Collective and Independent-Particle Motion in Simple Atoms and Molecules: a Unification?

Abstract

The evidence is reviewed that implies electrons in doubly-excited states of helium behave like the atoms of a linear triatomic molecule. The relation between molecule-like collective motion and independent- particle, solar-system-like motion is explored via the model problem of two interacting particles on concentric spheres. The state of understanding of independent-particle motion for atoms in small polyatomic molecules is surveyed briefly and the proposal is explored that some small molecules, such as dihydrides, might exhibit independent-particle rotational motion in sufficiently highly excited local mode states.

This is a summary and brief review of the accumulating evidence that atomic and molecular few-body problems, that is, the description of electrons in simple atoms and the description of atoms in small molecules and clusters, share characteristics that let us see these problems on a common footing. By exploiting these commonalities in our attacks on these problems, we find powerful new ways to achieve accur­ate, efficient descriptions of small atoms and molecules, and new insights into the physics of their behavior. There are three components to this presentation: 1) the now-convincing evidence that some atomic states are characterized far better in terms of molecule-like collective vibrations and rotations than of independent-particle, solar-system-like motions; 2) the information that emerges from the set of model problems of the quantum states ofparticles on concentric spheres (POCS) and from other model problems such as the quantum states of a particle in a Hénon- Heiles potential, and 3) the examples and possibilities that atoms ex­hibit independent-particle motion in small molecules. One of us reviewed this subject recently for another symposium (Berry, 1982), but even in the brief interval between that presentation and this, new ideas have emerged that move the subject ahead and bear mention here.