Classical Motion in an Atomic Potential. Atomic Structure

Abstract

The foundations of radiation theory for a classically moving particle (electron) in a given potential V(r) are stated in numerous books on classical electrodynamics [2.1, 2]. In accordance with [2.3–6], we shall dwell on a number of classical spectral peculiarities with the attractive potential V(r) = − |V(r)| playing an important role in the applicability of the classical method to atomic physics. The essence of the problem involves the situation when an emitting electron in an attractive field experiences an acceleration and may obtain the kinetic energy W = E+ |V(r)|, considerably exceeding its initial energy E at infinity. In this case the classical nature of electron motion is preserved even when the quantum energy ħω emitted by the electron exceeds its initial energy E. The circumstance essentially expands the applicability domain of classical description methods for atomic processes, including the inelastic domain ħω ≥ E. Below, we will focus on the Coulomb field case playing an important part in atomic processes in plasmas. Atomic potentials of a more general type are investigated in [2.4]. The results of following consideration will be used later in the quasiclassical approximation constructions for radiation transition probabilities.