Excess Energy: E 1 + E 2

1. Note the strong similarity in the TDCSs for He and D2. This can be summarized using Feagin’s He-like model with Gaussian parameterisation (black curves) with different half-widths 1/291 (He),78 (D2) e H+ H+ e e e He++ Characteristic two lobes with node at 12 = . Photodouble Ionization of Molecular HydrogenT.J. Reddish1†, D.P. Seccombe1, and A. Huetz21 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†Email: reddish@uwindsor.ca Web-Site: http://zeus.uwindsor.ca/courses/physics/reddish/TJRWelcome.htm Comparison between the (, 2e) ‘TDCS’ of He and D2 at E = 25 eV, 1 = 0, S1 = 1 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! h + H2 H+ + H+ + e- + e- Photon Beam Direction He / D2 TDCS with E1 = E2 = 10eV, S1 = 0.67 H2/D2 (,2e) 5C Predictions for selected molecular orientations at E1 = E2 = 10eV Polarization () h + He  He++ + e- + e- R paper Schematic Diagrams of Toroidal Photoelectron Spectrometers • Why Study Double Ionization? • Fundamental theoretical interest: Electron-Electron (& Ion) Correlation, to which angular distributions are sensitive probe. • Development of sensitive detection techniques (++ ~ 10-20 cm2) • 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: S1, S2, S3) and high photon flux. • Note: Triple" Differential Cross Section “TDCS” Appropriate terminology for helium - with electron energies (E1 and E2) and directions (1 and 2). We can still use "TDCS" for H2 by implying a fixed equilibrium internuclear separation: Re = 1.4 Å and ignoring any possible coupling between electronic and nuclear motion during double ionisation. (a) & (b) similar electron repulsion Perpendicular Plane Geometry k, k1 and k2 Evolution of Similarities and Differences with E2/E1 He D2 (,2e) D2 5C and He 3C from Walter and Briggs for R = E2/E1 = 24, 11.5, 4, 2.67, S1 = 1, 1 = 0. Coplanar Reddish et al Rev. Sci. Instrum. 68 (1997) 2685 • Data obtained with ‘identical’ spectrometer conditions. • Note variations in y-scales • Velocity gauges arbitrary normalised to data at 2 = 180 (d) nuclei suppresses electron repulsion Coplanar DetectionGeometry k, , k1 and k2 all coplanar Photon Energy extra lobes due to higher L components Excess Energy: E1 + E2 Mazeau et al J. Phys. B. 30 (1997) L293 Total Ion Energy ~18.8eV 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. D2seems to have similar structure…. but with ‘narrower’ lobes and a ‘filled-in’ node (highlighted in ratio plot) Walter and Briggs J. Phys. B (1999) 32 2487 He and D2 TDCS in perpendicular plane geometry with E1 = 5eV, E2 = 20eV, S1 = 0.9 Helium HRM-SOW Theory 1 = 0 (20), 10(10), 20(10) and 90 (7) Binding Energy 31.7eV Fitted curves using Feagin’s He-like model with 1/2 = 77 1: 98 115 132 Data from: Seccombe et al J Phys B 35 (2002) 3767 Future Prospects D2 (,2e) 5C calculations for E1 = E2 = 10eV integrated over all molecular orientations The main challenge now is 2-centered systems. Double ionization of H2 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. Double ionisation potential depends upon internuclear separation - nominally at 51.1eV. ( He  He++ : 79eV ) Mutual Angle (12) - Degrees Acknowledgements Observations • Even the simple E1 = E2 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%, 1Se1Po character. ·Explained yield at 12 = : Selection rule differences and solid angle effects. ·Atom-like when  >> Re Publications S Collins S Cvejanovic C Dawson J Wightman M Walter J Briggs A Kheifets LURE LIXAM SRS EPSRC Leverhulme Trust EU Newcastle University D. P. Seccombe et al J. Phys. B. (2002) 35 3767 S. A. Collins et al Physical Review A (2001) 64 062706 J. P. Wightman et al J Phys B. (1998) 31 1753 T. J. Reddish et al Phys Rev Letts (1997) 79 2438 Wightman et al J. Phys B. 31 (1998) 1753 Feagin (1998) J. Phys. B. 31 L729 Reddish and Feagin (1999) J. Phys. B. 32 2473 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 Collins et al Physical Review A (2001) 64 062706