Experimental progress and theoretical issues

The time scale of valence electrons is typically of the order of 10 femtoseconds, while that of the inner shell is of course much faster and becomes close to the speed of light velocity for heavy atoms. Just as the femto-scale laser technology made a great contribution to the analyses of chemical dynamics of nuclear motions, the attosecond laser is anticipated to play the similar role for electron dynamics. 

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 

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