Correlation And Quantum Corrections in the Thomas Fermi Model of the Atom

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Correlation And Quantum Corrections in the Thomas Fermi Model of the Atom
Gene a Baraff
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9) (5. 10) where GG = / d(r^-r^)d(t^-tj^)G(5, ^)G(4, 5) X exp ■; - 1 I'^ly^k^-''^''^-^ / dp'dw', "i = ^ / -^^ r ii^ G^(R, p'u)') ft^ 5 (R, IH-p', uH-to'). (5. 12b) Lest the handling of the powers of ii here seem artificial, let us note that the form of the set of equations (3. *+) indicates that each of the coefficients G, contains a factor^ . The combination^ G. Which appears in (5. 12b) has J (J been chosen only to remove this h dependence from the terms n..
J We may insert the expansion of ©
... and of GG into Eq. (5*10) with the re- sult that Q(R, pw) = Zmj '^ Q. (R, P«) (5. 15a) p6 ^ " - Qi. = (kne^i/X) 2. ®mC^/P^^'"n(S'r^^ ' (5. 15b) Finally, we may insert the expansions of V^©, and Q into Eq.

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