Photo double ionization of H2

resp. of D2or

the correlated motion of electrons in a two center coulomb potential

• Fragmentation of molecules: Franck-Condon model• Experimental technique: Imaging of the momentum space• Dynamics of the electrons in a single and a two center potential

…if time permits: One more goody at the end ;-)

Co-workers & friends:

FRANKFURT:Th. WeberR. DörnerV. MergelA. CzaschO. JagutzkiM. WeckenbrockM. HattaßH. Schmidt-Böcking

KANSAS:L. CockeT. Ossipov

BERKELEY:M. Prior

FREIBURG:M. WalterJ. Briggs

MICHIGAN:A. Landers

... motivation - problem - principal task ...

e1

H+

H+ e2

80 eV h + H2 2 e- + 2 H+

Interaction / correlation

Emission of two electrons from a single- and a double center - coulomb potential

HELIUM HYDROGEN MOLECULE

Fixed in space molecular axis breaks symmetry

>> ALIGNMENT <<

Franck-Condon model:… the energy levels in the molecule (static)

photonenergy

bindingenergy

excess

ion energy

fragmentation kin. energy of the nuclei

how to describe a simple molecule ?... the pro’s and contra’s and the limitations ...

Heitler - London• solution of SE with sym. wave functions (including the spin)• consideration of all exchanges/interactions• establishment of a stabile H2 possible (error in binding energy = 1.4 eV)• description of wave function only very roughly

Linear Combination of Atomic Orbitals (LCAO)• description of two electrons in the field of a H2

+ ion• molecular orbital: Linear combination of atomic wave functions• good prediction of the electronic probability distribution in the molecule• error in binding energy is bigger than in H - L model

Born - Oppenheimer• separation of the electronic motion and the motion of the nuclei• adiabatic modulation of the electrons• simplified calculations; nuclei momenta set up along molecular axis• open question: How do these systems interact or couple...?

The “strange” nature of the molecule/atom … which effects play an important role ?

Electron emission for “equal energy-sharing”

e2e1 k k • Coulomb repulsion favorites

“back-to-back emission”

e2e1 k- k • selection rules:...electrons are fermions... complete wave function is antisymmetricrule of Hundt: Spin is antisym. r-/k-space has to be sym.

e1

e2

e1

e2

…more effects (interactions): coupling of the electrons to the binding system

HELIUM

Atom:The electronic two body systems vibrates with respect to the nucleus

HYDROGEN MOELCULE

Born-Oppenheimer:The electrons movein respect to the CM-system of the nuclei

Reality:A complex 4 body system vibrates in a correlated state

CM

The COLTRIMS - setup… an imaging-system also for molecular fragmentation ?!

reco

il-io

n de

tect

orelectron-detector

electric field magnetic field

...more features:

pulsed extraction for the recoil-ions:

electron double hit

recoil-iondouble hit 60 V/cm3 V/cm

4 solid angle

Magnetic field to guide the electrons • electrons up to 100 eV (for 10 Gauss)

Time of Flight and 2dim position• 3dim momentum vector

High resolution for 0 eV• < 10 meV electronic energy

Characteristics of the experiment … more facts :

Target = Deuterium (instead of Hydrogen)• 31.68 eV (31.752 eV for D2) dissociation energy• 2 • 9.4 eV = 18.8 eV energy of the Coulomb explosion 24.5 eV kin. sum energy of the electrons

Projectiles = Photons• 75 eV energy of the photons • linear polarized (99.5 %)

Imaging system• multi hit• pulsed recoil-ion extraction• data acquisition in “list mode”• two 80 mm MCP-detectors with delay line anode

experiment at the ALS

powered by:

The new detector: … multihit rulez …!?

HITECpowered by AOC & ROENTDEK

t < 5ns

t < 8nst < 100ns

t < 10ns

Hexanode:

DL80anode:

5200 lines computer code

Coordinates/systems of reference … where does the action takes place ?

laboratory frame

internal scattering plane

2

1

2

Energy distribution:… the kin. energy of the fragments after the photon absorption

balance:

Detection of the molecular fragments: … An image of the Coulomb explosion

• The pulsed recoil-ion spectrometer• …. and its consequences:

50.4 a.u.50.4 a.u.

Kin. energy of the electrons in the final state: … which role does the molecule play …?

H2

e1

e2

Interference effect:

First maximum ?

e1

Momentum distribution of the electrons :• A comparison ...

HELIUM

HYDROGEN MOLECULE

Helium

Hydrogen m

olecule

He/H2

H2

e1

Hydrogenmolecule

more details

Azimuthal angle of the electrons: ... the - parameter

d

d dE

EE

0 12

2

41 3 1

( )( ) cos

P.S.: valid near photo double ionization threshold

as a function of the alignment of the molecule ?!

Helium Hydrogen molecule

And how about the recoil ions…?

H. Kossmann & V. SchmidtPRL (1989), 63, p. 2040-2043

= - 0.685

Let’s compare with the literature:

Distribution of the polar angles... do we see correlated electron emission ?

1. The H

elium-atom

equal energysharing

E1 = E2

unequal energysharing

e1 fast

e1

sl ow

… let’s switch to the hydrogen-molecule

equal energysharing

H2

all orientations

… just to get an overview :animated Triple Differential Cross Sections (TDCS)

Hyd

roge

n m

olec

ule

equal energysharing

Helium atom and hydrogen molecule … a comparison of both systems:

H2

equal energysharing

Helium

Hydrogen m

olecule

all orientations

… more movies : How does the distribution depend on the molecular orientation ?

Hyd

roge

n m

olec

ule

equal energysharing

unequal energysharing

e1 = fast

Hydrogen molecule :

H2

all orientations

… let’s get a more detailed insight Influence of the molecular orientation:

H2

e1equal energysharing

unequal energysharing

H2

e1 fast

e1 slow

TRANSFER OF ANGULAR MOMENTUM:Coupling of the electrons to the molecule ?!

...which orientation is relevant ?

H2

e1

H2

e2

e1+2No angular mo-

mentum transfer

e1

equal energysharing

Let’s probe the molecule:…molecules illuminated from within...

equal energysharing

Hyd

roge

n m

olec

ule

electron-electron

interaction

… go even deeper : let’s scan the coulomb explosion !

Hyd

roge

n m

olec

ule

equal energysharing

… summary and future prospect What is still to do ? What comes next...?

…goody

…Future:• more D2 : What’s going on with circular polarized light ?• new experiment with HD (angular momentum transfer)/ ALS (Berkeley)• simple molecules in strong laser-fields/ Roskos (FFM)/ Corkum (Canada)

COLTRIMS: An imaging-system for molecules• pulsed extraction• multi hit capable detectors• 4 solid angle• snapshots of 2

2121

k,k,k,k DDee

Experimental results• Energy-sharing depends on the orientation of the molecule !?• Final state of the electrons in momentum space• Highly differential cross sections as a function of the molecular orientation

finish line

...goody…: “Alignment” even in atoms ?!

• linear polarized

• circular polarized

Hel

ium