PHOTO DOUBLE IONIZATION OF FIXED IN SPACE H2
M. Gisselbrecht1, M. Lavolle1, A. Huetz1, P. Bolognesi2, L. Avaldi2, D. Seccombe3and T.
3 d'interaction du rayonnement X avec la matire (LIXAM), Universit Paris Sud Bat 350. Centre d'Orsay 91405. Orsay, France
1)
Laboratoire
Reddish
2) CNR Istituto di Metodologie Inorganiche e dei Plasmi Area della Ricerca di Roma 1, CP 10 00016 Monterotondo Scalo, Italy
3) Department of Physics, University of Windsor, 401 Sunset Ave, Ontario, Canada N9B 3P4.
I  Introduction
e
Electric field
We have studied the fourbody fragmentation of molecular
hydrogen at a photon energy h=76 eV (25 eV nominal
excess energy above threshold), at the GAS PHASE
BEAMLINE of the ELETTRA synchrotron source (Italy).
The goal of these experiments is the understanding of
electronic correlations in a molecular field, by the detailed
investigation of the (,2e) differential cross sections for
various orientations of the molecule and kinetic energy
release of the ions.
H+
H+
II  3D Momentum imaging with CIEL
e
h + H2 H+ + H+ + e1 + e2
Magnetic field
(xe,ye,te)
e1
H+
e2
H

+
(xH,yH,tH)
Photon
Excess Energy
The Coulomb explosion of molecular hydrogen yields two electrons and two
protons. The latter gain a total kinetic energy release (KER) of about 18.8
eV, due to their repulsion. Energy conservation (see the diagram beside)
leads to an excess energy E for the electrons given by:
E=E1+E2= hKER
Both KER and E are spread over a few eV due to the extension of the Franck
Condon region.
In the present experiment the photon energy has been chosen close to the
maximum of the double photoionization integral cross section. In the equal
sharing case this gives E1=E2 ~12.5 eV. With these energies the electrons
are much faster than the ions. In addition their De Broglie wave lengths are
about 8a.u., which is larger than the initial internuclear separation of the
nuclei (1.4a.u.). One would then expect that asymptotically, in the final
state, they do not see precisely the molecular orientation.
However in the initial state their wave lengths are much shorter, and the
electronic orbitals are strongly oriented in space, depending upon the
orientation of the molecular axis. Consequently a strong effect of molecular
orientation onto the (,2e) differential cross sections is expected.
Position Sentive Detector: Segmented Anode
Photon Energy
Small multihit deadtime~1.5 ns  Time resolution 500 ps
Ion KER
~18.8eV
Lines instead of pixels  x,y resolution 500m
Complex nuclear physic electronics
Binding
Energy
31.7eV
px
py
pz
x
y
t
R0
The experimental setup CIEL mainly consist in a double
momentum imaging system, with static electric field and
magnetic confinement of the electrons. 4 detection
efficiency has been achieved for both electrons and ions.
The two detectors are equipped with segmented pixel
anodes, characterized by a very short deadtime
M. Lavolle,
between the detection of two particles.
RSI 70 2968 (1999)
The principle of the 3Dmomentum imaging technique relies on
the measurement, for each particle, of 3 experimental
quantities, the position on the detector (x, y) and the time of
flight t. The 8 bunch mode of ELETTRA has been used to get the
time of flight of electrons. Then from the analysis of
M. Gisselbrecht et al,
trajectories the vector momenta can
RSI 013105 (2005)
be reconstructed for all particles
E
III Results
(preliminary analysis of ~ 1.1 106 photo double ionisation events recorded at ELETTRA on H2 (December 2004)
Comparison Helium and H2 with no alignement
Coplanar geometry
H2
E1=E2=12.5 2.5 eV
ke1
k
He
E1=E2=12.5 2.5 eV
ke1
k
ke2
barn.eV 1.sr 2
ke2
barn.eV1.sr 2
For helium, the differential cross section
is proportional to cos22 (Huetz et al,
1991).
ke1
Dead angle
ke1
E1=E2=12.5 4 eV
Counts (arb. Unit.)
