Potential and Energy Relations

Chemical Potential and Energy Relations.—As followed from the scaling property (42) characteristic of the TF theory, so formula (48) implies certain relations which we shall now examine. First, the chemical potential fi=(dE/dN) z can at least be determined formally. 

In the TF limit when Z and N become very large, we know that n - 0 for the neutral atom case N=Z and hence /q(1)=0. March and Parr12 argue that this property must also imply /J(l)=/ (1)=/ (1)=0 and possibly also /i(l)=0, leaving p(Z, Z) Z-1/3, but again this has not been presently proved. One can also obtain Ken from the Hellman-Feynman theorem 

From equations (48) and (62) we then find, for the neutral atom case 

The virial theorem yields, with exchange and correlation now in Kee, 

It is worth emphasizing that Kee has no term in Z2, as expected from the origin of this term discussed above. 

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