A Collective Description of Electron Interactions: IV. Electron Interaction in Metals

TLDR

The Coulomb interaction among free electrons in an electron gas influences a range of phenomena. The study investigates whether a free‑electron gas can become ferromagnetic, concluding it cannot regardless of density. The authors use a collective description of long‑range Coulomb correlations, modeling them as collective oscillations, and verify semiclassical predictions by quantum‑mechanical calculations of their excitation by fast charged particles. The analysis shows that an independent‑electron model accurately describes metallic electrons, with ground‑state and correlation energies matching Wigner, exchange effects reduced leading to ~80 % of the free‑electron specific heat, and that long‑range Coulomb correlations preclude ferromagnetism; the theory also agrees with electron‑scattering and stopping‑power experiments.

Abstract

The effects of the Coulomb interaction between free electrons in an electron gas are considered for a variety of phenomena. The analysis is based on the collective description, which describes the long-range correlations in electronic positions (due to the Coulomb force) in terms of the collective oscillations of the system as a whole. It is shown that an independent electron model should provide a good description of the electrons in a metal in many cases of interest. The ground state energy of the free electron gas is determined, and an estimate of the correlation energy is obtained, with results in good agreement with those of Wigner. The exchange energy is shown to be greatly reduced by the long-range correlations, so that its effect on the level density and the specific heat is comparatively slight, leading to an electronic specific heat for Na which is approximately 80 percent of the free-electron value. The possible ferromagnetism of a free-electron gas is investigated, and it is found that the long-range Coulomb correlations are such that a free-electron gas will never become ferromagnetic (no matter how low the density). The excitation of the collective oscillations by a fast charged particle is studied, and the semiclassical results obtained by Bohm and Pines are verified by a quantum-mechanical calculation. The results are applied to the experiments of Ruthermann and Lang on the scattering of electrons by thin metallic films and to experiments on the stopping power of light metals for fast charged particles, with resulting good agreement between theory and experiment.