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On the basis of the correlated wave function theory, we have solved the real space integral equation for the pair correlation function, and obtained the pair correlation function, correlation energy and many-body wave function for the metals Al (rs=2.07) and Cs (rs=5.65). This work improves on the imperfections of other many-body theories. The pair correlation functions obtained in this paper are positive definite and satisfy the normalization condition.
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