Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
41 (2000), S. 260-283
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
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. © 2000 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.533132
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