Interplay Between Electronic and Nuclear Motion in the Photodouble Ionization of H 2

1. DAMOP 2008 Interplay Between Electronic and Nuclear Motion in the Photodouble Ionization of H2 T J Reddish, J Colgan, P Bolognesi, L Avaldi, M Gisselbrecht, M Lavollée, M. S. Pindzola, and A Huetz

2.   e where are the polar angles of electrons 1 and 2 and the molecular axis, N, with respect to , and where and (with e = 1 or 2). Photodouble Ionisation of H2 h (76 eV) + H2 H+ + H+ + e1- + e2- Ions escape much faster than molecular rotation. Detecting ion’s momenta gives: ‘fixed-in-space’ molecule.  Fully differential Cross Sections (FDCS)

3. Fast ‘Coulomb Explosion’ h (76 eV) + H2 H+ + H+ + e1- + e2- Double Ionisation ‘threshold’: ~51 eV (R-dependent). Total energy is conserved by electron and ion pairs, (and the dissociation limit). Final ion pair “kinetic energy release” (KER) reflects internuclear separation (R) at moment of double ionisation. Filter data set via KER to map FDCS as a function of R. R0 = 1.4 a0

4. Electric field Magnetic field e1- H+ (xe,ye,te) (xH,yH,tH) e2- H+ Photon x y E px q t py f pz Momentum Imaging Apparatus Gisselbrecht et al, Rev Sci Instrum 76 (2005) 013105

5. k ke1 ke1 e e ke2 Coplanar Geometry:All 4 particles and  lie in the same plane. This configuration probes both electron-ion and electron-electron interactions. Coulomb repulsion favours “back-to-back emission”, yet PDI Selection rules: Node for back-to-back emission for “equal energy- electrons What happens to FDCS when R changes? Gisselbrecht et al Phys Rev Lett 96 (2006) 153002 (TDCC) Colgan et al, Phys Rev Lett 98 (2007) 153001 Walter and Briggs, Phys Rev Lett 85 (2000) 1630

6. R ~ 1.6a0 R ~ 1.2a0 Coplanar FDCS“KER Effect”: q1 = 90ºE1 = E2 = 12.5  10 eV, N = 10º ‘Pure’ P component shows no KER effect. Dramatic R-dependence at qN 20º, especially at large Rwhere most yield is in 4th quadrant. KER averaged at qN = 30º. ‘Pure’ S component shows small KER effect. TDCC bandwidth averaged FDCS TDCC unaveraged FDCS

7. Coplanar FDCS “KER Effect”q1 = 0ºE1 = E2 = 12.5  10 eVN = 10º KER averaged at qN = 60, 30º. Again a dramatic movement of FDCS yield to the 2nd quadrant as qN= 40 º  20º, but only for large internuclear separation. TDCC bandwidth averaged FDCS TDCC unaveraged FDCS

8. Coplanar FDCS “KER Effect”q1 = 60º N= 10º R ~ 1.6a0 R ~ 1.2a0 A significant change In FDCS yield as a Function of R when qN= 20 º or 160º. All these FDCS have E1 = E2 = 12.5  10 eV: Therefore KER effects are not overly sensitive to electron energies. Reddish et al Phys Rev Lett 100 (2008) 193001 TDCC bandwidth averaged FDCS TDCC unaveraged FDCS

9. Why is N ~ 20º (or 160 º) so critical to observe these KER effects? FDCS is the coherent sum of  and  components. We extract the  and  components, and cross term contributions, in TDCC FDCS. At N = 20º, both components make significant contributions to the FDCS. FDCS Contributions: ,P,Cross term,Total. (1, N) values are (20º, 160º) left, (60º, 20º) right. R = 1.6 (upper) and 1.2 (lower). Only the  component displays an appreciable dependence on R. Changes in sign (and shape) of the cross term with R ‘amplifies’ the small changes with R of the pure  component.

10. Why does the only the  amplitude have an angular dependence sensitive to R? Magnitude of the  amplitude decreases monotonically with R. Whereasamplitude has a shallow minimum near R0. This same behaviour is also seen in the photoionisation of H2+. Hence it is a feature of the axially symmetric nuclear potential, rather than electron correlation. ECS Horner et al Phys Rev Lett 98, 073001 (2007). Reddish et al Phys Rev Lett 100 193001 (2008) Colgan et al, J Phys B 41, 085202 (2008).

11. puFinal State suFinal State Photoionisation of H2+. A strong cancellation exists for the p-wave component for the gu transition, at a given (Ek, R). * Like an Cooper minimum* Then the f-wave dominates  different angular distributions. p, f ‘mix’ is sensitive to R value. No such cancellation occurs for the g πu transition. The photoelectron angular distribution, with respect to the molecular axis. Colgan et al, J Phys B 41, 085202 (2008).

12. Summary and Conclusions Excellent agreement between TDCC and experiment. Dramatic changes in coplanar FDCS for qN ~20, 160º with internuclear separation, R, due to interference between S and P components, whose contributions have similar magnitudes at these qN values. Only S component has R dependence: larger (1,2) are necessary for convergence of the TDCC S amplitude than for P - particularly for large R. By our analogy with H2+, main R-dependent trends of the S and P amplitudes observed in PDI of H2 are due to electron-ion rather than electron-electron interactions.

14. KER Effect in Perpendicular Plane E1 to E2, R, and  “Frozen correlation” (q12 = 90º) We do not see a clear KER effect in this geometry. ECS Vanroose et al, Science 310 1787 (2005) TDCC J. Colgan et al, J. Phys. B 40, 4391 (2007). Weber et al, Nature 431 437(2004)

15. e- H+ H+ e- h + H2 H+ + H+ + e1- + e2- Photodouble Ionisation of H2 Motivation: • Fundamental theoretical interest: Correlation and Dynamics • Angular distributions are sensitive probe (amplitude and phase) • Development of sensitive imaging techniques (++ ~ 10-20 cm2) • Accurate test for theory in a ‘simple’ system Double electron escape in an axial symmetric potential

16. 3D Momentum Imaging Apparatus • Time-of-Flight and (x,y) ion and electron multihit position-sensitive detection. • 4p Detection Solid Angles: Absolute . • 10 Gauss magnetic field confines electrons up to 20 eV. • Synchrotron radiation with well defined polarisation properties and high photon flux. ‘Complete’ kinematical description of ionization process.

17. Electron - electron distribution doesdepend on molecular alignment! • Symmetric two ‘lobes’ for N = (a) 90 (), (d) 0 (). • Absolute  reduces by ~4 from  →  orientations. H2 Coplanar FDCS Gisselbrecht et al Phys Rev Lett 96 (2006) 153002 Weber et al Phys Rev Lett 92 (2004) 163001 What happens to FDCS when R changes? E1= E2 = 12.5  2.5 eV, q1= 90  15°, f12=  20°, DqN=  20°, f1N =  45°