He
Perpendicular geometry
1= 0 25; 2= 90 17
e2
Full line: a cos22
Full line: HRMSOW calculation
In the coplanar geometry, the electron momenta and the polarization vector belong to the same plane (yellow). Integration over the
azimutal angle around has been performed, using cylindrical symmetry.
For helium the results are in excellent agreement with HRMSOW calculations (P. Selles and L. Malegat)
For molecular hydrogen a filling of the node is noticeable, together with an higher angular correlation. These observations are
consistent with previous findings ( Reddish et al, 1997)
H2
In the perpendicular geometry the first
electron e1 is at right angle with the plane
(yellow) defined by the second electron e2
and the polarization vector
In the preliminary results presented here
integration around
has not been
performed. Thus the first electron is vertical
and the second electron belongs to the
horizontal plane.
In this geometry the effect of angular
correlation is frozen, as the angle
between the electrons is constant (90)
E1=E2=12.5 12 eV
E1=E2=12.5 8 eV
E1=E2=12.5 4 eV
Counts (arb. Unit.)
d1= 10 ; d2= 5
d12= 20
For molecular hydrogen, the differential
cross section does not follow the law
(a cos22 + b) such as predicted by
integration of the heliumlike model over
molecular orientation.
(Feagin 1998, see below)
In addition the shape of the angular
distribution
changes
rapidly
when
selecting different energy bandwidths.
Full line: a cos22+bb
Fixed in space H2
z
Helium like model
In this model, for a given orientation of the molecule, the polarization vector is expanded into two components and ,
respectively parallel and perpendicular to the internuclear axis. The ionization amplitude is calculated as the coherent
sum of two terms, with amplitudes a and a. The angular dependence of each term is similar to the helium case (Huetz et
al, 1991), with spherical angles referred to two different body fixed frames, with z axis along or . The final differential
cross section is obtained by frame transformation to the laboratory frame. The amplitudes depend only on the energies
and mutual angle of the two electrons. They can be extracted from experiments.
J.M. Feagin,
JPB L729 (1998)
y
x
Perpendicular geometry
E1=E2=12.5 8 eV
Full line: Yl0 expansion 0 l 3
Full line: constructive interference
Our results show a spectacular evolution of the electron correlation
patterns with molecular orientation.
They are compatible with the helium like model. Two specific
orientations of the molecule (respectively parallel and perpendicular
to see the LHS figure) allow to disentangle and to extract the two
amplitudes a and aP, which are supposed to be Gaussians with
different widths.
A constant phase has been assumed between them, and the observed
shapes indicate that the phase is close to zero (constructive
interference).
barn.eV1.sr2
barn.eV1.sr2
barn.eV 1.sr 2
E1=E2=12.5 8 eV
Counts (arb. Unit.)
Counts (arb. Unit.)
barn.eV1.sr2
barn.eV 1.sr 2
barn.eV1.sr2
Coplanar geometry
Dashed line: destructive interference
a/aa
Phase
This work
2.9 0.5
84 2
110 15
Weber et al
2.2
61 .5
83.5
0
2.1 0.5
76 3
76 3
1.2
88
84
Wightman et al
Kheifets
Full line: Yl0 expansion 0 l 3
In the perpendicular geometry and for oriented molecules, our observations are not consistent with the helium like
model. In the LHS figure the molecule is vertical, along the first electron, and at right angle with the horizontal plane
where the second electron is detected. In the RHS figure, the molecule is in the horizontal plane, at right angle with
the polarization vector . In the two cases the angular distributions are well reproduced by partial wave expansions
up to l=3. On the contrary the Helium like model predicts an identical cos 22 shape in both cases.
A more detailed analysis of the perpendicular geometry with oriented molecules is under progress. It will take
advantage of cylindrical symmetry around , and will allow to select narrower energy bandwiths to compare with the
measurements of Weber et al (Nature, 2004).