Pump-probe spectroscopy excitation density

At high excitation densities in the solid state, the decay of the singlet exciton becomes excitation dependant, bimolecular annihilation of the singlet exci-tons introduces a fast component to the decay [41,42,77,78], this is shown in Fig. 21. In a number of publications pump-probe spectroscopy has been used to study the phenomena surrounding this accelerated decay. The bimolecular annihilation reaction is effectively energy transfer from one excited singlet to... 

A final study that must be mentioned is a study by Hartmann et al. [249] on the ultrafast spectroscopy of the Na3F2 cluster. They derived an expression for the calculation of a pump-probe signal using a Wigner-type density matrix approach, which requires a time-dependent ensemble to be calculated after the initial excitation. This ensemble was obtained using fewest switches surface hopping, with trajectories initially sampled from the thermalized vibronic Wigner function vertically excited onto the upper surface. 

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