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Franck Gilleron

Publications and source records attributed to Franck Gilleron.

At least 19 recordsLinked to original sources

Helioseismic inference of the solar radiative opacity

The Sun is the most studied of all stars, and thus constitutes a benchmark for stellar models. However, our vision of the Sun is still incomplete, as illustrated by the current debate on its chemical composition. The problem reaches far beyond chemical abundances and is intimately linked to microscopic and macroscopic physical ingredients of solar models such as radiative opacity, for which experimental results have been recently measured that still await theoretical explanations. We present opacity profiles derived from helioseismic inferences and compare them with detailed theoretical computations of individual element contributions using three different opacity computation codes, in a complementary way to experimental results. We find that our seismic opacity is about 10% higher than theoretical values used in current solar models around 2 million degrees, but lower by 35% than some recent available theoretical values. Using the Sun as a laboratory of fundamental physics, we show that quantitative comparisons between various opacity tables are required to understand the origin of the discrepancies between reported helioseismic, theoretical and experimental opacity values.

astro-ph.SR

Detailed computation of hot-plasma atomic spectra

We present recent evolutions of the detailed opacity code SCO-RCG which combines statistical modelings of levels and lines with fine-structure calculations. The code now includes the Partially-Resolved-Transition-Array model, which allows one to replace a complex transition array by a small-scale detailed calculation preserving energy and variance of the genuine transition array and yielding improved high-order moments. An approximate method for studying the impact of strong magnetic field on opacity and emissivity was also recently implemented. The Zeeman line profile is modeled by fourth-order Gram-Charlier expansion series, which is a Gaussian multiplied by a linear combination of Hermite polynomials. Electron collisional line broadening is often modeled by a Lorentzian function and one has to calculate the convolution of a Lorentzian with Gram-Charlier distribution for a huge number of spectral lines. Since the numerical cost of the direct convolution would be prohibitive, we propose, in order to obtain the resulting profile, a fast and precise algorithm, relying on a representation of the Gaussian by cubic splines.

astro-ph.SR

New sum rules for Wigner 3jm symbols: application to expectation values of hydrogenic ions

We present new sum rules for $3jm$ coefficients, which involve, in addition to the usual weighting factor $(2j + 1)$ where $j$ is an angular momentum, the quantity $[j(j + 1)]^k$ with $k \ge 1$. The sum rules appear for instance in the statistical modeling of rotational spectra within the theory of moments, and enable one to deduce the expectation values of $r^k$ (used in the theory of Stark effect for hydrogenic ions) in parabolic coordinates from the expectation values of $r^k$ in spherical coordinates.

quant-ph

Optimized recursion relation for the computation of partition functions in the superconfiguration approach

Partition functions of a canonical ensemble of non-interacting bound electrons are a key ingredient of the super-transition-array approach to the computation of radiative opacity. A few years ago, we published a robust and stable recursion relation for the calculation of such partition functions. In this paper, we propose an optimization of the latter method and explain how to implement it in practice. The formalism relies on the evaluation of elementary symmetric polynomials, which opens the way to further improvements.

cond-mat.stat-mech

Electron broadening operator including penetrating collisions for hydrogen

The expression of the electron broadening operator including the effect of penetrating collisions, i.e. for which the incoming electron enters the extent of bound-electron wavefunctions, is rather complicated, even for hydrogen. It involves integrals of special functions, which evaluation deserves scrutiny. We present a simple approximate form of the electron collision operator for hydrogen including penetration effects, both in direct and interference terms. The new expression is accurate and easy to compute. In the Penetration Standard Theory, the collision operator is convergent whatever the value of the maximum impact parameter. However, when penetration theory is not valid anymore, it should be questioned. We discuss the problem of strong collisions when penetration effects are taken into account.

