Recently developed analytic approximation for the equation of state of fully ionized nonideal electron-ion plasma mixtures [A. Y. Potekhin, G. Chabrier, and F. J. Rogers, Phys. Rev. E 79, 016411 (2009)], which covers the transition between the weak and strong Coulomb coupling regimes and reproduces numerical results obtained in the hypernetted-chain (HNC) approximation, is modified in order to fit the small deviations from the linear mixing in the strong-coupling regime, revealed by recent Monte Carlo simulations. In addition, a mixing rule is proposed for the regime of weak coupling, which generalizes post-Debye density corrections to the case of mixtures and numerically agrees with the HNC approximation in that regime.

Using the results of extensive Monte Carlo simulations we discuss corrections to the linear mixing rule in strongly coupled binary ionic mixtures. We analyze the plasma screening function at zero separation, H jk (0), for two ions (of types j = 1,2 and k = 1, 2) in a strongly coupled binary mixture. The function H jk (0) is estimated by two methods: (1) from the difference of Helmholtz Coulomb free energies at large and zero separations; (2) by fitting the Widom expansion of H jk ( x ) in powers of interionic distance x to Monte Carlo data on the radial pair distribution function g jk ( x ). These methods are shown to be in good agreement. For illustration, we analyze the plasma screening enhancement of nuclear burning rates in dense stellar matter (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

We analyze the effect of plasma screening on nuclear reaction rates in dense matter composed of atomic nuclei of one or two types. We perform semiclassical calculations of the Coulomb barrier penetrability taking into account a radial mean-field potential of plasma ions. The mean-field potential is extracted from the results of extensive Monte Carlo calculations of radial pair distribution functions of ions in binary ionic mixtures. We calculate the reaction rates in a wide range of plasma parameters and approximate these rates by an analytical expression that is expected to be applicable to multicomponent ion mixtures. Also, we analyze Gamow-peak energies of reacting ions in various nuclear burning regimes. For illustration, we study nuclear burning in {sup 12}C-{sup 16}O mixtures.

It is well known that an activity expansion of the grand canonical partition function works well for attractive interactions, but poorly for repulsive interactions, such as occur between atoms and molecules. The virial expansion of the canonical partition function shows just the opposite behavior. This poses a problem for applications that involve both types of interactions, such as occur in the outer layers of low-mass stars. We show that it is possible to obtain expansions for repulsive systems that convert the poorly performing Mayer activity expansion into a series of rational polynomials that converge uniformly to the virial expansion. In the current work we limit our discussion to the second virial approximation. In contrast to the Mayer activity expansion, the activity expansion presented herein converges for both attractive and repulsive systems.

We compare Path Integral Monte Carlo calculations by Militzer and Pollock [Phys. Rev. B 71, 134303 (2005)] of Coulomb tunneling in nuclear reactions in dense matter to semiclassical calculations assuming WKB Coulomb barrier penetration through the radial mean-field potential. We find very good agreement of the two approaches at temperatures higher than $\ensuremath{\sim}\frac{1}{5}$ of the ion plasma temperature. We obtain a simple parametrization of the mean-field potential and of the respective reaction rates. We analyze Gamow-peak energies of reacting ions in various reaction regimes and discuss theoretical uncertainties of nuclear reaction rates taking carbon burning in dense stellar matter as an example.

Molecular dynamics simulations of the cooling of highly-charged ions captured into a Penning ion trap (RETRAP) along with Be+ ions are described. Experimentally, the Be+ ions were directly cooled continuously using a laser, and collisional coupling to these laser-cooled ions cooled the highly-charged ions. The simulation is described as a tool for experimental interpretation and refinement. Under conditions closely related to the experimental parameters, the highly charged ions were found to form ordered structures, and to exhibit characteristics of a magnetized non-neutral plasma.

Starting from a general quantum statistical formula for the pressure in terms of thermodynamic Green's functions, different contributions to the equation of state (EOS) for the one component plasma (OCP) are given analytically and by numerical calculations. Exact results for the EOS of a quantum electron gas are presented in the shape of a low density expansion up to the order (ne(2))(5/2) including ladder type contributions and ''beyond Montroll-Ward'' terms.

Over the past five years, we have pursued a program of theoretical research, partially funded by the Office of Naval Research, on the Equation of State (EOS) and transport properties of dense, partially ionized, reacting plasmas. Although originally motivated by the failure of older, simpler theories to describe plasmas produced in new, innovative power sources, this program developed into a far-ranging, multi-faceted study of the basic properties of such complicated systems. Our research efforts, nevertheless, can be divided into three basic categories: (1) Theory of Equation of State and Static Structure; (2) Electrical Conductivity and Dynamic Properties, and (3) Computer Simulation Studies. While these categories are fairly well defined, they are very closely related, and results from each impact on results from the others. Since all of the most significant results have already appeared in published form, the progress made in each of these areas is described only briefly.

