Interplay Between Electronic and Interplay Between Electronic and Nuclear Motion in theNuclear Motion in the

Photodouble Ionization of H Photodouble Ionization of H22

T J Reddish, J Colgan, P Bolognesi, L Avaldi, M Gisselbrecht, M Lavollée,

M. S. Pindzola, and A Huetz

DAMOP 2008

Ions escape much fasterthan molecular rotation.

Detecting ion’s momenta gives: ‘fixed-in-space’molecule.

Fully differential Cross Sections (FDCS)

2112217 / dEdEdddddd eNN

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). 2112 NeeN N,2,1

h (76 eV) + H2 H+ + H+ + e1- + e2

-

Photodouble Ionisation of HPhotodouble Ionisation of H22

Double Ionisation ‘threshold’:~51 eV (R-dependent).

Total energy is conserved by electron and ion pairs, (andthe dissociation limit).

Final ion pair “kinetic energyrelease” (KER) reflectsinternuclear separation (R) atmoment of double ionisation.

Filter data set via KER to mapFDCS as a function of R.

h (76 eV) + H2 H+ + H+ + e1- + e2

-

Excess Energy

Photon Energy

Dissociation 0

KER

H+ + H+

H + H

0 0.5 1.0 1.5 2.0 2.5 3.0

10

0

20

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En

erg

y (e

V)

Internuclear Separation (x10-10 m)

Fast ‘Coulomb Explosion’Fast ‘Coulomb Explosion’

R0 = 1.4 a0

(xe,ye,te) (xH,yH,tH)H+

H+e1-

e2-

Electric field

Magnetic field

Photon

px

py

pz

xyt

E

Momentum Imaging ApparatusMomentum Imaging Apparatus

Gisselbrecht et al, Rev Sci Instrum 76 (2005) 013105

Coplanar Geometry:Coplanar Geometry:All 4 particles and All 4 particles and lie in the same plane. lie in the same plane.

This configuration probes both electron-ion and electron-electron interactions.

Coulomb repulsionfavours “back-to-backemission”, yet

PDI Selection rules: Node for back-to-backemission for “equal energy- electrons

ke1

ke2

k

Walter and Briggs,Phys Rev Lett 85 (2000) 1630

ke1

Gisselbrecht et al Phys Rev Lett 96 (2006) 153002

(TDCC) Colgan et al, Phys Rev Lett 98 (2007) 153001

What happens to FDCS when R changes?

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(a)

(b)

(c)

Coplanar FDCSCoplanar FDCS“KER Effect”: “KER Effect”: 11 = 90 = 90ººEE11 = E = E22 = 12.5 = 12.5 10 eV, 10 eV, NN = = 1010ºº

N =30o

‘Pure’ component shows no KER effect.

‘Pure’ component shows small KER effect.

KER averagedat N = 30º.

DramaticR-dependenceat N 20º,especially atlarge R wheremost yield isin 4th quadrant.

R ~ 1.6a0 R ~ 1.2a0

TDCC bandwidth averaged FDCSTDCC unaveraged FDCS

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N =30oN = 60o

1 = 0o

Coplanar FDCS Coplanar FDCS “KER Effect”“KER Effect”

11 = 0 = 0ºº

EE11 = E = E22 = 12.5 = 12.5 10 eV 10 eV

NN = = 1010ºº KER averaged at N = 60, 30º.

Again a dramatic movement of FDCS yield to the 2nd quadrant as N = 40 º 20º, but only for large internuclear separation.

TDCC bandwidth averaged FDCSTDCC unaveraged FDCS

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Coplanar FDCS Coplanar FDCS “KER Effect”“KER Effect”

11 = 60 = 60ºº

A significant changeIn FDCS yield as a Function of R whenN = 20 º or 160º.

All these FDCS haveE1 = E2 = 12.5 10 eV:

Therefore KER effects are not overly sensitiveto electron energies.

TDCC bandwidth averaged FDCSTDCC unaveraged FDCS

Reddish et alPhys Rev Lett 100 (2008) 193001

NN == 1010ºº

Why is Why is NN ~ 20º (or 160 º) so critical ~ 20º (or 160 º) so critical

to observe these KER effects?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 componentsmake significant contributions to the FDCS. Only the component displaysan appreciable dependence on R.

Changes in sign (and shape) ofthe cross term with R ‘amplifies’ the small changes with R of thepure component. R

ela

tive

Co

ntr

ibu

tio

ns

to

TD

CS

0

4

2

0 60 120 360180 240 300

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1

3600 60 120 180 240 300

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1

Mutual Angle, 12

0

4

-2

2

2

FDCS Contributions: , , Cross term, Total.

(1, N) values are(20º, 160º) left, (60º, 20º) right.

R = 1.6 (upper) and 1.2 (lower).

Why does the only the Why does the only the amplitude have amplitude have

an angular dependence sensitive to an angular dependence sensitive to RR?? Magnitude of the amplitudedecreases monotonically with R. Whereas amplitude has ashallow minimum near R0.

This same behaviour is also seenin the photoionisation of H2

+.

Hence it is a feature of the axiallysymmetric nuclear potential,rather than electron correlation.

ECS Horner et al Phys Rev Lett 98, 073001 (2007).

Reddish et alPhys Rev Lett 100 193001 (2008)

Colgan et al, J Phys B 41, 085202 (2008).

PhotoionisationPhotoionisation of H of H22

++..

The photoelectron angular distribution,with respect to the molecular axis.

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(Degrees)

u Final Stateu Final

State

A strong cancellation existsfor the p-wave component forthe 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 occursfor the g πu transition.

045

90135

180

(Degrees)

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2.2

1.2

R (a0) 1.8

pu Final Statepu Final State

Colgan et al, J Phys B 41, 085202 (2008).

Summary and ConclusionsSummary and Conclusions

Excellent agreement between TDCC and experiment.

Dramatic changes in coplanar FDCS for N ~20, 160º with internuclear separation, R, due to interference between and components, whose contributions have similar magnitudes at these N values.

Only component has R dependence: larger (1,2) are necessary for convergence of the TDCC amplitude than for particularly for large R.

By our analogy with H2+, main R-dependent

trends of the and amplitudes observed

in PDI of H2 are due to electron-ion ratherthan electron-electron interactions.

KER Effect in Perpendicular KER Effect in Perpendicular PlanePlane

Weber et al, Nature 431 437(2004)

ECS Vanroose et al, Science 310 1787 (2005)

E1 to E2, R, and “Frozen correlation” (12 = 90º)

We do not see a clear KER effect

in this geometry.

TDCC J. Colgan et al, J. Phys. B 40, 4391 (2007).

Photodouble Ionisation of HPhotodouble Ionisation of H22

e-

e-

H+

H+

h + H2 H+ + H+ + e1- + e2

-

Double electron Double electron escape in an axial escape in an axial

symmetric symmetric potentialpotential

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

3D Momentum Imaging Apparatus3D 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.

HH2 2 Coplanar FDCSCoplanar FDCS

E1= E2 = 12.5 2.5 eV, 1= 90 15°,

12= 20°, N= 20°, 1N = 45°

1 = 90o

d)c)

b)a)

N = 0oN =30o

N = 60oN = 90o

Electron - electron distribution does depend on molecular alignment!

Symmetric two ‘lobes’ for N = (a) 90 (), (d) 0 ().

Absolute reduces by ~4 from → orientations.

Gisselbrecht et alPhys Rev Lett 96 (2006) 153002

Weber et al Phys Rev Lett 92 (2004) 163001

What happens to FDCS when R changes?