physics.atom-ph

A quantitative study of some sources of uncertainty in opacity measurements

Laboratory (laser and Z-pinch) opacity measurements of well-characterized plasmas provide data to assist inertial confinement fusion, astrophysics and atomic-physics research. In order to test the atomic-physics codes devoted to the calculation of radiative properties of hot plasmas, such experiments must fulfill a number of requirements. In this work, we discuss some sources of uncertainty in absorption-spectroscopy experiments, concerning areal mass, background emission, intensity of the backlighter and self-emission of the plasma. We also study the impact of spatial non-uniformities of the sample.

physics.plasm-ph

Modeling penetrating collisions in the standard line broadening impact theory for hydrogen

Spectral lines emitted by plasmas provide information about the thermodynamic conditions, the degree of randomness or the interactions prevailing in the medium. Collisions by plasma electrons penetrating the extent of bound-electron wavefunctions is important at high density, where short-range interactions become dominant. Such collisions are usually not taken into account properly in the standard lineshape theory, assuming long-range dipole approximation. The formalism of penetrating collisions for hydrogen relies on the introduction of a family of integrals calculated using a recursion relation. In this work, we show that such integrals can be expressed analytically, as a finite sum involving binomial coefficients and modified Bessel functions of the third kind. The explicit expression enabled us to obtain a simple approximate analytical form for the collision operator, making numerical implementation and physical interpretation easier. We also propose simple analytical forms of coefficients and integrals important for the modeling of penetrating collisions.

physics.atom-ph

Opacity calculations for stellar astrophysics

Opacity is a key ingredient of stellar structure and evolution. In the present work, we recall the role of opacity in asteroseismology, focusing mainly on two kinds of astrophysical objects: $β$ Cephei-type stars, and the Sun. The detailed opacity code SCO-RCG for local-thermodynamic-equilibrium plasmas is described and interpretation of laser and Z-pinch experiments are presented and discussed. The possible role of multi-photon processes on radiative accelerations is outlined, and the main aspects of opacity modeling which should be improved are mentioned.

astro-ph.SR

Detailed Opacity Calculations for Stellar Models

Radiative opacity is an important quantity in the modeling of stellar structure and evolution. In the present work we recall the role of opacity in the interpretation of pulsations of different kinds of stars. The detailed opacity code SCO-RCG for local-thermodynamic-equilibrium (LTE) plasmas is described, as well as the OPAMCDF project dedicated to the spectroscopy of LTE and non-LTE plasmas. Interpretations, with the latter codes, of several laser and Z pinch experiments in conditions relevant to astrophysical applications are also presented and our work in progress as concerns the internal solar conditions is illustrated.

astro-ph.SR

A project based on Multi-Configuration Dirac-Fock calculations for plasma spectroscopy

We present a project dedicated to hot plasma spectroscopy based on a Multi-Configuration Dirac-Fock (MCDF) code, initially developed by J. Bruneau. The code is briefly described and the use of the transition-state method for plasma spectroscopy is detailed. Then an opacity code for local-thermodynamic-equilibrium plasmas using MCDF data, named OPAMCDF, is presented. Transition arrays for which the number of lines is too large to be handled in a Detailed-Line-Accounting calculation can be modeled within the Partially-Resolved-Transition-Array method or using the Unresolved-Transition-Arrays formalism in jj-coupling. An improvement of the original Partially-Resolved-Transition-Array method is presented which gives a better agreement with Detailed-Line-Accounting computations. Comparisons with some absorption and emission experimental spectra are shown. Finally, the capability of the MCDF code to compute atomic data required for collisional-radiative modeling of plasma at non local thermodynamic equilibrium is illustrated. Additionally to photoexcitation, this code can be used to calculate photoionization, electron impact excitation and ionization cross-sections as well as autoionization rates in the Distorted-Wave or Close Coupling approximations. Comparisons with cross-sections and rates available in the literature are discussed.

