Origin of Corrections to TF Neutral Atom Energy

Origin of Corrections to TF Neutral Atom Energy.—Since presently we do not know how to write the kinetic energy density tr in any precise way, let us use the Coulomb example of Section 4 to estimate the error in the TF energy for this case. It is then easy to verify for particles moving in this bare r 1 potential that, using equation (3) with V(r)= —Ze2/r, yields, forZ electrons, 

The inhomogeneity correction in this case is seen to be Z2. Scott, to whom this result is due,14 examined the origin of this correction, and found it came 

Evidently, the kinetic energy T is reduced from the TF value in equation (54) by iZ2 because of the virial theorem this then is the inhomogeneity correction for the Coulomb field, in the sense of the Z-1/3 expansion. 

Scott14 evaluated the integral involving the neutral atom solution f (x) of the TF equation (10) and thus obtained 

March and Plaskett18 investigated corrections to 0(Z5/3) other than exchange and concluded that formula (56) should be extended to read 

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