5/5/11

Thomas-Fermi Screening

A basic illustration of screening involves considering a positive ion in an electron gas, which will aggregate electrons around itself. The presence of this negative charge surrounding the ion reduces the electric field of the ion; this is called screening.
The Thomas-Fermi theory of screening considers a slowly varying (in r) potential. The modification in the electron number density due to the presence of this potential is then calculated, as in the lectures. From this, after some maths, the total potential as a function of r, which is found to decay exponentially in r. The distance at which the charge is effectively screened (becomes negligible) is of the same order as the inter-atomic spacing, meaning the effect of the charge is not long ranged at all.
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2 comments:

  1. AnonymousMay 5, 2011 at 10:57 PM

    The effect of TF Screening increases with the increase in dimension i.e. it is less in one dimension(single filament) and more in three dimension(cylinder).The screening between filament and cylinder varies as (exp(keff*r))/r,where keff is effective wave number.

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  2. ThurayaMay 6, 2011 at 2:40 PM

    There is a disadvantage on this method as Ashcroft and Nermin said "The Thomas-Fermi method is reliable only for very slowly varying external potentials"

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