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Jean-Christophe Pain

Publications and source records attributed to Jean-Christophe Pain.

At least 145 records · Page 8Linked to original sources
arXiv2016

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↗
arXiv2015

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↗
arXiv2015

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↗
arXiv2013

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↗
arXiv2013

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↗
arXiv2013

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↗
arXiv2012

Random-matrix theory and complex atomic spectra

Around 1950, Wigner introduced the idea of modelling physical reality with an ensemble of random matrices while studying the energy levels of heavy atomic nuclei. Since then, the field of random-matrix theory has grown tremendously, with applications ranging from fluctuations on the economic markets to complex atomic spectra. The purpose of this short article is to review several attempts to apply the basic concepts of random-matrix theory to the structure and radiative transitions of atoms and ions, using the random matrices originally introduced by Wigner in the framework of the gaussian orthogonal ensemble. Some intrinsic properties of complex-atom physics, which could be enlightened by random-matrix theory, are presented.

physics.atom-ph↗
arXiv2012

Statistics of electric-quadrupole lines in atomic spectra

In hot plasmas, a temperature of a few tens of eV is sufficient for producing highly stripped ions where multipole transitions become important. At low density, the transitions from tightly bound inner shells lead to electric-quadrupole (E2) lines which are comparable in strength with electric-dipole ones. In this work, we propose analytical formulas for the estimation of the number of E2 lines in a transition array. Such expressions rely on statistical descriptions of electron states and J-levels. A generalized 'J-file' sum rule for E2 lines and the strength-weighted shift and variance of the line energies of a transition array nl^N+1 \rightarrow nl^Nn'l' of inter-configuration E2 lines are also presented.

physics.atom-ph↗
arXiv2012

Characterization of anomalous Zeeman patterns in complex atomic spectra

The modeling of complex atomic spectra is a difficult task, due to the huge number of levels and lines involved. In the presence of a magnetic field, the computation becomes even more difficult. The anomalous Zeeman pattern is a superposition of many absorption or emission profiles with different Zeeman relative strengths, shifts, widths, asymmetries and sharpnesses. We propose a statistical approach to study the effect of a magnetic field on the broadening of spectral lines and transition arrays in atomic spectra. In this model, the sigma and pi profiles are described using the moments of the Zeeman components, which depend on quantum numbers and Landé factors. A graphical calculation of these moments, together with a statistical modeling of Zeeman profiles as expansions in terms of Hermite polynomials are presented. It is shown that the procedure is more efficient, in terms of convergence and validity range, than the Taylor-series expansion in powers of the magnetic field which was suggested in the past. Finally, a simple approximate method to estimate the contribution of a magnetic field to the width of transition arrays is proposed. It relies on our recently published recursive technique for the numbering of LS-terms of an arbitrary configuration.

physics.atom-ph↗
arXiv2011

Equation of state of dense plasma mixtures: application to the Sun center

We present a self-consistent approach to the modeling of dense plasma mixtures in local thermodynamic equilibrium. In each electron configuration the nucleus is totally screened by electrons in a Wigner-Seitz sphere (ion-sphere model). Bound and free electrons are treated quantum-mechanically. The assumption that all species should have the same electronic environment leads to the equality of the electronic pressure for all ions of all elements having therefore different cell volumes. The variation of the average atomic radii of the different elements with respect to temperature is investigated, and the procedure is applied to the determination of pressure in the Sun center.

astro-ph.SR↗
arXiv2011

A note on recursive calculations of particular 9j coefficients

The calculation of angular-momentum coupling transformation matrices can be very time consuming and alternative methods, even if they apply only in special cases, are helpful. We present a recursion relation for the calculation of particular 9j symbols used in the quantum theory of angular momentum.

physics.atom-ph↗
arXiv2011

Special 6j and 9j symbols for a single-j shell

In this Brief Report, we propose general expressions for 6j and 9j coefficients arising in the study of the J-pairing interaction of identical fermions in a single-j shell. In the literature such coefficients are available only for a number of given angular momenta.

