Theoretical Analysis of Wave Packet Propagation

With this short overview of molecular wave packet dynamics in mind, the wave packet propagation in small prototype molecules will now be examined more concretely. Different theoretical methods exist to describe ultrafast multiphoton ionization processes in diatomics and have been discussed in detail in previous work [3, 33-35, 291-294]. The theoretical approach used here is adapted specially to the presented 3d problems and was improved in Manz s group, mainly by de Vivie-Riedle [295] assisted by Reischl [81]. A few special features of their theoretical ansatz applied to the pumpfeprobe experiments carried out on the model molecules K2 and Naa are now briefly summarized. 

The starting point of their approach is the Hamiltonian Hmo of the molecular system, which is defined as the sum of the operators for the kinetic energy of the nucleus 71 = P /(2m) and of the electrons Tq and the potential energy V of the system  

As a result of the interaction with ultrashort laser pulses, molecular wave packets are generated on one or several PESs. The dynamics of the molecule 

The time-dependent Hamiltonian is separated into a time-independent part (diagonal elements Ha of the Hamilton matrix) 

Ha describes the time-independent interaction of the coupled PES and Vu is the PES of the molecule in the absence of any laser fields. Hij represents the interaction of the molecule with the laser pulse. The ij are the dipole transition moments and E i) the time-dependent electromagnetic field generated by the superposition 

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