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CAF123
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The corrections to the energy per electron in a jellium model (uniform distribution of positive ion charge approximation to the regulated long range order ionic array) is given by (in units of Ry) $$E/N = \frac{2.21}{(r_s/a_o)^2} - \frac{0.916}{(r_s/a_o)} + 0.0622 \ln (r_s/a_o) - 0.096 + O(r_s/a_o) $$ (##r_s## is the radius of a sphere that holds the same volume as one conduction electron and ##a_o## is the bohr radius, but I don't think is so important to my questions). See e.g the derivation and this same result in Ashcroft and Mermin P.336
My question is why does the last three terms contain contributions to the kinetic and potential energy? It seems to me that it should only be potential energy since the source of the extra terms comes from the perturbation which is precisely due to the e-e interactions, but I have been told otherwise.
My other question is this whole procedure was implemented to better account for the interaction between the electrons in a metal. This expansion above is only valid for ##r_s/a_o \ll 1 ## and for most metals this value is from 2 to 6. So what is the usefulness of this result then if it does not apply to the very thing it sought out to describe?
Thanks for any replies.
My question is why does the last three terms contain contributions to the kinetic and potential energy? It seems to me that it should only be potential energy since the source of the extra terms comes from the perturbation which is precisely due to the e-e interactions, but I have been told otherwise.
My other question is this whole procedure was implemented to better account for the interaction between the electrons in a metal. This expansion above is only valid for ##r_s/a_o \ll 1 ## and for most metals this value is from 2 to 6. So what is the usefulness of this result then if it does not apply to the very thing it sought out to describe?
Thanks for any replies.