Collective motion in heavy atoms

Abstract

A theoretical model for the collective oscillations of an individual shell in heavy atoms is discussed. Using a formulation of the dielectric response for inhomogeneous electron density, a simple model suitable for a collective description of the atom has been developed. In this model, the detailed nature of the particle-hole excitation spectrum is neglected, and the response is determined by the electron density and its gradient. It is necessary to consider the quantum-mechanical electron density, and for a given frequency range close to the excitation frequency of a particular shell, only the density of that shell is important. For large (n, l) quantum numbers, the hump-like shape of the density over the majority of the shell, and the presence of a density gradient in the response lead to dipolar density oscillation modes at two frequencies close to the excitation frequency of the shell. For the 4d¹⁰ shell of Xe atom, dipolar modes are found at 95 eV and 160 eV, the latter having about 20% relative oscillator strength. The role of the particle-hole excitations in damping these modes is also discussed.