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Articles

Many-electron strong-field physics

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Pages 199-223 | Received 02 May 2008, Accepted 24 Jun 2008, Published online: 17 Oct 2008
 

Abstract

Double and multiple ionisation cannot be understood without the contribution of a non-sequential mechanism, which is due to electron–electron correlation. This paper discusses the experimental manifestations of this effect, from its first footprint in the total yields of multiply charged ions to the highly differential cross-sections for ion and electron production, and the theoretical models that have been set up for their description. Except for the ab initio solution of the time-dependent Schrödinger equation, most models implement the recollision mechanism. The kinematical constraints imposed by the former are extensively discussed. A fully quantum-mechanical formalisation of the recollision model in terms of the lowest-order S-matrix element for this process is introduced and its limitations are discussed. Various simplifications are proposed that drop more and more of the quantum features. This is contrasted with purely classical trajectory descriptions with no approximations to the dynamics.

Acknowledgements

We are grateful to P.L. Knight for the invitation to write this article. The paper greatly benefitted from extended discussions with J.H. Eberly and his critical comments. We would also like to thank B. Feuerstein, C. Figueira de Morisson Faria, S.P. Goreslavski, P.J. Ho, R. Kopold, M. Lezius, X. Liu, D.B. Milošević, R. Moshammer, G.G. Paulus, S.V. Popruzhenko, W. Sandner, N.I. Shvetsov-Shilovski, and J. Ullrich for enjoyable and fruitful collaboration over many years and A. Becker, J. Chen, R. Dörner, U. Eichmann, F.H.M. Faisal, A. Rudenko, C. Ruiz, and A. Staudte for many invaluable insights. We are especially grateful to Phay Ho for the permission to present unpublished results from his Ph.D. thesis.

Notes

1. Here, and in some figures below, so-called atomic units (au) are used for energy and momentum. Masses are measured in multiples of the electron mass m, charges in multiples of the electron charge |e|, and actions in multiples of Planck's constant ℏ(briefly, ). Hence, the atomic unit of energy is and particle momenta are measured by p(au) = [2ME(eV)/27.2]1/2 with E(eV) denoting the corresponding energy in electron volts and M the mass in multiples of the electron mass.

2. Because the recolliding electron loses energy in the recollision, there is no actual divergence.

3. It is to be feared that the origin of this name will forever remain shrouded in mystery. Occasionally, one or the other of the authors pretended it was an acronym but consistently refused to disclose of what.

4. The weights of the orbits are given by . The index s in the sum (22) runs over the relevant saddle points, those that are visited by an appropriate deformation of the real integration contour, which is the real five-dimensional (t, t′, k )space, to complex values, and denotes the five-dimensional matrix of the second derivatives of the action (19) with respect to t, t′ and k , evaluated at the saddle points. The time dependence of the form factors is considered as slow. The sum also includes orbits that have revisited the ions several times before the recollision event. For these orbits, the ‘travel time’, namely, the difference between recollision time and ionisation time, amounts to several cycles of the laser field. Hence, owing to wave-packet spreading, the contribution of each individual such orbit is minor. However, under certain conditions, the contributions of many such orbits may interfere constructively. In high-order ATI, this causes order-of-magnitude enhancements of groups of ATI peaks Citation68. In NSDI, a similar effect has been predicted Citation69, but observation will be difficult.

5. To be sure, is for neon and for different intensity. Since, however, the momenta are scaled by , the difference is not expected to be all that large.

6. This value can be derived from the quasistatic rate (2) by the substitution and expanding to first order in . This means that the kinetic energy of the transverse motion, which is free since there is no force acting in this direction, effectively adds to the binding energy Citation82.

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