Body frames and frame singularities for three-atom systems
Abstract
The subject of body frames and their singularities for three-particle systems is important not only for large-amplitude rovibrational coupling in molecular spectroscopy, but also for reactive scattering calculations. This paper presents a geometrical analysis of the meaning of body frame conventions and their singularities in three-particle systems. Special attention is devoted to the principal axis frame, a certain version of the Eckart frame, and the topological inevitability of frame singularities. The emphasis is on a geometrical picture, which is intended as a preliminary study for the more difficult case of four-particle systems, where one must work in higher-dimensional spaces. The analysis makes extensive use of kinematic rotations.
- Publication:
-
Physical Review A
- Pub Date:
- November 1998
- DOI:
- 10.1103/PhysRevA.58.3705
- Bibcode:
- 1998PhRvA..58.3705L
- Keywords:
-
- 34.50.-s;
- 31.15.-p;
- 02.40.-k;
- Scattering of atoms and molecules;
- Calculations and mathematical techniques in atomic and molecular physics;
- Geometry differential geometry and topology