package includes the improvements reported in [Atoms 11 (2023) 12] in terms of redesigned and efficient constructions of direct- and exchange potentials, as well as Lagrange multipliers, and additional parallelization of the diagonalization procedure. Tools have been developed for predicting configuration state functions (CSFs) that are unimportant and can be discarded for large MCDHF or CI calculations based on results from smaller calculations, thus providing efficient methods for a priori condensation. The package provides a seamless interoperability with Grasp2018. From extensive test runs and benchmarking, we have demonstrated reductions in the execution time and disk file sizes with factors of 37 and 98, respectively, for MCDHF calculations based on large orbital sets compared to corresponding Grasp2018 calculations. For CI calculations, reductions of the execution time with factors over 200 have been attained. With a sensible use of the new possibilities for a priori condensation, CI calculations with nominally hundreds of millions of CSFs can be handled.

physics.atom-ph↗

arXiv2022

Signs in isotope shifts: a perennial headache

Signs of the different contributions to the isotope shift of an atomic line are discussed in details to clarify some confusing differences between the electronic parameters calculated with RIS (Naz\'e et al. Comput. Phys. Commun. 184 (2013) 2187 ; Ekman et al. Comput. Phys. Commun. 235 (2019) 433) and those appearing in other commonly used expressions.

physics.atom-ph↗

arXiv2021

Relativistic variational methods and the Virial Theorem

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. It shows that some Slater integrals impose conditions on a single subshell but others impose conditions between subshells. The latter slow the rate of convergence of the self-consistent field process in which radial functions are updated one at a time. Several cases are considered.

physics.atom-ph↗

arXiv2021

Weak Correlation and Strong Relativistic Effects on the Hyperfine Interaction in Fluorine

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.

physics.atom-ph↗

arXiv2021

S stars and s-process in the Gaia era II. Constraining the luminosity of the third dredge-up with Tc-rich S stars

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.

astro-ph.SR↗

arXiv2021

Benchmarking calculations with spectroscopic accuracy of level energies and wavelengths in W LVII - W LXII tungsten ions

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 \approx 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.

physics.atom-ph↗

arXiv2021

Ab initio MCDHF calculations of the In and Tl electron affinities and their isotope shifts

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 Tl$^-$. 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 $^3P_{0,1,2}$ are confirmed in the $5s^25p^2$ configuration of In$^-$ while only the ground state $^3P_{0}$ is bound in the $6s^26p^2$ configuration of Tl$^-$. The isotope shifts on the In and Tl electron affinities are also estimated. The E2/M1 intraconfiguration radiative transition rates within $5s^25p^2 \; ^3P_{0,1,2}$ of In$^-$ are used to calculate the radiative lifetimes of the metastable $^3P_{1,2}$ levels.

physics.atom-ph↗

arXiv2020

Electronic isotope shift factors for the Ir $5d^{7}6s^{2} \ ^{4}\!F_{9/2} \to (\mbox{odd},J= 9/2)$ line at 247.587 nm

We present the theoretical calculations of the electronic isotope shift factors of the $5d^{7}6s^{2} \ ^{4}\!F_{9/2} \to (\mbox{odd},J= 9/2)$ line at 247.587 nm, that were recently used to extract nuclear mean square radii and nuclear deformations of iridium isotopes [Mukai $\textit{et al.}$ (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 $\textit{sharing rule}$, Landé $g$ factors or $\textit{phase tracking}$ were employed to ensure an adequate description of the targeted odd level.

physics.atom-ph↗

arXiv2020

$\textit{Ab initio}$ electronic factors of the $A$ and $B$ hyperfine structure constants for the $5s^25p6s \; ^{1,3}\! P^{\rm o}_{1}$ states in Sn I

