Collective motion in heavy atoms

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 shown that, in contrast with the usual Thomas-Fermi type of approach, 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, 1) 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. As an illustration, for the 4d10 shell of Xe atom, dipolar modes at 95 eV and 160 eV are found, the latter having about 20% relative oscillator strength. The role of the particle-hole excitations in damping these modes is also discussed. (author)