A Collective Description of Electron Interactions: II. CollectivevsIndividual Particle Aspects of the Interactions

The behavior of the electrons in a dense electron gas is analyzed in terms of their density fluctuations. These density fluctuations may be split into two components. One component is associated with the organized oscillation of the system as a whole, the so-called "plasma" oscillation. The other is associated with the random thermal motion of the individual electrons and shows no collective behavior. It represents a collection of individual electrons surrounded by comoving clouds of charge which screen the electron fields within a distance of the order of magnitude of the Debye length. This split up of the density fluctuations corresponds to an effective separation of the Coulomb interaction into long-range and short-range parts; the separation occurs at roughly the Debye length.The relation between the individual and collective aspects of the electron gas is discussed in detail, and a general physical picture of the behavior of the system is given. It is shown that for phenomena involving distances greater than the Debye length, the system behaves collectively; for distances shorter than this length, it may be treated as a collection of approximately free individual particles, whose interactions may be described in terms of two-body collisions.This approach is used to study the interaction of a specified electron with the remainder of the electron gas. It is shown that the collective part of the response of this remainder to the field of the specified particle screens this field within a distance of the order of the Debye length; this furnishes a detailed description of the screening process. Moreover, if the specified particle moves with greater than the mean thermal speed, it excites collective oscillations in the form of a wake trailing the particle. The frequency of these collective oscillations and the energy emitted by the particle are calculated. A correspondence theoretical method is used to treat this phenomenon for the electrons in a metal. The results are in good agreement with the experiments of Ruthemann and Lang on the energy loss of kilovolt electrons in this metallic films.The generalization of these methods to an arbitrary interparticle force is carried out, and a criterion is obtained for the validity of a collective description of the particle interactions. It is shown that strong forces and high particle density favor collective behavior, while high random thermal velocities oppose it.