DOI: 10.1007/s00340-004-1484-8 Appl. Phys. B 78, 829–833 (2004) Lasers and Optics Applied Physics B c. ruiz ✉ l. plaja j.r. v ´ azquez de aldana l. roso Influence of Pauli exclusion principle on the strong field ionization of two electron atoms Departamento de F´ ısica Aplicada, Universidad de Salamanca, 37008 Salamanca, Spain Received: 5 November 2003/Revised version: 7 January 2004 Published online: 7 April 2004 • © Springer-Verlag 2004 ABSTRACT We investigate the double ionization of helium under an intense laser pulse. This process is known to be one of the prototypical manifestation of electron–electron correlation. In this work, we present a numerical study on the influence of Pauli’s exclusion principle in the double ionization. We make a comparative analysis of two almost degenerated states with different character with respect to the exchange symmetry. We show that there exists a significant difference in the double ion- ization of parahelium and orthohelium. The symmetric charac- ter of the spatial electronic wavefunction affects strongly double ionization. It is found that the double ionization is partially sup- pressed in the orthohelium case. The mechanisms relevant for this suppression are discussed. PACS 31.15.Ar; 31.25.Jf 1 Introduction Nonsequential double ionization is probably one of the clearest examples of the importance of the electron– electron correlation [1–3]. During the past few years, [4], de- tailed experiments that can reconstruct the rescattering events have helped to identify the mechanism for energy sharing in the double ionization of helium in intense laser field. This has led to a considerable effort to study this kind of processes, but open questions still remain. The double ionization yields can not be fully explained by using the single active electron (SAE) approximation, or the density functional theory with local density approxima- tion where only the Coulomb repulsion is included. Instead, for a complete description of the correlation, the full two elec- tron wavefunction should be calculated. The numerical calculation of this wavefunction is a very complicated task. A full six dimensional description is ne- cessary and the computational resources needed are very large. Few groups have faced the problem in 3D space [5–9] but experimental laser parameters are still very hard to model. On the other hand, S-Matrix theories based in the strong filed approximation are capable to reproduce most of ✉ Fax: +34-923/294584344, E-mail: camilo@usal.es the experimental rates of multiple ionization of atoms and molecules [10, 11]. Despite their success, these treatments are based in the identification of particular relevant ioniza- tion mechanisms, and therefore they are not able to provide with a complete picture of the interaction dynamics and other related phenomena (harmonic generation, etc.). One way to simplify the description is by reducing the dimensionality. The one dimensional “ab initio” calcula- tion [13–15] have reproduced qualitatively many of the phenomena present in real systems. In particular, electron cor- relation as well as exchange symmetry, are included naturally. These two aspects makes the 1D model an effective tool. In this paper we point out the importance of the symmetry of the total wavefunction for the double ionization yield [12]. We do this by comparing two almost degenerate states with different symmetry. Our results indicate that the Pauli exclusion plays an important role as it inhibits the recollision in the antisym- metric wavefunction, which corresponds to the orthohelium (triplet, aligned spins). On the contrary, in the parahelium (antialigned spins), such suppression does not appear. 2 Theoretical model The electron correlation in the double ionization of helium is fundamental to understand the ionization pro- cess. Single active particle (SAE) or time dependent Hartree Fock (TDHF) models fail to reproduce the experimental ob- served yield of double ionized helium because the correlation is included only approximately. Electron–electron correlation includes the Coulomb repulsion, but it also includes the exclu- sion principle. These two features are completely described by using the two electron wavefunction. The one dimensional model with a soft core potential was first introduced by Eberly [15]. It is accepted that it in- cludes most of the relevant information about the structure of the atom. The electrons are restricted to moving parallel to the laser polarization direction. Therefore, most of the rel- evant dynamics is qualitatively well described. The atom is described by the following Hamiltonian (in atomic units) H = p 2 1 2 + p 2 2 2 − 2  x 2 1 + a 2 − 2  x 2 2 + a 2 + 1  (x 1 − x 2 ) 2 + a 2 (1)