Knowledge Bank

The rovibronic structure of the double minimum states of $H2$ exhibits the effects of strong interactions. these interactions couple rotational, vibrational, and electronic motion, and are of such a magnitude that the Born-Oppenheimer picture is not even approximately correct. In fact predictions, for vibronic energies based on the straightforward solution of the one dimensional Schrodinger equation on the Born-Oppenheimer potential energy curves disagree with experiment by hundreds of wavenumber units. Two theoretical approaches hove been used to study the rovibronic structure of the fundamental system. Dressler and co-workers have calculated with adiabatic corrections to the Born-Oppenheimer potential energy curves and the non-adiabatic interaction functions between the lower $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}\Sigma 6$ Rydberg states. These results they than combine into a coupled equations treatment of the rovibronic structure of the related state. The results they obtain using this traditional” approach reproduce the experimental novibronic energies of the lower Rydberg states to within several $cm^{-1}$. Our approach has been to study the same states using scattering theory. Multichannel Quantum Defect Theory (MQDT) is a version of scattering theory ideally suited to the study of such systems. In MQDT the concept of individual states is replaced by that of channels”. A channel consists of an entire Rydberg series and the continuum lying above it. By carefully determining the channels and their interactions a simple picture of a small number of interacting channels is thus sufficient to describe the entire {infinite} set of interacting states. MQDT thus avoid having to consider this infinity of mutually interacting states individually while still accounting for the effects of their interaction. In this talk the basis ideas of MQDT will be explained, with particular reference to our work on the double minimum states of $H2$. the rovibronic energies we obtain are of similar quality to those of Dressler and co-workers from the more traditional technique. We plan to extend our technique to progressively higher states and eventually into the continuum, which will allow us to provide a single unified treatment of both bound an continuum states, including the possibility of determining cross sections for such processes as dissociative recombination and photoionization.