Abstract
This paper presents in the first section the exact evaluation of three single integrals relating to the dielectric behavior of two-dimensional electron plasmas. In the second section we present a procedure for reducing 3 d-dimensional integrals of the form: ∫∫∫ d q d p d kD(q)α( p+ k+ q)ƒ( p)[1−ƒ( p+ q)]ƒ(k)[1−ƒ( k+ q)] , where the vectors lie in d-dimensional space and ƒ denotes the Fermi function, to tractable form. The second-order exchange integral for a d-dimensional electron gas is taken as an example and is evaluated in closed form as a function of d.
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