Fragmentation of molecules: Franck-Condon model
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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 ;-)
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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
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... motivation - problem - principal task ...
e1
H+
H+ e2
80 eV h + H2 2 e- + 2 H+
Interaction / correlation
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Emission of two electrons from a single- and a double center - coulomb potential
HELIUM HYDROGEN MOLECULE
Fixed in space molecular axis breaks symmetry
>> ALIGNMENT <<
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Franck-Condon model:… the energy levels in the molecule (static)
photonenergy
bindingenergy
excess
ion energy
fragmentation kin. energy of the nuclei
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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...?
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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
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…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
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The COLTRIMS - setup… an imaging-system also for molecular fragmentation ?!
reco
il-io
n de
tect
orelectron-detector
electric field magnetic field
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...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
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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:
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The new detector: … multihit rulez …!?
HITECpowered by AOC & ROENTDEK
t < 5ns
t < 8nst < 100ns
t < 10ns
Hexanode:
DL80anode:
5200 lines computer code
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Coordinates/systems of reference … where does the action takes place ?
laboratory frame
internal scattering plane
2
1
2
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Energy distribution:… the kin. energy of the fragments after the photon absorption
balance:
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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.
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Kin. energy of the electrons in the final state: … which role does the molecule play …?
H2
e1
e2
Interference effect:
First maximum ?
e1
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Momentum distribution of the electrons :• A comparison ...
HELIUM
HYDROGEN MOLECULE
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Helium
Hydrogen m
olecule
He/H2
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H2
e1
Hydrogenmolecule
more details
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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
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And how about the recoil ions…?
H. Kossmann & V. SchmidtPRL (1989), 63, p. 2040-2043
= - 0.685
Let’s compare with the literature:
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Distribution of the polar angles... do we see correlated electron emission ?
1. The H
elium-atom
equal energysharing
E1 = E2
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unequal energysharing
e1 fast
e1
sl ow
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… let’s switch to the hydrogen-molecule
equal energysharing
H2
all orientations
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… just to get an overview :animated Triple Differential Cross Sections (TDCS)
Hyd
roge
n m
olec
ule
equal energysharing
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Helium atom and hydrogen molecule … a comparison of both systems:
H2
equal energysharing
Helium
Hydrogen m
olecule
all orientations
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… more movies : How does the distribution depend on the molecular orientation ?
Hyd
roge
n m
olec
ule
equal energysharing
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unequal energysharing
e1 = fast
Hydrogen molecule :
H2
all orientations
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… let’s get a more detailed insight Influence of the molecular orientation:
H2
e1equal energysharing
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unequal energysharing
H2
e1 fast
e1 slow
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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
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Let’s probe the molecule:…molecules illuminated from within...
equal energysharing
Hyd
roge
n m
olec
ule
electron-electron
interaction
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… go even deeper : let’s scan the coulomb explosion !
Hyd
roge
n m
olec
ule
equal energysharing
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… 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
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...goody…: “Alignment” even in atoms ?!
• linear polarized
• circular polarized
Hel
ium