SPECTROSCOPY OF POTENTIAL BARRIERS - AN ANALYTIC LINE-SHAPE FORMULA FOR BROAD RESONANCES

Using a time-dependent formulation of Franck-Condon spectra, we analyze the spectra associated with the transitions into a saddle-point region of an unbound Born-Oppenheimer potential. We find a spectral peak at an energy near the barrier top, which we associate with the existence of a quasi-bound-state. We refer to this state as ''barrier resonance.'' Employing a quadratic approximation to the potential and the quantum dynamics of Gaussian wave packets, we develop a line-shape formula that accurately fits this spectral feature. This line-shape formula corresponds to an infinite set of complex energy poles rather than the usual single-pole approach used in the Breit-Wigner theory. We apply the lineshape formula to barrier resonances on the Eckart potential and in the H+H-2 chemical reaction.