ATOMIC AND MOLECULAR SPECTRA

In this section studies of classical dynamics will be combined with the quantum-classical correspondence principle to describe, predict and interpret quantum phenomena which appear in the energy spectra of atoms and molecules. Specific objectives are described below.

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The ``good quantum numbers'' used to describe bands, branches, multiplets, polyads, etc in quantum energy spectra will be related to the geometry and approximate dynamical symmetries of the corresponding classical problem. Bifurcations and re-arrangments of these structures that occur as excitation increases or external parameters are varied will be classified. A `quantum-classical dictionary' for these phenomena will be compiled.

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Global bifurcation diagrams for REs and RPOs will be computed for (a) small, mainly triatomic, molecules and (b) Rydberg atoms and molecules. Normal forms for the dynamics near REs and RPOs will be constructed, analysed and the quantum-classical correspondence principle and results of objective 3.1 applied to describe the energies and symmetries of associated localized quantum states.

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Existing semiclassical methods based on invariant tori and periodic orbits, and used to approximate quantum spectra, will be extended to EBK-type quantisation schemes for singular torus-structures (pinched tori, heteroclinic cycles, separatrices) and for near-integrable dynamics including Arnold diffusion. The methods will be applied to atoms and small molecules.

Major breakthroughs are expected to include the development of new and effective techniques for predicting and interpreting phenomena in the spectra of highly excited atoms and molecules. Particular emphasis will be placed on comparing the results obtained in this section with exact quantum computations and experimental data, and on investigating and predicting phenomena which will occur for real atoms and molecules under physically realizable conditions.