Correlation diagrams for rigid and nonrigid three-body systems

A correlation diagram is constructed for the energy levels of a three-body system. The principle limiting cases for which the diagram is constructed are the equilateral triangle of three identical particles and the completely nonrigid cluster with pairwise harmonic forces. The artificial symmetries of these limits can be broken by conventional methods to make the diagram suitable for real molecules. The degree of nonrigidity can be expressed with a single parameter, a ratio of two excitation energies, one of which becomes the energy of the first rotational excitation and the other, the energy of the first vibrational excitation, in the idealized rigid limit. For real molecules, the parameter is a ratio of averages of the excitation energies to those states that correlate with the corresponding ideal limiting cases. The method is related to, and gives some insights regarding the Elliott model of nuclei.