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 Lavollé,
M. S. Pindzola, and A Huetz

2. Photodouble Ionisation of H2
h + H2  H+ + H+ + e1- + e2- e- H+
Motivation:
Fundamental theoretical interest: Correlation and Dynamics
Angular distributions are sensitive probe (amplitude and phase)
Development of sensitive imaging techniques (++ ~ cm2)
Accurate test for theory in a ‘simple’ system
Extension of theory and experiment to more complex systems
4-body dynamics in an axial symmetric potential

3. Fast ‘Coulomb Explosion’
Ions escape much faster
than molecular rotation.
Detecting (just) one ion
gives: ‘fixed-in-space’
molecule. e
 Fully differential Cross Sections (FDCS)
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).

4. Photodouble Ionisation of H2
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.

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

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

7. H2 Coplanar FDCS What happens to FDCS when R changes?
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 al
Phys Rev Lett 96 (2006)
Weber et al
Phys Rev Lett 92 (2004)
What happens to FDCS when R changes?
E1= E2 = 12.5  2.5 eV, q1= 90  15°,
f12=  20°, DqN=  20°, f1N =  45°

8. Coplanar FDCS “KER Effect”: q1 = 90º
R ~ 1.6a R ~ 1.2a0
Coplanar FDCS “KER Effect”: q1 = 90º
‘Pure’ P component shows no
KER effect.
Dramatic
R-dependence
at qN  20º,
especially at
large R where
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

9. Coplanar FDCS “KER Effect” q1 = 0º TDCC bandwidth averaged FDCS
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

10. Coplanar FDCS “KER Effect” q1 = 60º TDCC bandwidth averaged FDCS
R ~ 1.6a 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)
TDCC bandwidth averaged FDCS
TDCC unaveraged FDCS

11. 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.

12. 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.
Horner et al
Phys Rev Lett 98, (2007).
Reddish et al
Phys Rev Lett (2008)
Colgan et al,
J Phys B 41, (2008).

13. Photoionisation of H2+. su Final A strong cancellation exists
State
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.
pu Final State
The photoelectron angular distribution,
with respect to the molecular axis.
Colgan et al,
J Phys B 41, (2008).

14. 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 S amplitude than for P - particularly for large R. (Similar trends are found in H2+.)
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.

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. 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 (2005)
TDCC J. Colgan et al,
J. Phys. B 40, 4391 (2007).
Weber et al, Nature
(2004)