physics.atom-ph

Detailed opacity calculations for astrophysical applications

Nowadays, several opacity codes are able to provide data for stellar structure models, but the computed opacities may show significant differences. In this work, we present state-of-the-art precise spectral opacity calculations, illustrated by stellar applications. The essential role of laboratory experiments to check the quality of the computed data is underlined. We review some X-ray and XUV laser and Z-pinch photo-absorption measurements as well as X-ray emission spectroscopy experiments involving hot dense plasmas produced by ultra-high-intensity laser irradiation. The measured spectra are systematically compared with the fine-structure opacity code SCO-RCG. Focus is put on iron, due to its crucial role in understanding asteroseismic observations of $β$ Cephei-type and Slowly Pulsating B stars, as well as of the Sun. For instance, in $β$ Cephei-type stars, the iron-group opacity peak excites acoustic modes through the "kappa-mechanism". A particular attention is paid to the higher-than-predicted iron opacity measured at the Sandia Z-machine at solar interior conditions. We discuss some theoretical aspects such as density effects, photo-ionization, autoionization or the "filling-the-gap" effect of highly excited states.

astro-ph.SR

K-shell spectroscopy in hot plasmas: Stark effect, Breit interaction and QED corrections

The broadening of lines by Stark effect is widely used for inferring electron density and temperature in plasmas. Stark-effect calculations often rely on atomic data (transition rates, energy levels,...) not always exhaustive and/or valid only for isolated atoms. In this work, we first present a recent development in the detailed opacity code SCO-RCG for K-shell spectroscopy. The approach is adapted from the work of Gilles and Peyrusse. Neglecting non-diagonal terms in dipolar and collision operators, the line profile is expressed as a sum of Voigt functions associated to the Stark components. The formalism relies on the use of parabolic coordinates and the relativistic fine-structure of Lyman lines is included by diagonalizing the hamiltonian matrix associated to quantum states having the same principal quantum number n. The SCO-RCG code enables one to investigate plasma environment effects, the impact of the microfield distribution, the decoupling between electron and ion temperatures and the role of satellite lines (such as Li-like 1s nl n'l' - 1s2 nl, Be-like, etc.). Atomic-structure calculations have reached levels of accuracy which require evaluation of Breit interaction and many-electron quantum electro-dynamics (QED) contributions. Although much work was done for QED effects (self-energy and vacuum polarization) in hydrogenic atoms, the case of an arbitrary number of electrons is more complicated. Since exact analytic solutions do not exist, a number of heuristic methods have been used to approximate the screening of additional électrons in the self-energy part. We compare different ways of including such effects in atomic-structure codes (Slater-Condon, Multi-Configuration Dirac-Fock, etc.).

physics.atom-ph

Statistical properties of levels and lines in complex spectra

We review recent developments of the statistical properties of complex atomic spectra, based on the pioneering work of Claire Bauche-Arnoult and Jacques Bauche. We discuss several improvements of the statistical methods (UTA, SOSA) for the modeling of the lines in a transition array: impact of high-order moments, choice of the distribution (Generalized Gaussian, Normal Inverse Gaussian) and corrections at low temperatures. The second part of the paper concerns general properties of transition arrays, such as propensity rule and generalized J-file sum rule (for E1 or E2 lines), emphasizing the particular role of the G1 exchange Slater integral. The statistical modeling introduced by J. Bauche and C. Bauche-Arnoult for the distribution of the M values (projection of total angular momentum J) in an electron configuration, written P(M), was extended in order to account for configurations with a high-l spectator and a new analytical formula for the evaluation of the number of E1 lines with a wider range of applicability was derived.

physics.atom-ph

Stark effect modeling in the detailed opacity code SCO-RCG

The broadening of lines by Stark effect is an important tool for inferring electron density and temperature in plasmas. Stark-effect calculations often rely on atomic data (transition rates, energy levels,...) not always exhaustive and/or valid for isolated atoms. We present a recent development in the detailed opacity code SCO-RCG for K-shell spectroscopy (hydrogen- and helium-like ions). This approach is adapted from the work of Gilles and Peyrusse. Neglecting non-diagonal terms in dipolar and collision operators, the line profile is expressed as a sum of Voigt functions associated to the Stark components. The formalism relies on the use of parabolic coordinates within SO(4) symmetry. The relativistic fine-structure of Lyman lines is included by diagonalizing the hamiltonian matrix associated to quantum states having the same principal quantum number $n$. The resulting code enables one to investigate plasma environment effects, the impact of the microfield distribution, the decoupling between electron and ion temperatures and the role of satellite lines (such as Li-like $1sn\ell n'\ell' - 1s^2n\ell$, Be-like, etc.). Comparisons with simpler and widely-used semi-empirical models are presented.

