Excess Energy: E 1 + E 2 Binding Energy 31.7eV Photodouble Ionization of Molecular Hydrogen T.J. Reddish 1†, D.P. Seccombe 1, and A. Huetz 2 1 Physics Department, University of Windsor, 401 Sunset Ave, Windsor, Ontario, Canada, N9B 3P4. 2 LIXAM, UMR 8624, Université Paris Sud, Bâtiment 350, Orsay Cedex, France † Web-Site: Collins et al Physical Review A (2001) He and D 2 TDCS in perpendicular plane geometry with E 1 = 5eV, E 2 = 20eV, S 1 = 0.9 Helium HRM-SOW Theory  1 = 0  (  20  ), 10  (  10  ), 20  (  10  ) and 90  (  7  ) Photon Beam Direction Polarization (  ) Evolution of Similarities and Differences with E 2 /E 1 R  paper (a) & (b) similar electron repulsion (d) nuclei suppresses electron repulsion Coplanar H 2 /D 2 ( ,2e) 5C Predictions for selected molecular orientations at E 1 = E 2 = 10eV extra lobes due to higher L components D 2 ( ,2e) 5C calculations for E 1 = E 2 = 10eV integrated over all molecular orientations Data: Wightman et al J. Phys B. 31 (1998) 1753 Scherer et al J. Phys. B. 31 (1998) L817 Theory: Walter and Briggs J. Phys. B 32 (1999) 2487 Mutual Angle (  12 ) - Degrees  1 : 98  115  132  Note the strong similarity in the TDCSs for He and D 2. This can be summarized using Feagin’s He-like model with Gaussian parameterisation (black curves) with different half-widths  1/2 91  (He), 78  (D 2 ) Fitted curves using Feagin’s He-like model with  1/2 = 77  D 2 seems to have similar structure…. but with ‘narrower’ lobes and a ‘filled- in’ node (highlighted in ratio plot) HeD2D2 Wightman et al J. Phys B. 31 (1998) 1753 Feagin (1998) J. Phys. B. 31 L729 Reddish and Feagin (1999) J. Phys. B Characteristic two lobes with node at  12 = . Data from: Seccombe et al J Phys B 35 (2002) 3767 ( ,2e) D 2 5C and He 3C from Walter and Briggs for R = E 2 /E 1 = 24, 11.5, 4, 2.67, S 1 = 1,  1 = 0 . Despite large gauge variation in 5C (&3C), plus its tendency to exaggerate the yield at small mutual angles, there is nevertheless a remarkable consistency with the data to evolving shape of the ratio trends at E = 25eV! The reason for this is not yet understood. Data obtained with ‘identical’ spectrometer conditions. Note variations in y-scales Velocity gauges arbitrary normalised to data at  2 = 180  Total Ion Energy ~18.8eV Double ionisation potential depends upon internuclear separation - nominally at 51.1eV. ( He  He ++ : 79eV ) Perpendicular Plane Geometry k   , k 1 and k 2 Coplanar Detection Geometry k , , k 1 and k 2 all coplanar S Collins S Cvejanovic C Dawson J Wightman M Walter J Briggs A Kheifets LURE LIXAM SRS EPSRC Leverhulme Trust EU Newcastle University Acknowledgements The main challenge now is 2-centered systems. Double ionization of H 2 is in its infancy. The main theoretical challenge is to adapt the ab initio methods developed for helium to 2-centered systems. Ideally one needs to have a "fixed-in-space” molecular axis, which is technically possible with suitable equipment. Such studies will be most sensitive to electron- ion correlation / dichroism / interference effects in the ionization/dissociation of light molecules. Experimentally, this requires helical / linear VUV undulators at synchrotron sources and/or ultra-fast laser facilities, together with the continued development of detector technology. Publications Future Prospects Schematic Diagrams of Toroidal Photoelectron Spectrometers h + H 2  H + + H + + e - + e - e e H+H+ H+H+ e e He ++ h + He  He ++ + e - + e - Why Study Double Ionization?  Fundamental theoretical interest: Electron-Electron (& Ion) Correlation, to which angular distributions are sensitive probe.  Development of sensitive detection techniques (  ++ ~ cm 2 )  Accurate test for theory in a ‘simple’ system, which can then be extended to more complex targets. Requirement:  Synchrotron radiation with well defined polarization properties (Stokes Parameters: S 1, S 2, S 3 ) and high photon flux.  Note: Triple" Differential Cross Section “TDCS” Appropriate terminology for helium - with electron energies (E 1 and E 2 ) and directions (  1 and  2 ). We can still use "TDCS" for H 2 by implying a fixed equilibrium internuclear separation: R e = 1.4 Å and ignoring any possible coupling between electronic and nuclear motion during double ionisation. Photon Energy D. P. Seccombe et al J. Phys. B. (2002) S. A. Collins et al Physical Review A (2001) J. P. Wightman et al J Phys B. (1998) T. J. Reddish et al Phys Rev Letts (1997) Comparison between the ( , 2e) ‘TDCS’ of He and D 2 at E = 25 eV,  1 = 0 , S 1 = 1 Observations  Even the simple E 1 = E 2 case is intrinsically more complex in diatomic molecules than for helium.  5C provides some justification for observed ‘narrower’ lobes compared to the corresponding He case.  Extra lobes due to higher L components? He-Like Model:  Based on dominant, 96%, 1 S e  1 P o character.  Explained yield at  12 =  : Selection rule differences and solid angle effects.  Atom-like when >> R e He / D 2 TDCS with E 1 = E 2 = 10eV, S 1 = 0.67 Walter and Briggs J. Phys. B (1999) Reddish et al Rev. Sci. Instrum. 68 (1997) 2685 Mazeau et al J. Phys. B. 30 (1997) L293 What happens when a hydrogen molecule absorbs a photon of sufficient energy to eject both electrons? In which directions do the electrons go? What happens to the ions during the Coulomb explosion? Why don’t two equal energy electrons leave in opposite directions? These are the sorts of fundamental questions that this project has tried to address. The experiments are difficult, requiring very efficient coincidence techniques to ensure the electrons come from the same event. Theoretically, even the simplest molecule creates an unexpected challenge!