Simple Decay Models for Ultrafast Photodissociation

The availability of powerful lasers providing ultrashort pulses in a wide range of frequencies has stimulated - besides rapid development of experimental techniques - the theorists to develop sophisticated methods to treat photodissociation processes, at least for small molecules, in an essentially exact quantum mechanical way. The marvellous book by Schinke [122] gives an excellent overview of the state-of-the-art. However, for clusters only very simple models have been used up to now to analyze the real-time photodissociation. 

In this section a rather simple energy-level model is first briefly described, which enables a rough analysis of real-time decay processes obtained by MPI. It has been successfully applied to the investigations of the Nas state. To use the model for the larger alkali clusters, however, it has to be modified. Both models can be regarded as a first approximation to estimate the time constants of the induced photodissociation process. It has to be stated that neither of the two models takes into account the dynamics of wave packets prepared on the repulsive PES. 

As a first approximation the obtained ion signal is proportional to the number of excited aggregates. In this approach the ion signal which is recorded as a function of the time delay At between the pump and probe pulses gives information directly about the population of the excited state at 

With these assumptions, the temporal evolution of the excited state can be explained in the following way. The pump pulse will generate an initial population Nq in the excited state within its pulse width. Owing to fragmentation with a probability l/rfrag, this population decreases with time T The decay is characterized by the lifetime rfrag of the excited ensemble. 

As a resume, the temporal change of the population density n t) of the excited state can be described by the following rate equation  

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