Abstract
The domain of validity of the Coulomb-Corrected Strong-Field Approximation (CCSFA) is going to be analyzed in relation to the semi-classical dynamics of electrons during ionization of hydrogen-like targets. Our analysis is limited to ionization driven by Ti-sapphire laser pulses with intensities up to roughly 1014 Wcm−2. For such parameters, the effects related to radiation pressure are small and the laser field can be described in the dipole approximation. By applying the Magnus expansion for the exact retarded electron propagator we obtain an effective action which is free of Coulomb singularities and branch points when the complex-time trajectories are used. Furthermore, we show that the classical action is exactly recovered as the asymptotic limit of its effective counterpart. The applicability of such limit is also discussed.
Highlights
The great English mathematician and philosopher Bertrand Russell (1872-1970) has once written that ‘all exact science is dominated by the idea of approximation.’ One could continue his line of thought by saying that the most beautiful aspects of all exact science are the approximations
We demonstrate that the effective Corrected Strong Field Approximation (CCSFA), in the appropriate limits, leads to the exact Born expansion or to the classical dynamics
In order to define our effective CCSFA, let us modify the classical trajectory of the electron in the laser field Rp(r′, τ ) by a correction that is linear in λ
Summary
The great English mathematician and philosopher Bertrand Russell (1872-1970) has once written that ‘all exact science is dominated by the idea of approximation.’ One could continue his line of thought by saying that the most beautiful aspects of all exact science are the approximations. We shall refer to those approaches as the Coulomb-Corrected Strong-Field Approximation (CCSFA) [33,34,35,36] In connection to these theoretical investigations is the purely classical analysis of laser-assisted atomic or molecular processes [37] such as ionization [38, 39], plasma dynamics in atomic clusters [40], and re-collisions [41]. We apply this approximation up to the linear term with respect to the binding potential and show under which conditions the classical dynamics is restored This determines the domain of validity of the ordinary CCSFA [33,34,35,36] and it allows us to remove the artificial Coulomb singularities and branch points. Note that the method presented here and in [30,31,32] allows to incorporate further terms, which are nonlinear with respect to the static binding potential, into the effective action
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