Effective Potentials between the Components of a Hydrogeneous Plasma

Barker, A. A.

doi:10.1063/1.1676306

Cited by 51 publications

(7 citation statements)

References 31 publications

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“…The general molecular dynamic method used is described in Paper II, and only the salient features will be given here. The method is an extension of Hansen (1973) and Hansen & McDonald (1978, 1981 with the potential between the electrons corrected for exchange (Barker 1971). While the protons are essentially classical, the electrons at a density of n \ 1026/cc start to show quantum e †ects.…”

Section: Definition Of the Plasma Screening Effectmentioning

confidence: 99%

The Electrostatic Screening of Nuclear Reactions in the Sun

Shaviv

Shaviv²

2001

ApJ

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We apply the method of Shaviv & Shaviv to evaluate from Ðrst principles the plasma screening correction to the rate of nuclear reactions under conditions similar to those prevailing in the present-day Sun. We calculate the screening factor for the p-p chain and the CN cycle nuclear reactions. We Ðnd the following :1. The mean Ðeld approximation la is not strictly valid under the conditions prevaila`Debye-Huckel ing in the core of the Sun. A kinetic approach should be implemented.2. The mean energy exchange between any two scattering particles and the plasma is positive for low relative kinetic energies and negative for high relative kinetic energies. The turnover in a pure hydrogen plasma occurs at about for the p-p reaction, for example, and changes E kin~rel B 2kT \ E Gamow B 6kT with the particular reaction. The net energy exchange, namely, the sum over all pairs of scattering particles in the system, vanishes in equilibrium.3. The turnover from energy gain to energy loss of the scattering particles is generally below the Gamow peak. The details depend on the masses of the interacting particles relative to the mass of the particles in the ambient plasma.4. The Ñuctuations and nonspherical e †ects are crucial in a †ecting the screening. We investigate the source of the Ñuctuations and their power spectrum. In view of the particular behavior of the Ñuctua-tions we derive the net e †ect of the plasma on the reaction rate for each reaction investigated here.5. The derived screening corrections, which are a function of the relative kinetic energy and depend on the environment, are averaged over the distribution of relative velocities and cross section to obtain the total screening correction. The preliminary results are obtained in two easy-to-handle limits. The p-p reaction is found to be enhanced relative to reaction in vacuum, while higher Z reactions, like the Be7 ] p reaction, are suppressed relative to the classical Salpeter theory.6. In the Appendix we show the connection between the screening and the coefficients in the FokkerPlanck equation. We use the same computer program to calculate the coefficient in the Fokker-Planck equation and Ðnd a behavior that supports the present Ðndings of the general values and behavior of the screening.

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Section: Definition Of the Plasma Screening Effectmentioning

confidence: 99%

The Electrostatic Screening of Nuclear Reactions in the Sun

Shaviv

Shaviv²

2001

ApJ

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“…The effective pair potentials derived for a hydrogen plasma by Barker (1971), Deutsch (1977), Deutsch et al (1978Deutsch et al ( , 1979 were employed to include quantum corrections. The temperature and density of the solar core (T = 1.6 × 10 7 K, ρ = 1.6 × 10 5 kg/m 3 ) were used to determine the velocities and density of the particles in the box.…”

Section: Methodsmentioning

confidence: 99%

Dynamic screening in solar and stellar nuclear reactions

Mussack¹,

Däppen²

2010

Astrophys Space Sci

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In the hot, dense plasma of solar and stellar interiors, the Coulomb interaction is screened by the surrounding plasma. Although the standard Salpeter approximation for static screening is widely accepted and used in stellar modeling, the question of dynamic screening has been revisited. In particular, Shaviv and Shaviv apply the techniques of molecular dynamics to the conditions in the solar core in order to numerically determine the dynamic screening effect. By directly calculating the motion of ions and electrons due to Coulomb interactions, they compute the effect of screening without the mean-field assumption inherent in the Salpeter approximation. Here we reproduce their numerical analysis of the screening energy in the plasma of the solar core and conclude that the effects of dynamic screening are relevant and should be included in the treatment of the plasma, especially in the computation of stellar nuclear reaction rates.Comment: Astrophysics and Space Science, Special Issue Solar & Stellar Modelling Corrected sign error. Now consistent with final published versio

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“…These particles interact via the Coulomb potential. Quantum corrections are provided by the effective pair potentials derived for a hydrogen plasma by Barker (1971), Deutsch (1977), Deutsch et al (1978Deutsch et al ( , 1979. The quantum diffraction effects are described by…”

Section: Modelmentioning

confidence: 99%

Dynamic screening in solar p-p reactions: is the mean-field approach applicable in solar plasma?

Mussack

2010

Astrophys Space Sci

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Although the Salpeter approximation for static screening is widely accepted and used in stellar modeling, the question of dynamic screening has been revisited. Here we reproduce Shaviv and Shaviv's numerical analysis of the screening energy for p-p reactions in the solar core using the techniques of molecular dynamics to directly calculate the motion of ions and electrons due to Coulomb interactions without the mean-field assumption that is inherent in the Salpeter approximation. We conclude that the effects of dynamic screening are relevant and should be included in the treatment of the plasma, especially in the computation of nuclear reaction rates.

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Effective Potentials between the Components of a Hydrogeneous Plasma

Cited by 51 publications

References 31 publications

The Electrostatic Screening of Nuclear Reactions in the Sun

The Electrostatic Screening of Nuclear Reactions in the Sun

Dynamic screening in solar and stellar nuclear reactions

Dynamic screening in solar p-p reactions: is the mean-field approach applicable in solar plasma?

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