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- W2032022570 abstract "The coupled-cluster or $mathrm{exp}(S)$ formalism is applied to the problem of correlations in a many-electron system. In this first work in a series of papers we concentrate on exact results and restrict ourselves to various ring approximations applicable essentially to the high-density regime. It is shown that the well-known random-phase approximation (RPA) can be formulated as a nonlinear three-dimensional integral equation for the four-point function ${S}_{2}$ which provides a measure of the two-particle---hole pair component in the true ground-state wave function. Exact analytic solutions are presented for both ${S}_{2}$ and the three-point particle-hole vertex function in the RPA, and their properties are discussed. The Tamm-Dancoff approximation to the ring summation is also formulated, and the analagous exact solutions are presented for the first time. It is demonstrated that both solutions are unique, and a comparison of the two approximations is presented in terms of the correlation energy." @default.
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- W2032022570 date "1978-05-15" @default.
- W2032022570 modified "2023-09-26" @default.
- W2032022570 title "Electron correlations: I. Ground-state results in the high-density regime" @default.
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- W2032022570 doi "https://doi.org/10.1103/physrevb.17.3757" @default.
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