We have measured the coincident momenta of both electrons emitted in argon double ionization at 780 nm
For electrons which are emitted with very small momentum
transverse to the electric field, we find that the two electrons have very unequal momentum. This is in
contrast to the situation for larger transverse momenta for which most electrons are found with
similar momentum. We interpret this observation as a manifestation of electron repulsion.
We also identify contributions from electron impact excitation.
The most likely scenario today for the correlation dynamics of electrons is
given by the rescattering model (for further informations
The first experimental work observing the correlated momentum of the
electrons (view the article: Nature 405, 658 - 661 (2000) as.ps(752kb) or as .zip(147kb)) showed a collective emission of both electrons to the same half sphere.
Most likely the electrons were found having the same momentum component along the polarization axis.
This is surprising since electron repulsion would push the electrons to opposite directions.
In the strong field case the electron and ion final state momenta are influenced
by electron repulsion and the action of the laser field on the charged
particles. While the effect of the acceleration in the laser field is obvious in the
coincident electron momenta (view the article: Nature 405, 658 - 661 (2000) as.ps(752kb) or as .zip(147kb)) surprisingly the influence of electron
repulsion is not evident in any of the previous experiments.
Here we succeeded in measuring the full momentum vector. The effect of the repulsion of the electrons becomes visible.
The experiment was performed using COLTRIMS.
The laser pulse (150 fsec, 780nm) has been focused by a lens of 5 cm focal length
into a supersonic Argon gas jet. The ions were guided by a weak electric field (3.5 V/cm) onto a position
sensitive channel plate detector with delay-line readout.
From the position of impact and the time-of-flight the three dimensional momentum vector can be determined.
The electrons are guided by the electric field and
a parallel magnetic field (10.4 Gauss) onto a second position sensitive
detector. The electron momentum vector is determined from the
time-of-flight and the position of impact.
click on the image above to see an animation of the process (175kb).
One of the electrons has a transverse momentum of:
(a) 0.0<p_perp<0.1 a.u.
(b) 0.1<p_perp<0.2 a.u.
(c) 0.2<p_perp<0.3 a.u.
(d) 0.3<p_perp<0.4 a.u.
The color coding shows the differential rate in arbitrary units. The vertical axis shows the momentum
component of the one electron in the direction of polarization (pez1)
and the horizontal axis the same momentum component of the other electron. For one of the electrons
the transverse momentum has been fixed to a certain interval.
We observe a strong dependence of the correlation pattern on this transverse momentum.
If one electron is emitted off the polarization axis, then both
electrons are found to have most likely similar parallel momenta (figure d). In contrast
if one electron is fixed along the polarization with very small transverse moment (figure a), then we find mostly
one fast and one slow electron.
We interpret our finding as a direct consequence of electron-electron
repulsion. The 1/r12 potential forces the electrons into different regions in the three dimensional
phase space. As a consequence for electrons to have equal parallel momentum requires some angle (i.e. transverse
momentum) between them. The peak at pez1=pez2=1 a.u. is therefore most pronounced if at least one of the
electrons has considerable transverse momentum. If in contrast one electron is fixed to move along the polarization
axis the second electron is repelled longitudinal to be either faster or slower then the first one.
The horizontal axis gives the phase of the laser field at the instant of recollision
(a) return energy of the rescattered electron,
(b) initial phase at which the electrons was set free. The arrows i and ii
indicate the threshold for excitation and ionization, respectivly
(c) electric field at return. The line indicate the critical
field for over the barrier ionization of
the first excited states (i) of Ar1+
In most cases excitation occurs at return phases where the field is high enough quench the excited state instantaniously.
To discuss the measured distribution more quantitatively figure 3 shows the
classically allowed region of phase space calculated within the rescattering model.
We discuss the figure using the classical phase relations shown in figure 2.
Classically allowed phase space within the rescattering model.
The red area is for ionization the curved yellow line shows the
locus of events for rescattering with excitation between the first excited state and the continuum,
assuming instantanious quenching. The green area indicates the region of the most likely
We point out that this curve in figure 2 relies on the fact that the
excited electron will be field ionized instantaneously. If this is the case depends
on the field at the return and thus also on the laser power and the atom under consideration.
The critical field for over the barrier ionization can be estimated to be 2.97*106 V/m for a binding energy of 11 eV
(first excited state of Ar1+).
Electron impact excitation shows dominant resonant structure.
These resonances result from intermediate doubly excited states which autoionize.
Once the returning electron has sufficient energy to ionize the two
electrons can share their energy arbitrarily in the collision and then both acquire additional momentum from the field.
The field determines a maximum return energy (3.17 times the pondoremotive potential) and hence a maximum momentum for
the electrons. This region of phase space classically allowed for ionization is shown by the shaded area. Most of the
intensity in our measured distributions is well within this classically allowed phase space.
From our data we conclude that at larger transverse momenta rescattering with excitation dominates while at smaller
transverse momenta the (e,2e) ionization is dominant. In the latter channel electron-electron repulsion leads to the
dominance of one fast electron accompanied by one slower.
Please check out
M. Weckenbrock et al, J. Phys. B. 34 (2001) L449M. (120kb) for further information.