Mathematics – Mathematical Physics
Scientific paper
Jan 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000jmp....41..260b&link_type=abstract
Journal of Mathematical Physics, Volume 41, Issue 1, pp. 260-283 (2000).
Mathematics
Mathematical Physics
1
Stellar Structure, Interiors, Evolution, Nucleosynthesis, Ages, Magnetohydrodynamics And Plasmas, Corrections To Electronic Structure, Plasma Kinetic Equations, Elementary Processes In Plasmas
Scientific paper
We calculate the effect of weak electrostatic screening of ions in a plasma. The original calculation by Salpeter is based on a linearization of the Poisson-Boltzmann equation for the screened electrostatic potential. This approximation is valid where the potential is small, but is formally invalid in the vicinity of the ions where the solutions for the potential and the associated charge distribution diverge. In reality, quantum exclusion must prevent the divergence of the charge density of the screening cloud. Nevertheless, in the limit in which screening is weak, Salpeter's value for the total screening energy is essentially correct. Here we extend Salpeter's calculation to account approximately for both quantum-mechanical exclusion in the vicinity of the ions, using what we call the Poisson-Boltzmann-Fermi-Dirac approximation, and the polarization of the screening cloud. By matching the solution onto an expression for the two-center Poisson-Boltzmann charge distribution far from the ions we are able to construct a consistent solution over all space. We obtain the first-order term in the expansion of that solution, from which we calculate the free-energy associated with the screened ion pair.
Brüggen Marcus
Gough Douglas O.
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