Large-scale $\textit{ab initio}$ calculations of the electric field gradient, which constitutes the electronic contribution to the electric quadrupole hyperfine constant $B$, were performed for the $5s^25p6s$ $^{1,3}\!P^{\rm o}_1$ excited states of tin, using three independent computational strategies of the variational multiconfiguration Dirac-Hartree-Fock method and a fourth approach based on the configuration interaction Dirac-Fock-Sturm theory. For the $5s^25p6s$ $^{1}\!P^{\rm o}_1$ state, the final value of $B/Q =703(50)$ MHz/b differs by $0.4\%$ from the one recently used by Yordanov ${\it et~al.}$ [Communications Physics ${\bf 3}$, 107 (2020)] to extract the nuclear quadrupole moments, $Q$, for tin isotopes in the range $^{(117-131)}$Sn from collinear laser spectroscopy measurements. Efforts were made to provide a realistic theoretical uncertainty for the final $B/Q$ value of the $5s^25p6s\,^{1}\!P^{\rm o}_1$ state based on statistical principles and on correlation with the magnetic dipole hyperfine constant $A$.

physics.atom-ph↗

arXiv2020

Benchmarking calculations with spectroscopic accuracy of excitation energies and wavelengths in sulfur-like tungsten

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.

physics.atom-ph↗

arXiv2020

Natural orbitals in multiconfiguration calculations of hyperfine structure parameters

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 Jönsson 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.

physics.atom-ph↗

arXiv2018

Theoretical Hyperfine Structures of $^{19}$F~I and $^{17}$O~I

Multiconfiguration Hartree-Fock (MCHF) and multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations are performed for the $2p^{5}~^{2}P^{o}$, $2p^4(^{3}P)3s~^{4}P$, $2p^4(^{3}P)3s~^{2}P$ and $2p^4(^{3}P)3p~^{4}S^o$ states of $^{19}$F~I to determine their hyperfine constants. Several computing strategies are considered to investigate electron correlation and relativistic effects. High-order correlation contributions are included in MCHF calculations based on single and double multireference (SD-MR) expansions. The largest components of the single reference MCHF wave functions are selected to define the MR sets. In this scheme, relativistic corrections are evaluated in the Breit-Pauli approximation. A similar strategy is used for the calculation of MCDHF relativistic wave functions and hyperfine parameters. While correlation and relativistic corrections are found to be rather small for the ground state, we highlight large relativistic effects on the hyperfine constant $A_{3/2}$ of $2p^4(^{3}P)3p~^{4}S^o$ and, to a lesser extent, on $A_{1/2}$ of $2p^4(^{3}P)3s~^{4}P$. As expected for such a light system, electron correlation effects dominate over relativity in the calculation of the hyperfine interaction of all other levels considered. We also revisit the hyperfine constants of $2p^3(^{4}S)3s~^{5}S^{o}$ and $2p^3(^{4}S)3p~^{5}P$ in $^{17}$O using similar strategies. The results are found to be in excellent agreement with experiment.

physics.atom-ph↗

arXiv2018

Ab initio calculations of hyperfine structures of zinc and evaluation of the nuclear quadrupole moment $Q(^{67}{\rm Zn})$

The relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) and the non-relativistic multiconfiguration Hartree-Fock (MCHF) methods have been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants of zinc. The calculated electric field gradients for the $ 4s 4p \,\, ^3 \! P^o_{1} $ and $ 4s 4p \,\, ^3 \! P^o_{2} $ states, together with experimental values of the electric quadrupole hyperfine structure constants, made it possible to extract a nuclear electric quadrupole moment $ Q(^{67}{\rm Zn}) = 0.122(10) $ b. The error bar has been evaluated in a quasi-statistical approach - the calculations had been carried out with eleven different methods, and then the error bar has been estimated from the differences between the results obtained with those methods.

physics.atom-ph↗

arXiv2017

Relativistic semiempirical-core-potential calculations in Ca$^+$, Sr$^+$, and Ba$^+$ ions on Lagrange meshes

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 $^2D_{3/2,5/2}$ states of Ca$^{+}$, Sr$^{+}$, and 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 alkali-like systems.

physics.atom-ph↗

arXiv2017

Multiconfiguration calculations of electronic isotope shift factors in Zn I

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.

physics.atom-ph↗