Dimensional Expansions for Excited States

David Z. Goodson Department of Chemistry Harvard University 12 Oxford street Cambridge MA 02138, USA and 

Deborah K. Watson Department of Physics and Astronomy University of Oklahoma Norman, OK 73019-0225, USA 

We report calculations of dimensional expansions for the energies of the three excited S states of helium that correspond to one quantum in either of the three normal modes of the Langmuir vibrations. Very accurate energies are obtained for the 1 25 states, which arise from 

One of the major goals in atomic and molecular physics is the accurate calculation of observable properties, such as energies, for many-body systems. There is another goal, however, which is perhaps even more important, and often considerably more difficult—the understanding, in terms of simplified physical models, of why a given property has the value it does. Dimensional perturbation theory has the potential of achieving both these goals. 

The large-dimension limit has recently resolved at least some of the difficulties of the molecular model. The molecule-like structure falls out quite naturally from the rigid bent triatomic Lewis configuration obtained in the limit D — oo [5], and the Langmuir vibrations at finite D can be analyzed in terms of normal modes, which provide a set of approximate quantum numbers [6,7]. These results are obtained directly from the Schrodinger equation, in contrast to the phenomenological basis of some of the earlier studies. When coupled with an analysis of the rotations of the Lewis structure, this approach provides an excellent alternative classification scheme for the doubly-excited spectrum [8]. Furthermore, an analysis [7] of the normal modes offers a simple explanation of the connection between the explicitly molecular approaches of Herrick and of Briggs on the one hand, and the hyperspherical approach, which is rather different in its formulation and basic philosophy. 

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