Recent Monte Carlo calculations from Paris and from Livermore for dense one and two component plasmas have led to systematic and accurate results for the thermodynamic properties of dense Coulombic fluids. This talk will summarize the results of these numerical experiments, and the simple analytic expressions for the equation of state and other thermodynamic functions that have been obtained. The thermal energy for the one component plasma has a simple power law dependence on temperature that is identical to Monte Carlo results on strongly coupled fluids governed by l/r/sup n/ potentials. A universal model for fluids governed by simple repulsive forces is suggested. For two component plasmas the ion-sphere model is shown to accurately reproduce the Monte Carlo data for the static portion of the energy. Electron screening is included using the Lindhard dielectric function and linear response theory. Free energy expressions have been constructed for one and two component plasmas that allow easy computation of all thermodynamic functions.

published or not.The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

view Abstract Citations (306) References (20) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Screening Factors for Nuclear Reactions. II. Intermediate Screen-Ing and Astrophysical Applications Graboske, H. C. ; Dewitt, H. E. ; Grossman, A. S. ; Cooper, M. S. Abstract The theory of intermediate screening is developed from the cluster expansion for the screening function. This systematic perturbation technique is used to extend weak-screening theory analytically to higher order in the screening parameter, and is solved numerically to yield screeningfunction data for intermediate and strong screening regions. For both the one-component system, equal charge reactions, and the two-component system in the form of 10 mixtures of low-Z elements, the resultant intermediate-screening function is shown to obey a simple power-law dependence on the screening parameter, H13(0) x f(zt)A23b, where b = 0.860. This result is found to be equivalent to the general screening function presented in Paper I. The new screening theory is studied in relation to various astrophysical situations. Three areas are found where screening effects may produce quantitative changes in evolutionary star models: minimum mass limits for H, D, He, C, and 0 main sequences; the structure and extent of flash events in red-giant interiors; and the strength of detonations in degenerate carbon and oxygen cores. This latter case may require screening-factor increases of two orders of magnitude. Subject headings: interiors, stellar - late-type stars - nuclear reactions - plasmas Publication: The Astrophysical Journal Pub Date: April 1973 DOI: 10.1086/152062 Bibcode: 1973ApJ...181..457G full text sources ADS | Related Materials (1) Part 1: 1973ApJ...181..439D

view Abstract Citations (232) References (9) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Screening Factors for Nuclear Reactions. I. General Theory Dewitt, H. E. ; Graboske, H. C. ; Cooper, M. S. Abstract A generalized statistical-mechanical theory is developed to describe the effect of plasma screening on nuclear reactions. The screening function [H12(0) oa ln j\ where f is the screening factor] is generally describable in terms of pair distribution functions of the plasma electrons and ions, and is demonstrated to be a thermodynamic quantity, a function of the chemical potentials of the reacting charges. This theory recovers the previous weak- and strong-screening results of Salpeter, in the appropriate charge and screening strength limits for which they are valid. A new theoretical study of strong screening is next made for the case of equal-charge reactions, based on Monte Carlo calculations of the pair distribution function of the Coulomb fluid. This result, which has wide astrophysical applications, is combined with the theory of Salpeter to construct a generalized screening function for arbitrary charge conditions. The generalized screening factor is extended to describe intermediate-screening effects. Subject headings: nuclear reactions - plasmas Publication: The Astrophysical Journal Pub Date: April 1973 DOI: 10.1086/152061 Bibcode: 1973ApJ...181..439D full text sources ADS | Related Materials (1) Part 2: 1973ApJ...181..457G

The screening effects on two like charges at short distances in a classical plasma are computed using a cluster expansion for the pair correlation function. We obtain numerically accurate results for the intermediate screening region, Λ ∼ 1, where Λ is Coulomb interaction parameter.

The theory of dense hydrogenic plasmas beginning with the two component quantum grand partition function is reviewed. It is shown that ionization equilibrium and molecular dissociation equilibrium can be treated in the same manner with proper consideration of all two-body states. A quantum perturbation expansion is used to give an accurate calculation of the equation of state of the gas for any degree of dissociation and ionization. In this theory, the effective interaction between any two charges is the dynamic screened potential obtained from the plasma dielectric function. We make the static approximation; and we carry out detailed numerical calculations with the bound and scattering states of the Debye potential, using the Beth-Uhlenbeck form of the quantum second virial coefficient. We compare our results with calculations from the Saha equation; we find our results to be considerably different from the Saha results because of the proper inclusion of hydrogenic scattering states. The hydrogenic energy levels are functions of density and, as density increases, the levels move upward into the continuum, giving pressure ionization.

The thermodynamic equilibrium properties of strongly ionized multicomponent gas mixtures are investigated by application of the free-energy minimization method. For high-temperature regions where the Coulomb interaction is the dominant perturbation, the many-body partition function is developed from quantum cluster-expansion theory. The Coulomb free energy is given as the sum of the first- and second-order direct-interaction terms, plus the first three exchange-interaction terms. All five terms are exact in the classical limit, i. e., where Maxwell-Boltzmann statistics apply. The direct terms are correct for weak electron degeneracy and include wave-mechanical effects, while the first-order exchange term is exact for all degrees of degeneracy. The theoretical model is applied to multicomponent mixtures of hydrogen and of helium in the temperature range 50-2000 eV. The combination of the ring term plus higher-order terms significantly extends the region of applicability of the model over a classical electrostatic model. Specifically, electron degeneracy, the short-range cutoff in the ring term, and the three-rung ladder (second-order direct) term all operate to produce much less divergent thermodynamic results at a given density and temperature. First-order exchange is important even at moderate values of the electron-degeneracy parameter. The thermodynamic results indicate that evaluation of the exact quantum-mechanical ring term is essential for wider application of the perturbation-expansion theory, as is the development of a second-order exchange term for arbitrary degeneracy.