Uniform semiclassical methods of analyzing undulations in far-wing line spectra

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Abstract
Two uniform, semiclassical methods are presented for analytically evaluating matrix elements using stationary-phase techniques. The analytic expressions are appropriate for electronic transitions between molecular states that have monotonic difference potentials. Such a situation is encountered in the calculation of the spectra in excimer (e.g., Xe2*) and excimer-like (e.g., RbXe*) vapor systems. One method utilizes uniform JWKB wave functions throughout the analytic evaluation of the matrix elements, while the second uses simple JWKB wave functions that are modified at the end. The first proves to be more accurate for such systems. The uniform nature of its derivation assures its applicability even to transitions that occur near classical turning points. Numerical results are presented for the far red-wing emission spectrum of RbXe, and a detailed interpretive analysis of the undulatory structure is given. Using the uniform-JWKB, stationary-phase approximation, modifications of the RbXe*(AΠ122) potential are suggested based on a comparison of the predicted and experimental spectra.