Separability approximations for correlation in the electron gas

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Abstract
This work considers the accuracy of the approximation which takes the correlation in the reduced two--body density matrix to be separable. It is shown that consistency with Hermitian symmetry and the exchange--correlation hole sum--rule allows only one such approximation. The use of this uniquely determined approximation in variational calculations reproduces very closely the leading order term in the correlation energy of the random phase approximation (RPA), but with the computational complexity of simple, static Hartree--Fock (HF) calculations.

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