nucl-th↗
arXiv2011

Koopmans' theorem in statistical Hartree-Fock theory

In this short paper, the validity of Koopmans' theorem in the Hartree-Fock theory at non-zero temperature (Hartree-Fock statistical theory) is investigated. It is shown that Koopmans' theorem does not apply in the grand-canonical ensemble, due to a missing contribution to the energy proportional to the interaction between two electrons belonging to the same orbital. Hartree-Fock statistical theory has also been applied in the canonical ensemble [Blenski et al., Phys. Rev. E 55, R4889 (1997)] for the purpose of photo-absorption calculations. In that case, the Hartree-Fock self-consistent-field equations are derived in the super-configuration approximation. It is shown that Koopmans' theorem does not hold in the canonical ensemble, but that a restricted version of the theorem can be obtained, by assuming that a particular quantity multiplying the interaction matrix element in the expression of the energy does not change during the removal of an electron.

physics.atom-ph↗
arXiv2011

Generating functions for canonical systems of fermions

The method proposed by Pratt to derive recursion relations for systems of degenerate fermions [Phys. Rev. Lett. 84, 4255 (2000), arXiv:nucl-th/9905055] relies on diagrammatic techniques. This efficient formalism assumes no explicit two-body interactions, makes possible the inclusion of conservation laws and requires low computational time. In this brief report, we show that such recursion relations can be obtained from generating functions, without any restriction as concerns the number of conservation laws (e.g. total energy or angular momentum).

physics.atom-ph↗
arXiv2011

Comment on "A note on generalized radial mesh generation for plasma electronic structure"

In a recent note [High Energy Density Phys. 7, 161 (2011)], B.G. Wilson and V. Sonnad proposed a very useful closed form expression for the efficient generation of analytic log-linear radial meshes. The central point of the note is an implicit equation for the parameter h, involving Lambert's function W[x]. The authors mention that they are unaware of any direct proof of this equation (they obtained it by re-summing the Taylor expansion of h using high-order coefficients obtained by analytic differentiation of the implicit definition using symbolic manipulation). In the present comment, we present a direct proof of that equation.

physics.comp-ph↗
arXiv2011

A consistent approach for mixed detailed and statistical calculation of opacities in hot plasmas

Absorption and emission spectra of plasmas with multicharged-ions contain transition arrays with a huge number of coalescent electric-dipole (E1) lines, which are well suited for treatment by the unresolved transition array and derivative methods. But, some transition arrays show detailed features whose description requires diagonalization of the Hamiltonian matrix. We developed a hybrid opacity code, called SCORCG, which combines statistical approaches with fine-structure calculations consistently. Data required for the computation of detailed transition arrays (atomic configurations and atomic radial integrals) are calculated by the super-configuration code SCO (Super-Configuration Opacity), which provides an accurate description of the plasma screening effects on the wave-functions. Level energies as well as position and strength of spectral lines are computed by an adapted RCG routine of R. D. Cowan. The resulting code provides opacities for hot plasmas and can handle mid-Z elements. The code is also a powerful tool for the interpretation of recent laser and Z-pinch experimental spectra, as well as for validation of statistical methods.

physics.atom-ph↗
arXiv2009

Resistivity in warm dense plasmas beyond the average-atom model

The exploration of atomic properties of strongly coupled partially degenerate plasmas, also referred to as warm dense matter, is important in astrophysics, since this thermodynamic regime is encountered for instance in Jovian planets' interior. One of the most important issues is the need for accurate equations of state and transport coefficients. The Ziman formula has been widely used for the computation of the static (DC) electrical resistivity. Usually, the calculations are based on the continuum wavefunctions computed in the temperature and density-dependent self-consistent potential of a fictive atom, representing the average ionization state of the plasma (average-atom model). We present calculations of the electrical resistivity of a plasma based on the superconfiguration (SC) formalism. In this modeling, the contributions of all the electronic configurations are taken into account. It is possible to obtain all the situations between the two limiting cases: detailed configurations (a super-orbital is a single orbital) and detailed ions (all orbitals are gathered in the same super-orbital). The ingredients necessary for the calculation are computed in a self-consistent manner for each SC, using a density-functional description of the electrons. Electron exchange-correlation is handled in the local-density approximation. The momentum transfer cross-sections are calculated by using the phase shifts of the continuum electron wavefunctions computed, in the potential of each SC, by the Schroedinger equation with relativistic corrections (Pauli approximation). Comparisons with experimental data are also presented.

physics.plasm-ph↗