Quasi-bounded states

The wavepacket is propagated until a time where it is all scattered and is away from the interaction region. This time is short (typically 10-100 fs) for a direct reaction. Flowever, for some types of systems, e.g. for reactions with wells, the system can be trapped in resonances which are quasi-bound states (see section B3.4.7). There are eflScient ways to handle time-dependent scattering even with resonances, by propagating for a short time and then extracting the resonances and adding their contribution [69]. 

Figure B3.4.10. Schematic figure of a ID double-well potential surface. The reaction probabilities exliibit peaks whenever the collision energy matches the energy of the resonances, which are here the quasi-bound states in the well (with their energy indicated). Note that the peaks become wider for the higher energy resonances—the high-energy resonance here is less bound and Teaks more toward the asymptote than do the low-energy ones.

We have already mentioned (expressions 30—33) the widely used LEPS surface for atom-diatom reactions. This may be regarded as purely empirical or semi-empirical in any modification in which some integrals are evaluated. Another system for which fairly elaborate potential functions have been used is for non-reactive atom-diatom scattering. The experiment for which the potential is designed is the change of rotational or vibrational state of a diatomic molecule by collision with a third atom, and also the quasi bound states, which may be observed spectroscopically, of van der Waals molecules such as Ar—H2 (133). 

When there are many (quasi)bound states, healing can occur in an off-diagonal manner in that the (quasibound) state that they come back to need not be the same as the (quasibound) state that they dissociated from. Healing thus provides for an enhanced mixing of the bound phase space. 

Bound and Quasi-Bound States, it was shown in the last section how the problem of the evaluation of photofragment energy distributions can be reduced to the analysis of nuclear dynamics. Indeed, it is necessary to evaluate integrals containing the nuclear wavefunctions (see eqs. 28, 34, and 57). 

Threshold Behavior of the Formation of a Quasi-Bound State 225... 

Quasi-Bound States of Electronic and Positronic Few-Body Systems... 

Positronic bound states as quasi-bound states... 

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