## 5 Time-Resolved Coherent Excitation and Decay of Strongly Correlated Autoionizing States
The corresponding publications of 2007 [6, 16] contain theory and quantitative predictions pertaining to hyperfast electron processes of excitation and decay of autoionizing states, initiated by the interaction of femtosecond EUV pulses with the closed-shell \(He\ 1s^{2}1^{5}\) state [16] and the open-shell \(Al\ KL3s^{2}3p^{2}p^{o}\) state [6]. In the aluminum case, photoionization by the pulsed interaction creates the \(2s\)-hole autoionizing states \((1s^{2}2s2p^{6}3s^{2}3p)\ ^{3}p^{o}\) and \({}^{1}p^{o}\). Because of the open valence shell, the different electron couplings result in different self-consistent fields and electron correlations for the two states. Hence, the dynamics are channel-dependent. For reasons of economy, I will not discuss this case here. The reader is referred to the original paper [6] and the review [2]. In the helium case, the pulsed interaction causes the two-electron excitation above the ionization threshold,  
\[He\ 1s^{2}1^{5}\ S\rightarrow(2s2p)\ ^{1}p^{o}\ (\mathrm{A}).\]  
The label \((2s2p)\ ^{1}p^{o}\) represents the zero-order bound configuration of the resonance state inside the \(1 sep\ ^{1}p^{o}\) continuous spectrum at about 60.1 eV above the ground state. The energy-dependentstationary description of the resonance is a superposition of the correlated localized component corresponding to \((2s2p)\)\({}^{1}P^{o}\), with the energy-normalized scattering components \(1 sep\)\({}^{1}P^{o}\). The helium project extended the theory and calculations of [14] in order to rigorously treat, from first principles, a novel problem of time-dependent many-electron physics, namely tracking the creation of a resonance state (scheme A) as this is recorded by the time-dependent appearance of the cross-section resonance profile inside the continuous spectrum. The much more demanding work on _Al_[6] also produced results on this phenomenon. The work was inspired by the 2005 publication of [PERSON] et al. [52] who, using a model system that assumes data from (super) Coster-Kronig transitions with lifetimes of \(\sim 400\) attoseconds, \"_investigated the feasibility of observing the buildup of a Fano resonance in the time domain by attosecond streaking techniques_\" ([52], abstract), and produced results on the phenomenology of such a possibility. The theory and calculations in [16] were developed and carried out within two frameworks. One involved nonperturbatively solving the METDSE via the SSEA, which is valid for weak as well as strong fields. The other was based on a new time-dependent approach, whereby the METDSE is solved to first order in perturbation theory, while employing the Fano description of resonance states on the real energy axis. In both cases, the calculation is done ab initio, using accurate wavefunctions and matrix elements. The results were obtained for a \(\sin^{2}\) pulse of duration 450 a.u (11_fs_) and central energy of about 60.1 eV. (The lifetime of the \(He\)\((2s2p)\)\({}^{1}P^{o}\) resonance is about 17_fs_.) They were depicted as snapshots of \(P(\varepsilon,t)\equiv\mid<scattering\)\(state(\varepsilon)\)\(|\Psi_{SSEA}(t)>\mid^{2}\), where \(\varepsilon\) is the energy above the ionization threshold, at various femtosecond intervals. They showed quantitatively how, as the two electrons in the bound orbitals \(2s\) and \(2p\) are allowed to interact with the scattering continuum, the interference of the bound and scattering components evolves until the formation of the resonance asymmetric profile on the energy axis is completed. Upon completion of this profile, the agreement with the experimental values and the earlier theoretical results on the energy axis (energy position, width, and the Fano \(q\) parameter for the profile) is excellent [16]. The aforementioned analytic treatment, which is valid for weak fields only, produced a practical analytic formula (corrected for a misprint in [16]) that uses N-electron matrix elements and incorporates the pulse characteristics.