Time-resolved hyperfast processes of strongly correlated electrons during the coherent excitation and decay of multiply excited and inner-hole excited states

Abstract

In the framework of the state-specific expansion approach, we have solved nonperturbatively the time-dependent Schr\"odinger equation for systems involving the time-dependent excitation of nonstationary states by hypershort one or two electromagnetic pulses. The related problems concern the quantitative determination of the consequences of strong electron correlation in excited atomic states of the discrete or of the continuous spectrum. As prototypical applications we chose the time-resolved coherent excitation and decay of the $2s$-hole $1{s}^{2}2s2{p}^{6}3{s}^{2}3p\phantom{\rule{0.2em}{0ex}}^{1,3}P^{0}$ Auger states of aluminum, where dominant channels representing one- as well as two-electron continua are taken into account, and the preparation of nonstationary states and the subsequent electron correlation beats in Al and in ${\mathrm{N}}^{3+}$. Calculations for the problem of coherent inner-hole ionization and Auger decay in Al account for the effect of interference coming from the presence of the channel of direct two-electron ionization. The result is that for the ${\mathrm{Al}}^{+}\phantom{\rule{0.2em}{0ex}}^{1}P^{0}$ channel the Auger electron distribution is asymmetric. On the contrary, for the ${\mathrm{Al}}^{+}\phantom{\rule{0.2em}{0ex}}^{3}P^{0}$ channel the contribution of the direct two-electron ionization is weak and the corresponding Auger distribution is essentially symmetric. The intensities used were weak, so as to avoid shifts and to render high order processes beyond those in resonance or near-resonance essentially negligible. As a result, the transition probabilities are very small, a result that ought to guide experimental work. For example, for intensity $8.75\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$ the percentage of initial state population that ionizes is 0.02%. In spite of the overall reasonable approximations and size reductions, for the Al problem the system of coupled integrodifferential equations that had to be solved contains more than 300,000 basis wave functions.