physics.atom-ph

Accounting for highly excited states in detailed opacity calculations

In multiply-charged ion plasmas, a significant number of electrons may occupy high-energy orbitals. These "Rydberg" electrons, when they act as spectators, are responsible for a number of satellites of X-ray absorption or emission lines, yielding a broadening of the red wing of the resonance lines. The contribution of such satellite lines may be important, because of the high degeneracy of the relevant excited configurations which give these large Boltzmann weights. However, it is in general difficult to take these configurations into account since they are likely to give rise to a large number of lines. We propose to model the perturbation induced by the spectators in a way similar to the Partially-Resolved-Transition-Array approach recently published by C. Iglesias. It consists in a partial detailed-line-accounting calculation in which the effect of the Rydberg spectators is included through a shift and width, expressed in terms of the canonical partition functions, which are key-ingredients of the Super-Transition-Arrays model. The resulting method can a priori be used in any detailed-configuration/line-accounting opacity code.

physics.atom-ph

The Hybrid Detailed / Statistical Opacity Code SCO-RCG: New Developments and Applications

We present the hybrid opacity code SCO-RCG which combines statistical approaches with fine-structure calculations. Radial integrals needed for the computation of detailed transition arrays are calculated by the code SCO (Super-configuration Code for Opacity), which calculates atomic structure at finite temperature and density, taking into account plasma effects on the wave-functions. Levels and spectral lines are then computed by an adapted RCG routine of R. D. Cowan. SCO-RCG now includes the Partially Resolved Transition Array model, which allows one to replace a complex transition array by a small-scale detailed calculation preserving energy and variance of the genuine transition array and yielding improved high-order moments. An approximate method for studying the impact of strong magnetic field on opacity and emissivity was also recently implemented.

physics.atom-ph

The hybrid opacity code SCO-RCG: recent developments

Absorption and emission spectra of multicharged-ion plasmas contain a huge number of electron configurations and electric-dipolar lines, which can be handled by global methods. However, some transition arrays consist only of a small bunch of lines. For that reason, we developed the hybrid opacity code SCO-RCG combining the (statistical) super-transition-array method and the (detailed) fine-structure calculation (requiring the diagonalization of the Hamiltonian matrix) of atomic structure. In order to decide whether a detailed treatment of lines is necessary and to determine the validity of statistical methods, the code involves criteria taking into account coalescence of lines and porosity (localized absence of lines) in transition arrays. Data required for the calculation of detailed transition arrays (Slater, spin-orbit and dipolar integrals) are provided by the super-configuration code SCO, which takes into account plasma screening effects on wavefunctions. Then, level energies and lines are calculated by Cowan's code. Transition arrays for which a detailed treatment is not required or impossible are described statistically, by UTA (Unresolved Transition Arrays) and STA (Super Transition Arrays) formalisms used in SCO. Recent developments are presented, such as the extension of the PRTA (Partially Resolved Transition Array) model to the hybrid approach, as well as comparisons with experimental spectra (laser or Z-pinch).

physics.atom-ph

Description of anomalous Zeeman patterns in stellar astrophysics

The influence of a magnetic field on the broadening of spectral lines and transition arrays in complex spectra is investigated. The anomalous absorption or emission Zeeman pattern is a superposition of many profiles with different relative strengths, shifts, widths, asymmetries and sharpnesses. The "sigma" and "pi" profiles can be described statistically, using the moments of the Zeeman components. We present two statistical modellings: the first one provides a diagnostic of the magnetic field and the second one can be used to include the effect of a magnetic field on simulated atomic spectra in an approximate way.

physics.atom-ph