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Why the absorption cross section in direct dissociation process is wide and structureless while the absorption cross section in the predissociation process is structured and containing lines which are normally Lorentzian in shape?

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In direct dissociation the system is excited from a bound state to an unbound state. Because the translational energy of the unbound state is not quantised all energies above the dissociation energy are absorbed, so there is a continuous absorption spectrum with no sharp lines.

In pre-dissociation there is usually some selection rule that blocks direct dissociation, so there is a transition from the ground state to a an excited but bound state. This transition gives sharp lines like any other transition between bound states so you get a spectrum with sharp lines.

However the excited state may very quickly decay to the unbound state, and if this happens lifetime broadening will blur the lines in the spectrum. Typically you find that the probability for decay of the excited to unbound states depends on energy, so as you increase the energy you find the lines start sharp, then blur out, and finally get sharp again.

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@ John Rennie: I have a confusion (may be silly). In case of direct dissociation, the electrons are excited or not? Is it adiabatic or non adiabatic? If electrons are excited and cause dissociation, there is an electro-vibronic coupling and the Born Oppenheimer approximation is not valid! right? –  albedo Mar 11 '13 at 11:03
In a molecule an electronic excitation usually (always?) involves a vibrational transition as well. It's a long time since I did any work in this area, but IIRC we assume the transition is fast compared to the vibrational period so the Born Oppenheimer approximation still applies. –  John Rennie Mar 11 '13 at 11:13
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