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 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) M. Gisselbrecht 1, M. Lavollée 1, A. Huetz 1, P. Bolognesi 2, L. Avaldi 2, D. Seccombe 3 and T. Reddish 3 1)Laboratoire d'interaction du rayonnement X avec la matière (LIXAM), Université Paris Sud Bat 350. Centre d'Orsay Orsay, France 2) CNR- Istituto di Metodologie Inorganiche e dei Plasmi Area della Ricerca di Roma 1, CP Monterotondo Scalo, Italy 3) Department of Physics, University of Windsor, 401 Sunset Ave, Ontario, Canada N9B 3P4. Perpendicular geometry I - Introduction e-e- e-e- H+H+ H+H+ h + H 2  H + + H + + e e 2 - Excess Energy Binding Energy 31.7eV Photon Energy Ion KER ~18.8eV R0R0R0R0 II - 3D Momentum imaging with CIEL (x e,y e,t e ) (x H,y H,t H ) H+H+ H+H+ e1-e1- e2-e2- Electric field Magnetic field Photon Coplanar geometry Full line: HRM-SOW calculation Dead angle  e2 barn.eV -1.sr -2  E 1 =E 2 =12.5  2.5 eV k e1 k e2 k  d  1 =  10° ; d  2 =  5° d  12 =  20° barn.eV -1.sr -2 E 1 =E 2 =12.5  2.5 eV  k e1 barn.eV -1.sr -2 Full line: constructive interference Dashed line: destructive interference Full line: a cos 2  2 E 1 =E 2 =12.5  4 eV Counts (arb. Unit.)   1 = 0  25°;  2  = 90  17°  k e2 k e1 k Full line: a cos 2  2 +b E 1 =E 2 =12.5  4 eVE 1 =E 2 =12.5  8 eV E 1 =E 2 =12.5  12 eV Counts (arb. Unit.) PHOTO DOUBLE IONIZATION OF FIXED IN SPACE H 2 Full line: Y l0 expansion 0 ≤ l ≤ 3 Counts (arb. Unit.) E 1 =E 2 =12.5  8 eV  Full line: Y l0 expansion 0 ≤ l ≤ 3 Counts (arb. Unit.)  Fixed in space H 2 Comparison Helium and H 2 with no alignement barn.eV -1.sr -2 Position Sentive Detector: Segmented Anode Small multi-hit dead-time~1.5 ns - Time resolution 500 ps Lines instead of pixels - x,y resolution ± 500  m Complex nuclear physic electronics pxpx pypy pzpz x y t E   The experimental set-up 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 dead-time between the detection of two particles. M. Lavollée, RSI (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 trajectories the vector momenta can be reconstructed for all particles H2H2 He H2H2   Perpendicular geometry Coplanar geometry In the perpendicular geometry the first electron e 1 is at right angle with the plane (yellow) defined by the second electron e 2 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°) For helium, the differential cross section is proportional to cos 2  2 (Huetz et al, 1991). For molecular hydrogen, the differential cross section does not follow the law (a cos 2  2 + 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.  x y z   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 inter-nuclear 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. Helium like model J.M. Feagin, JPB L729 (1998) 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 a P, 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). |a  /a  |     Phase This work 2.9   2110  15 0 Weber et al  Wightman et al 2.1   3  Kheifets  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 2  2 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). III – Results (preliminary analysis of ~ photo double ionisation events recorded at ELETTRA on H 2 (December 2004) 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 ( ,2e) differential cross sections for various orientations of the molecule and kinetic energy release of the ions. 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=E 1 +E 2 = 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 E 1 =E 2 ~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. M. Gisselbrecht et al, RSI (2005)