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Dynamical Exchange Effects in the Dielectric Function of the Electron Gas

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Electron Correlations in Solids, Molecules, and Atoms

Part of the book series: NATO Advanced Study Institutes Series ((NSSB,volume 81))

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Abstract

This set of lectures is subdivided into 3 parts.

In part I, some elementary concepts related to the dielectric function of the electron gas are summarized, and related to the single-particle picture and the Hohenberg-Kohn formalism, in order to elucidate the meaning of the local field correction G(q,ω), describing exchange- and correlation effects in the dielectric function.

In part II, the dynamical exchange decoupling is applied on the equation of motion for the Wigner distribution function. A variational approach is used to treat the resulting integro-differential equation. An explicit expression for G(q, ω) is obtained as a sixfold integral, which is reduced to a double integral by analytical methods. Given the interest of this type of integral in related problems, the analytical methods are presented in quite some detail.

Finally, in part III, the numerical results obtained for the dielectric function and the dynamical structure factor are discussed. It is shown that dynamical exchange effects drastically lower the slope of the plasmon dispersion. Several sum rules and consistency requirements are examined. The variational result we derived is finally compared with the proper polarizability to first order in the electron-electron interaction.

Article Note

The formalism, presented in part II and part III, has been developed in collaboration with L.F. Lemmens.

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Author information

Authors and Affiliations

  1. Physics Department, Universitaire Instelling Antwerpen, Universiteitsplein 1, B-2610, Wilrijk, Belgium

    J. T. Devreese & F. Brosens

  2. Institute of Applied Mathematics, R.U.C.A., Groenenborgerlaan 171, B-2020, Antwerpen, Belgium

    J. T. Devreese

  3. University of Technology, Eindhoven, The Netherlands

    J. T. Devreese

  4. Research Associate of the National Fund for Scientific Research, Belgium

    F. Brosens

Authors
  1. J. T. Devreese
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  2. F. Brosens
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Editors and Affiliations

  1. University of Antwerpen (RUCA and UIA), Antwerpen, Belgium

    Jozef T. Devreese  & Fons Brosens  & 

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Devreese, J.T., Brosens, F. (1983). Dynamical Exchange Effects in the Dielectric Function of the Electron Gas. In: Devreese, J.T., Brosens, F. (eds) Electron Correlations in Solids, Molecules, and Atoms. NATO Advanced Study Institutes Series, vol 81. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3497-2_5

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  • DOI: https://doi.org/10.1007/978-1-4613-3497-2_5

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