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Franck Gilleron

Publications and source records attributed to Franck Gilleron.

25 records · Page 2Linked to original sources
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

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

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

Jensen-Feynman approach to the statistics of interacting electrons

Faussurier et al. [Phys. Rev. E 65, 016403 (2001)] proposed to use a variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov) inequality in order to optimize the accounting for two-particle interactions in the calculation of canonical partition functions. It consists in a decomposition into a reference electron system and a first-order correction. The procedure appears to be very efficient in order to evaluate the free energy and the orbital populations. In this work, we present numerical applications of the method and propose to extend it using a reference energy which includes the interaction between two electrons inside a given orbital. This is possible thanks to our efficient recursion relation for the calculation of partition functions. We also show that a linear reference energy, however, is usually sufficient to achieve a good precision and that the most promising way to improve the approach of Faussurier et al. is to apply Jensen's inequality to a more convenient convex function.

physics.atom-ph↗
arXiv2009

Effect of third- and fourth-order moments on the modeling of Unresolved Transition Arrays

The impact of the third (skewness) and fourth (kurtosis) reduced centered moments on the statistical modeling of E1 lines in complex atomic spectra is investigated through the use of Gram-Charlier, Normal Inverse Gaussian and Generalized Gaussian distributions. It is shown that the modeling of unresolved transition arrays with non-Gaussian distributions may reveal more detailed structures, due essentially to the large value of the kurtosis. In the present work, focus is put essentially on the Generalized Gaussian, the power of the argument in the exponential being constrained by the kurtosis value. The relevance of the new statistical line distribution is checked by comparisons with smoothed detailed line-by-line calculations and through the analysis of 2p-3d transitions of recent laser or Z-pinch absorption measurements. The issue of calculating high-order moments is also discussed (Racah algebra, Jucys graphical method, semi-empirical approach ...).

physics.atom-ph↗