Photoionization dynamics time-resolved photoelectron spectroscopy

We turn now to a more detailed description of the photoionization probe step in order to clarify the ideas presented above. Time-resolved photoelectron spectroscopy probes the excited-state dynamics using a time-delayed probe laser pulse that brings about ionization of the excited-state wave packet, usually with a single photon... 

Photoionization out of several neutral states to several cation states may be simply included as separate terms of a split-operator scheme, assuming the ionized states do not strongly couple. Alternately, when the different ionization channels interact weakly, ionization out of each channel may be computed separately and the results combined. Examples of nonadiabatic dynamics seen through time-resolved photoelectron spectroscopy will be seen in Secs. 5.2 and 5.4. In the rest of this section, we will see examples of the diabatic representation for two classes of nonadiabatic interaction, the avoided crossing (Sec. 5.2.1.1) and the conical intersection (Sec. 5.2.1.2), and then discuss the necessary extensions to the standard vibrational wavefunction time-propagating schemes. 

We use the transformation matrix U R) to represent the potential energy matrix, dipole moment matrix, and photoionization amplitudes in the diabatic representation. Then the vibrational wavefunctions are computed in the diabatic representation, but can also be transformed with U R) when we wish to see the adiabatic functions. The vibrational wavepacket dynamics and time-resolved photoelectron spectroscopy of the system is treated in Sec. 5.4. 

Attosecond dynamics is now one of the most active fields in science [222, 476] (see also the introductory section of Ref. [499], which shows a concise list of the studies covering many phenomena and relevant studies). In particular, tracking electronic motions in chemical dynamics is a fundamentally important process. To monitor those electron wavepacket dynamics in an attosecond intense laser field [476], Bandrauk and his coworkers have developed the theory of attosecond-scale time-resolved photoelectron spectroscopy [499, 500], Photoionization dynamics of small molecules like has been studied so far, for which direct numerical integrations of the related (low-dimensional) time-dependent Schrodinger equations are possible. The photoelectron signals are extracted from those numerical solutions... 

Electron dynamics of photoionization states in the course of nonadiabatic transition is one of the important molecular processes. It can be applied to the studies on the following dynamical processes Tracking the history of electronic and vibrational states wandering among the excited states in laser fields with designed optical pulses. These time-dependent transient states should be able to be monitored in terms of time-resolved photoelectron spectroscopy [14, 353]. Inner shell ionization from a deep core level and the concomitant electronic state avalanches (decay) towards the hole, which may be accompanied by autoionization, is also quite interesting. In a... 

When considering the femtosecond photoionization dynamics of complex systems, a completely exact evaluation of the time and energy resolved photoelectron spectrum is often not really necessary. Approximative schemes which require significantly lower computational effort are valuable in such cases. Within the nonperturbative formalism, Meier et al. have proposed an efficient computational scheme which incorporates the multi-configuration time-dependent Hartree method.An approximate method which is based on a classical-trajectory description of the nuclear dynamics has been elaborated by Hartmann, Heidenreich, Bonacic-Koutecky and coworkers and applied, among other systems,to the time-resolved photoionization spectroscopy of conical intersections in sodium fluoride clusters. 

I. Fischer, M.J.J. Vrakking, D.M. Villeneuve, and A. Stolow, Femtosecond Time-Resolved Zero Kinetic Energy Photoelectron and Photoionization Spectroscopy Studies of I2 Wave Packet Dynamics , Chem. Phys. 207, 331 (1996). 

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