Screening Enhancement of Thermonuclear Reactions in High Density Stars

Abstract

September 28, 1998This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the author. PREPRINT ABSTRACTThe screening function for zero separation for two is reacting nuclei in a strongly coupled OCP plasma is obtained using new very accurate Monte Carlo OCP fluid simulation data by two methods. The first method obtains, H(0), the screening function at x =0, from the difference of free energies before and after the reaction.The second method is a direct fitting of the Widom expansion in powers of x 2 to the MC data for the pair distribution function, g(x). The two methods agree to .2%. INTRODUCTIONThermonuclear reaction rates in high density stars, such as the onset of C -C reactions in white dwarf stars, are governed by the probability that the two reacting nuclei get sufficiently close that they can tunnel through the Coulomb barrier. Screening by neighboring ions significantly reduces this barrier. The dominant effect in the fluid portion of the white dwarfs is governed by the screening function defined by the ion-ion pair distribution function:

Equation of state of fully ionized electron-ion plasmas. II. Extension to relativistic densities and to the solid phase

“…[6] (DWS), and with some of our HNC results (triangles). Lower panel: residual differences between the fit (15) and (i) the analytic expansion (12) (dot-dashed line), (ii) results of HNC calculations (triangles), (iii) MC results of Ref.…”

“…The most accurate up to date numerical results for the internal energy of the liquid OCP at 1 ≤ Γ ≤ 200 have been obtained by MC simulations by DeWitt and Slattery [6] and by Caillol [7]. These authors have also constructed analytic fits to their data with the standard deviations comparable to the numerical MC noise.…”

“…(12) at small Γ. The best-fit parameters with respect to the data [6,7] are given in Table I. Then the free energy can be obtained from Eq.…”

“…In addition, we present simple formulae for the excess internal and free energies of a classical one-component plasma (OCP) liquid, which take into account the most recent Monte Carlo (MC) results [6,7], and which are accurate for any values of the Coulomb coupling parameter from the gaseous phase to the dense liquid regime. Analyzing various results for the free energy of the OCP liquid and solid, we revise the value of the coupling parameter at the solid-liquid phase transition.…”

Corrections to Linear Mixing in Binary Ionic Mixtures and Plasma Screening at Zero Separation

“…Following Ref. [6] we apply two approaches to calculate the screening enhancement: one is based on the thermodynamic relations and the other on fitting the mean-field potentials. The main advance of the present work is in using a much wider set of numerical data and most precise thermodynamic results.…”