Resonant ion-pair formation in electron recombination with HF^+

The cross section for resonant ion-pair formation in the collision of low-energy electrons with HF^+ is calculated by the solution of the time-dependent Schrodinger equation with multiple coupled states using a wave packet method. A diabatization procedure is proposed to obtain the electronic couplings between quasidiabatic potentials of ^1Sigma^+ symmetry for HF. By including these couplings between the neutral states, the cross section for ion-pair formation increases with about two orders of magnitude compared with the cross section for direct dissociation. Qualitative agreement with the measured cross section is obtained. The oscillations in the calculated cross section are analyzed. The cross section for ion-pair formation in electron recombination with DF^+ is calculated to determine the effect of isotopic substitution.Comment: 12 pages, 12 figure

A two-dimensional, two-electron model atom in a laser pulse: exact treatment, single active electron-analysis, time-dependent density functional theory, classical calculations, and non-sequential ionization

Owing to its numerical simplicity, a two-dimensional two-electron model atom, with each electron moving in one direction, is an ideal system to study non-perturbatively a fully correlated atom exposed to a laser field. Frequently made assumptions, such as the ``single active electron''- approach and calculational approximations, e.g. time dependent density functional theory or (semi-) classical techniques, can be tested. In this paper we examine the multiphoton short pulse-regime. We observe ``non-sequential'' ionization, i.e.\ double ionization at lower field strengths as expected from a sequential, single active electron-point of view. Since we find non-sequential ionization also in purely classical simulations, we are able to clarify the mechanism behind this effect in terms of single particle trajectories. PACS Number(s): 32.80.RmComment: 10 pages, 16 figures (gzipped postscript), see also http://www.physik.tu-darmstadt.de/tqe

On the absence of bound-state stabilization through short ultra-intense fields

We address the question of whether atomic bound states begin to stabilize in the short ultra-intense field limit. We provide a general theory of ionization probability and investigate its gauge invariance. For a wide range of potentials we find an upper and lower bound by non-perturbative methods, which clearly exclude the possibility that the ultra intense field might have a stabilizing effect on the atom. For short pulses we find almost complete ionization as the field strength increases.Comment: 34 pages Late

Exact boundary conditions at finite distance for the time-dependent Schrodinger equation

Exact boundary conditions at finite distance for the solutions of the time-dependent Schrodinger equation are derived. A numerical scheme based on Crank-Nicholson method is proposed to illustrate its applicability in several examples.Comment: Latex.tar.gz file, 20 pages, 9 figure

Existence criteria for stabilization from the scaling behaviour of ionization probabilities

We provide a systematic derivation of the scaling behaviour of various quantities and establish in particular the scale invariance of the ionization probability. We discuss the gauge invariance of the scaling properties and the manner in which they can be exploited as consistency check in explicit analytical expressions, in perturbation theory, in the Kramers-Henneberger and Floquet approximation, in upper and lower bound estimates and fully numerical solutions of the time dependent Schroedinger equation. The scaling invariance leads to a differential equation which has to be satisfied by the ionization probability and which yields an alternative criterium for the existence of atomic bound state stabilization.Comment: 12 pages of Latex, one figur

On the Influence of Pulse Shapes on Ionization Probability

We investigate analytical expressions for the upper and lower bounds for the ionization probability through ultra-intense shortly pulsed laser radiation. We take several different pulse shapes into account, including in particular those with a smooth adiabatic turn-on and turn-off. For all situations for which our bounds are applicable we do not find any evidence for bound-state stabilization.Comment: 21 pages LateX, 10 figure

Simple proof of gauge invariance for the S-matrix element of strong-field photoionization

The relationship between the length gauge (LG) and the velocity gauge (VG) exact forms of the photoionization probability amplitude is considered. Our motivation for this paper comes from applications of the Keldysh-Faisal-Reiss (KFR) theory, which describes atoms (or ions) in a strong laser field (in the nonrelativistic approach, in the dipole approximation). On the faith of a certain widely-accepted assumption, we present a simple proof that the well-known LG form of the exact photoionization (or photodetachment) probability amplitude is indeed the gauge-invariant result. In contrast, to obtain the VG form of this probability amplitude, one has to either (i) neglect the well-known Goeppert-Mayer exponential factor (which assures gauge invariance) during all the time evolution of the ionized electron or (ii) put some conditions on the vector potential of the laser field.Comment: The paper was initially submitted (in a previous version) on 16 October 2006 to J. Phys. A and rejected. This is the extended version (with 2 figures), which is identical to the paper published online on 12 December 2007 in Physica Script

Ionization Probabilities through ultra-intense Fields in the extreme Limit

We continue our investigation concerning the question of whether atomic bound states begin to stabilize in the ultra-intense field limit. The pulses considered are essentially arbitrary, but we distinguish between three situations. First the total classical momentum transfer is non-vanishing, second not both the total classical momentum transfer and the total classical displacement are vanishing together with the requirement that the potential has a finite number of bound states and third both the total classical momentum transfer and the total classical displacement are vanishing. For the first two cases we rigorously prove, that the ionization probability tends to one when the amplitude of the pulse tends to infinity and the pulse shape remains fixed. In the third case the limit is strictly smaller than one. This case is also related to the high frequency limit considered by Gavrila et al.Comment: 16 pages LateX, 2 figure

Nonsequential double ionization of helium

Published versio

Decay versus survival of a localized state subjected to harmonic forcing: exact results

We investigate the survival probability of a localized 1-d quantum particle subjected to a time dependent potential of the form $rU(x)\sin{\omega t}$ with $U(x)=2\delta (x-a)$ or $U(x)= 2\delta(x-a)-2\delta (x+a)$. The particle is initially in a bound state produced by the binding potential $-2\delta (x)$. We prove that this probability goes to zero as $t\to\infty$ for almost all values of $r$, $\omega$, and $a$. The decay is initially exponential followed by a $t^{-3}$ law if $\omega$ is not close to resonances and $r$ is small; otherwise the exponential disappears and Fermi's golden rule fails. For exceptional sets of parameters $r,\omega$ and $a$ the survival probability never decays to zero, corresponding to the Floquet operator having a bound state. We show similar behavior even in the absence of a binding potential: permitting a free particle to be trapped by harmonically oscillating delta function potential