Photoionization of two-electron ortho-atoms
Camilo Ruiz, Luis Plaja, J. R. Va
´
zquez de Aldana, and Luis Roso
Departamento de Fı ´sica Aplicada, Universidad de Salamanca, E-37008 Salamanca, Spain
Received 26 May 2003; published 28 August 2003
We present a numerical study on the influence of Pauli’s exclusion principle in the double ionization of
helium in strong laser fields. To this end, we compare the ionization dynamics of the helium in its triplet and
singlet configurations. The symmetric character of the electronic orbital wave-function affects strongly the
mechanism of ionization in helium. In particular, it is found that the double ionization is partially suppressed
in the ortho-helium case. The mechanisms relevant for this suppression are discussed.
DOI: 10.1103/PhysRevA.68.023409 PACS numbers: 42.50.Hz, 32.80.Fb, 32.80.Rm
I. INTRODUCTION
During the past decades, the advance of chirped pulse
amplification techniques has led to the rapid development of
the field of nonperturbative laser-matter interactions. As a
fundamental characteristic, this discipline encloses the physi-
cal processes that occur when the amplitude of the interact-
ing electromagnetic wave is above or about the same order as
the fields that bind the electric charges in the material. In
these situations, the dynamics of the matter components is
found to be much richer than what can be expected from a
perturbative analysis. In particular, special effort has been
devoted to an accurate description of the ionization processes
and the generation of high-frequency radiation, due to its
feasibility of experimental observation and the possibility of
developing new technical applications. At present, it can be
considered that the dynamics of simple systems, as one-
electron atoms, is well understood either in theory or experi-
ments for the usual laser parameters. This involves also the
explanation of new phenomena such as the above threshold
ionization and enhanced high-frequency radiation 1.
In most of the cases, the theoretical study of more com-
plex systems, as many-electron atoms or molecules, still con-
stitutes a challenge. S-matrix theories based on the strong
field approximation are capable of reproducing the experi-
mental rates of multiple ionization of atoms and molecules
2,3. Despite their success, these treatments are based on the
identification of particular relevant ionization mechanisms,
and therefore they are not able to give a complete picture of
the interaction dynamics, or other related phenomena har-
monic generation, etc.. On the other side, the exact integra-
tion of the Schro
¨
dinger equation, which constituted a funda-
mental tool to study the problem in single-electron systems,
becomes a formidable task even in the case of the simplest
multielectron systems, as the helium atom. Nowadays, only a
few groups have faced the problem in three-dimensional
3D space 4,5.
The pioneering works on ab initio one-dimensional mod-
els for hydrogen and helium as well as for other two-
electron systems by Eberly and co-workers 6–8 have
demonstrated that atomic models of reduced dimensionality
are capable of reproducing qualitatively many of the phe-
nomena present in the real systems. In particular, correlation
effects as well as symmetry in Hilbert space, like in the
present paper, are included naturally. These two aspects
make 1D computations an effective tool, in many aspects
more accurate than the 3D computations in the single active
electron approximation. On the other side, the computational
advantages of the dimensional reduction make feasible com-
putations of two- and three-electron atoms without funda-
mental difficulties. For this reason, many groups have been
working on the ab initio modeling of two-electron systems
on the basis of the time-dependent Schro
¨
dinger equation.
The experiments on double ionization 9–11 have dem-
onstrated the importance of the correlation effects for double
ionization in helium for certain laser parameters. In particu-
lar, the production of He
2 +
ions has been found to be orders
of magnitude larger than expected if only the sequential ion-
ization is assumed, as in the so-called single-electron ap-
proximation. This demonstrates that in these experiments,
the ionization takes place almost simultaneously, and that the
role of the electron correlation is fundamental. S-matrix theo-
ries have helped to identify the rescattering as the fundamen-
tal process which leads to this nonsequential double ioniza-
tion 12, and give explanation to the strong polarization of
the ejected electrons.
Although several papers have been published in the ion-
ization of excited para-helium 13,14, practically no atten-
tion has been devoted to the dynamics of the ortho-helium
case 15. While in the first case the antisymmetrization of
the wave function takes place in the spin space and therefore
has no dynamical consequences for the laser parameters con-
sidered here, in the second case the orbital wave function
should be antisymmetric. As discussed in this paper, in this
latter case the rescattering process is affected by the exclu-
sion principle.
The advent of new techniques that provide sources of
ortho-helium atoms 16 makes possible to think of experi-
ments that can be useful to measure the relevance of sym-
metry in the rescattering mechanism. In this case, our con-
clusion about the inhibition of the ionization rate due to the
spatial symmetrization of the wave function could be ob-
served.
II. TWO-ELECTRON ATOMIC MODEL
The complete numerical calculation of the 3D helium sys-
tem is a very complex task: the six dimensions needed for
complete description of the dynamics of the two electron
atoms makes the problem difficult to address with today’s
PHYSICAL REVIEW A 68, 023409 2003
1050-2947/2003/682/0234097/$20.00 ©2003 The American Physical Society 68 023409-1