INFLUENCE OF CORRELATIONS ON THE DIELECTRIC BEHAVIOR OF AN ELECTRON GAS. NONPERTURBATIVE APPROACH TO THE MANY-FERMION SYSTEM

Journal Article · Mon Oct 15 04:00:00 EDT 1962 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.128.911· OSTI ID:4770598

von Roos, O

Starting with the equation of motion for the density matrix operator of an electron gas in second quantization, a system of matrix equations is derived for matrix elements connecting states with various numbers of electronhole pairs. Allowing up to n electron-hole pairs and neglecting all states with more than n pairs yields a set of (n + 1)/sup 2/ coupled equations for the various amplitudes in close analogy to the nth order Tamm-Dancoff approximation. The starting point of this approximation, in which all matrix elements connecting the Fermi vacuum with arty pair states are neglected (zero-order Tamm-Dancoff approximation), is an equation for the self-consistent field rather than for free particles as in the usual TammDancoff method. Correlation effects are therefore automatically taken into account when pair states are included. In a certain sense the approximation scheme given here can be thought of as being an expansion in the deviation of the Fermi surface from the sharp edge of the free-particle ground state, the deviation being caused by the Coulomb interaction among the particles. In this paper, calculations based on the first Tamm-Dancoff approximation (taking into account only one electron-hole pair) are presented, An expression for the dielectric constant will be derived and applied to a determination of the effects of correlations on the wavelength dependence of plasma oscillations. The theory will be compared with the experiments by Watanabe on the energy loss of fast electrons in metal foils and it will be seen that the agreement with experiment is good considering the inherent simplicity of the theory. (auth)

• Research Organization: California Inst. of Tech., Pasadena
• NSA Number: NSA-17-000746
• OSTI ID: 4770598
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 128; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

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