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Jean-Christophe Pain

Publications and source records attributed to Jean-Christophe Pain.

At least 127 records · Page 7Linked to original sources

Expression of the Holtsmark function in terms of hypergeometric $_2F_2$ and Airy $\mathrm{Bi}$ functions

The Holtsmark distribution has applications in plasma physics, for the electric-microfield distribution involved in spectral line shapes for instance, as well as in astrophysics for the distribution of gravitating bodies. It is one of the few examples of a stable distribution for which a closed-form expression of the probability density function is known. However, the latter is not expressible in terms of elementary functions. In the present work, we mention that the Holtsmark probability density function can be expressed in terms of hypergeometric function $_2F_2$ and of Airy function of the second kind $\mathrm{Bi}$ and its derivative. The new formula is simpler than the one proposed by Lee involving $_2F_3$ and $_3F_4$ hypergeometric functions.

math-ph↗

Commutation relations of operator monomials

In this short paper, the commutator of monomials of operators obeying constant commutation relations is expressed in terms of anticommutators. The formula involves Bernoulli numbers or Euler polynomials evaluated in zero. The role of Bernoulli numbers in quantum-mechanical identities such as the Baker-Campbell-Hausdorff formula is emphasized and applications connected to ordering problems as well as to Ehrenfest theorem are proposed.

math-ph↗

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↗

On the vacuum-polarization Uehling potential for a Fermi charge distribution

We present analytical formulas for the vacuum-polarization Uehling potential in the case where the finite size of the nucleus is modeled by a Fermi charge distribution. Using a Sommerfeld-type development, the potential is expressed in terms of multiple derivatives of a particular integral. The latter and its derivatives can be evaluated exactly in terms of Bickley-Naylor functions, which connection to the Uehling potential was already pointed out in the pure Coulomb case, and of usual Bessel functions of the second kind. The cusp and asymptotic expressions for the Uehling potential with a Fermi charge distribution are also provided. Analytical results for the higher-order-contribution Källèn-Sabry potential are given.

quant-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↗

A new sum rule for Clebsch-Gordan coefficients using generalized characters of irreducible representations of the rotation group

We present a new sum rule for Clebsch-Gordan coefficients using generalized characters of irreducible representations of the rotation group. The identity is obtained from an integral involving Gegenbauer ultraspherical polynomials. A similar procedure can be applied for other types of integrals of such polynomials, and may therefore lead to the derivation of further new relations.

math-ph↗

On the Li-Rosmej analytical formula for energy level shifts in dense plasmas

Li and Rosmej derived analytical fits for the energy level shifts due to plasma screening on the basis of a free-electron potential published by Rosmej et al. one year earlier. The derivation of the fits, which were shown by Iglesias to be inconsistent with the fundamental premise of the ion-sphere model, was motivated by the belief that no analytical expression exists for the expectation value $\langle r^{3/2}\rangle$, an assertion that was also contradicted by Iglesias. In this short note, I point out that a simple expression for the latter quantity can be obtained as a particular case of a formula published by Shertzer, and I provide a corresponding compact analytical expression for the level shifts in the framework of Rosmej's formalism.

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↗

D'yakov-Kontorovitch instability of shock waves in hot plasmas

The D'yakov-Kontorovich stability criterion for spontaneous emission of acoustic waves behind shock fronts is investigated for high-temperature carbon, aluminum, silicon and niobium plasmas. The D'yakov and critical stability parameters are calculated along the principal Rankine-Hugoniot curve with an equation-of-state model in which the contribution of bound and free electrons is calculated through a relativistic quantum average-atom model, solving the Dirac equation. The pressure is determined using the stress-tensor formula in the relativistic framework. We find that the instability occurs at the end of the ionization of electronic shells, when the Hugoniot curve departs from the $ρ/ρ_0$=4 asymptote to tend to the $ρ/ρ_0$=7 limit. In such conditions, if the plasma is optically thick, the contribution of blackbody radiation to the EOS is dominant, and the system becomes always stable. Our results indicate that the conditions in which the instability takes place are different from previously published estimates, due to assumptions made in the corresponding equation-of-state models, especially as concerns the relativistic effects, and depend on the radiative opacity of the material.

physics.plasm-ph↗

Comment on electron-impact excitation cross-section measurements for He-like Xenon

We discuss lower-than-predicted collisional-excitation cross-sections for helium-like xenon measured at an Electron Beam Ion Trap facility. In a review paper (H. Chen and P. Beiersdorfer, Can. J. Phys. 86, 55 (2008)), the authors find a significant effect due to the Breit interaction between the free and the bound electrons in the excitation process of He-like xenon. The authors state that the agreement between the measured and calculated cross-section values can only be found when the generalized Breit interaction is included in the calculations. We have performed new calculations with a Multi-Configuration Dirac-Fock code, as well as with the Penn State University suite of codes, and our conclusions are that the contribution of the Breit interaction is much lower than found in the calculations presented in the abovementioned article. In fact, our predictions are subsequently almost twice as large as the experimental values. We present these considerations in hopes of motivating new experimental investigations.

physics.atom-ph↗

Number of spin-J states and odd-even staggering for identical particles in a single-j shell

In this work, new recursion relations for the number of spin-J states for identical particles in a single-j shell are presented. Such relations are obtained using the generating-function technique, which enables one to exhibit an odd-even staggering in the spin distribution of an even number of fermions in a single-j shell: the number of states with an even value of J is larger than the number of states with an odd value of J. An analytical expression of the excess of states with an even value of J is provided, and its asymptotic behavior for large values of j is discussed.

nucl-th↗

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↗

Recursive determination of phase shifts for screened Coulomb potentials

In the calculation of hot-plasma atomic structure, the continuum wavefunctions are characterized by phase shifts, which therefore determine the scattering cross-sections. In this short paper, we propose a recurrence relation for the phase shifts in the case of a particular type of parametric potentials widely used in atomic-structure codes. These potentials have to be linear combinations of static screened Coulomb potentials (Yukawa-type potentials) multiplied by polynomial functions.

physics.atom-ph↗

A note on the contribution of multi-photon processes to radiative opacity

Recently, Bailey et al. performed iron opacity measurements on the Z machine at Sandia National Laboratory in conditions close to the ones of the base of the convective zone of the Sun. Such experiments have raised questions about the physical models commonly used in opacity codes. To understand the discrepancy between experiment and theory, More et al. investigated the role of two-photon processes. In the present work we show, by a simple estimate and using hydrogenic formulas, that due to the intensity of the backlight radiation seen by the sample, such processes are likely to play an important role only for highly excited states.

physics.atom-ph↗

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↗