Excess Energy:E1 + E2

BindingEnergy31.7eV

Photodouble Ionization of Molecular HydrogenT.J. Reddish1†, D.P. Seccombe1, and A. Huetz2

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

†Email: reddish@uwindsor.ca Web-Site: http://zeus.uwindsor.ca/courses/physics/reddish/TJRWelcome.htm

Collins et al Physical Review A (2001) 64 062706

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)

E1 = 1 eV

E1 = 2 eV

E1 = 5 eV

E1 = 7 eV

He D2

Photon BeamDirection

Polarization ()

Evolution of Similarities and Differences with E2/E1

R paper

(a) & (b)similarelectron

repulsion

(d) nucleisuppresses

electronrepulsion

Coplanar

H2/D2 (,2e) 5C Predictions for selected

molecular orientations at E1 = E2 = 10eV

extra lobesdue to

higher L components

D2 (,2e) 5C calculations

for E1 = E2 = 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:

98115132

1 = 115o

1 = 98o

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 1/2 91

(He), 78 (D2)

Fitted curves using Feagin’s He-like model with 1/2 = 77

1 = 132o

D2 seems to have similar structure….

but with ‘narrower’ lobes and a ‘filled-in’ node (highlighted in ratio plot)

He D2

Wightman et al J. Phys B. 31 (1998) 1753Feagin (1998) J. Phys. B. 31 L729

Reddish and Feagin (1999) J. Phys. B. 32 2473

Characteristic two lobes with node at 12 = .

Data from: Seccombe et al J Phys B 35 (2002) 3767

0 60 120 180 240 300 3600

1

2

E1 = 1eV, E 2 = 24eV

D2/He

2

0 60 120 180 240 300 3600

1

2

3

E1 = 2eV, E 2 = 23eV

D2/He

2

0 60 120 180 240 300 3600

1

2

3

4

E1 = 5eV, E 2 = 20eV

D2/He

2

0 60 120 180 240 300 3600

2

4

6

8

E1 = 7eV, E 2 = 18eV

D2/He

2

(,2e) D2 5C and He 3C from Walter and Briggsfor R = E2/E1 = 24, 11.5, 4, 2.67, S1 = 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 )

Z Stack MCP Position Sensitive Detector(Resistive Anode Encoder)

ExitOptics

Inner Toroid

Outer Toroid

HemisphericalAnalyser

Gas BeamHemispherical Analyser

Entrance Optics

Toroidal AnalyserEntrance Optics

PerpendicularPlane Geometry

 

k , k1 and k2

Coplanar Detection Geometry

 k, , k1 and k2

all coplanar

S CollinsS CvejanovicC DawsonJ Wightman

M WalterJ Briggs

A Kheifets

LURELIXAM

SRS

EPSRCLeverhulme Trust

EUNewcastle University

Acknowledgements

He

D2 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.

Publications

Future Prospects

Schematic Diagrams of ToroidalPhotoelectron Spectrometers

h + H2 H+ + H+ + e- + e-

e

e

H+

H+

ee

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 (++ ~ 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 (E 1 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.

33331313

121

3

22

1

2

1

SSS

ETDCS yx

PhotonEnergy

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

Comparison between the (, 2e) ‘TDCS’of He and D2 at E = 25 eV, 1 = 0, S1 = 1

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

He / D2 TDCS with

E1 = E2 = 10eV, S1 = 0.67

Walter and Briggs J. Phys. B (1999) 32 2487

Reddish et al Rev. Sci. Instrum.

68 (1997) 2685

Mazeau et alJ. 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!