Transcript + e 2 - University of Windsor

PHOTO DOUBLE IONIZATION OF FIXED IN SPACE H2
M. Gisselbrecht1, M. Lavollée1, A. Huetz1, P. Bolognesi2, L. Avaldi2, D. Seccombe3and T. Reddish3
1) Laboratoire d'interaction du rayonnement X avec la matière (LIXAM), Université Paris Sud Bat 350. Centre d'Orsay 91405. Orsay, France
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 four-body 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 (g,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+
-
H+
e2
(xH,yH,tH)
Photon
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= h-KER
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 photo-ionization 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 (g,2e) differential cross sections is expected.
Excess Energy
Position Sentive Detector: Segmented Anode
Photon Energy
• Small multi-hit dead-time~1.5 ns - Time resolution 500 ps
• Lines instead of pixels - x,y resolution ± 500m
Ion KER
~18.8eV
• Complex nuclear physic electronics
Binding
Energy
31.7eV
x
y
t
px
py
pz
R0
The experimental set-up CIEL mainly consist in a double
momentum imaging system, with static electric field and
magnetic confinement of the electrons. 4p detection efficiency
has been achieved for both electrons and ions. The two
detectors are equipped with segmented pixel anodes,
characterized by a very short dead-time
M. Lavollée,
between the detection of two particles.
RSI 70 2968 (1999)
The principle of the 3D-momentum 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
q
f
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
E1=E2=12.5  2.5 eV
ke1
k
ke1
H2
E1=E2=12.5  2.5 eV
He
ke1
ke1
k
ke2
e
ke2
barn.eV -1.sr -2
e
barn.eV-1.sr -2
Dead angle
e
e
E1=E2=12.5  4 eV
Counts (arb. Unit.)
He
Perpendicular geometry
For helium, the differential cross section is
proportional to cos2q2 (Huetz et al, 1991).
e
Q1= 0  25°; Q2 = 90  17°
re2
Full line: a cos2q2
Full line: HRM-SOW calculation
In the coplanar geometry, the electron momenta and the polarization vector e belong to the same plane (yellow). Integration over the azimutal
angle around e has been performed, using cylindrical symmetry.
• For helium the results are in excellent agreement with HRM-SOW 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 e.
In the preliminary results presented here
integration around e 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.)
dq1=  10° ; dq2=  5°
df12=  20°
For molecular hydrogen, the differential
cross section does not follow the law
(a cos2q2 + b) such as predicted by
integration of the helium-like model over
molecular orientation.
(Feagin 1998, see below)
In addition the shape of the angular
distribution changes rapidly when selecting
different energy bandwidths.
e
Full line: a cos2q2+b
Fixed in space H2
Helium like model
z
eS
In this model, for a given orientation of the molecule, the polarization vector e is expanded into two components eS and eP,
respectively parallel and perpendicular to the inter-nuclear axis. The ionization amplitude is calculated as the coherent sum of two
terms, with amplitudes aS and aP. 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 eS or eP. 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.
y
e
J.M. Feagin,
JPB L729 (1998)
x
eP
Perpendicular geometry
E1=E2=12.5  8 eV
e
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 e, see the LHS
figure) allow to disentangle and to extract the two amplitudes aS 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).
e
barn.eV-1.sr-2
barn.eV-1.sr-2
barn.eV -1.sr -2
e
E1=E2=12.5  8 eV
Counts (arb. Unit.)
Counts (arb. Unit.)
barn.eV-1.sr-2
barn.eV -1.sr -2
barn.eV-1.sr-2
Coplanar geometry
Dashed line: destructive interference
|aP/aS |
DqP
DqS
Phase
This work
2.9 0.5
84  2
110  15
0
Weber et al
2.2
61 .5
83.5
p
2.1  0.5
76  3
76  3
p
1.2
88
84
p
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 e.
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 cos2q2 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 e, and will allow to select narrower energy bandwiths to compare with the measurements of
Weber et al (Nature, 2004).