Time-resolved analysis of large amplitude collective
motion inmetal clusters
Metal clusters : close « cousins » of nuclei
Time resolved : « Pump Probe » laser scenarios
Large amplitude collective motion : fission
M. Dinh(Toulouse), P. G. Reinhard (Erlangen), ES
Metal clusters and nuclei, theory and experimentsOptical response as preferred tool of analysis Pump probe scenarios
Coulomb repulsion
Neutrons
Scission
Collective variable
Pote
nti
al
Time resolved nuclear fission
Fission of a hot nucleus
1 source 2 sources
Measure i) number of emitted neutrons ii) angular distribution1 nucleus : « isotropic »2 nuclei : « anisotropic »
i) Fission time~ 10
-20 s
ii) Nuclear viscosity
Neutrons, Protons
Ions, Electrons
AtomicNuclei
Metal clusters
Sizes N < 300 3 < N < 105-7
ConstituentsFermions
Nuclei and metal clusters
Radius ~ r0,sN1/3 r0 ~ 1fm rs ~ 0.1-0.3 nm
r0,s relevant length/energy scales
Inter-constituents distance d ~ 1.5-2 r0,s
Fermi energy F = h2/2m (3)2/3 1/r0,s2
~ 2/ kF ~ r0,s
Strongly quantum systems
Long de Broglie wavelength (ground state)
Finite Fermi liquid droplets
Fermi gas estimate
Basic theory of nuclei and metal clusters
▶ Nuclei Nucleon-nucleon interaction between 1-300… nucleons
▶ Metal clusters Binding (delocalized electrons) between 1-10000… atoms
MEAN
FIELD
Shells, collective motion (resonances, fission…)
…82502820
82
…138
924020
82
Free nucleons Nucleons IN nucleus Nucleus
ClusterAtom IN clusterFree atom
Time Dependent Density Functional Theory (TDDFT)
Ensemble of orbitals (1 electron) / no correlation
One body density
Effective mean field theory (Kohn-Sham)
Model of metal clusters
Explicit ions via pseudo potentials
Detail of structure + ionic dynamics
Ions
Electrons
Kohn-Sham potential Ions + ext.
Local Density Approximation (LDA)
(+ Self Interaction Corrections)
Semi classical theory possible TDLDA Vlasov
Exch. + Corr. Hartree
Plasmon (collect. oscill.
electrons/ions)
Ionic times
Electron-electron collis.
Electron evaporation
A few time scales
Units : microscopic time in rs,0/vF - temperature in F
Alkalines (Li, Na, K, Rb, Cs)
1 fs
100 fs
10 fs
Nuclei
10 fm/c
1000 fm/c
100 fm/c
Experimental signals frommetal clusters
Lase
r pol
ariza
tion
Electron energy
Photoelectrons
Yie
ld
( )
d/dE
Photoabsorption
Yie
ld
Photon energy
Optical responseDeformations
AbundancesMagic numbers
Ionization potentialsSingle particle energies
Mass spectrumY
ield
Ion « mass » (m/q)
h
electrons
cluster
Experimental signals frommetal clusters
Lase
r pol
ariza
tion
Electron energy
Photoelectrons
Yie
ld
( )
d/dE
Photoabsorption
Yie
ld
Photon energy
Optical responseDeformations
AbundancesMagic numbers
Ionization potentialsSingle particle energies
Mass spectrumY
ield
Ion « mass » (m/q)
h
electrons
cluster
Optical response : deformation effects
Deformation vs
Optical response splitting
Optical follow up of fission …?
Collective motion of electrons / ions
K12++ K3
+ + K9+
What about fission ?
Experimental signals frommetal clusters
Lase
r pol
ariza
tion
Electron energy
Photoelectrons
Yie
ld
( )
d/dE
Photoabsorption
Yie
ld
Photon energy
Optical responseDeformations
AbundancesMagic numbers
Ionization potentialsSingle particle energies
Mass spectrumY
ield
Ion « mass » (m/q)
h
electrons
cluster
Experimental signals frommetal clusters
Lase
r pol
ariza
tion
Electron energy
Photoelectrons
Yie
ld
d/dE
Photoabsorption
Yie
ld
Photon energy
AbundancesMagic numbers
Ionization potentialsSingle particle energies
Mass spectrumY
ield
Ion « mass » (m/q)
h
electrons
cluster
Ionization
Yie
ld
Photon energy
Experimental signals frommetal clusters
Lase
r pol
ariza
tion
Electron energy
Photoelectrons
Yie
ld
d/dE
Photoabsorption
Yie
ld
Photon energy
AbundancesMagic numbers
Ionization potentialsSingle particle energies
Mass spectrumY
ield
Ion « mass » (m/q)
h
electrons
cluster
Ionization
Yie
ld
Photon energy
Experimental signals frommetal clusters
Lase
r pol
ariza
tion
Electron energy
Photoelectrons
Yie
ld
d/dE
Photoabsorption
Yie
ld
Photon energy
AbundancesMagic numbers
Ionization potentialsSingle particle energies
Mass spectrumY
ield
Ion « mass » (m/q)
h
electrons
cluster
Ionization
Yie
ld
Photon energy
Experimental signals frommetal clusters
Lase
r pol
ariza
tion
Electron energy
Photoelectrons
Yie
ld
d/dE
Photoabsorption
Yie
ld
Photon energy
AbundancesMagic numbers
Ionization potentialsSingle particle energies
Mass spectrumY
ield
Ion « mass » (m/q)
h
electrons
cluster
Ionization
Yie
ld
Photon energy
Pump – probe for fission : principle
Probe
Ionization
Pump
Time / Delay
Pla
smon
high
low
2 parameters :
delay AND frequency
/ Io
niz
.
Mie
Dinh et al, 2004
Pump – probe for fission : example
Na14 + Na143+
Na6+
+ Na82+
Access to fission time Fission dynamics Viscosity…
▶ Fast developping field of cluster dynamics
Linear and semi linear domain Ex: optical response, photoelectrons spectra …
Clusters in intense laser field Ex: pump/probe dynamics, Coulomb explosion…
Relations to other fields Ex: embedded/deposited clusters, biological systems …
Some conclusions and perspectives
▶ Dynamics of metal clusters
Similarities between metal clusters and nuclei
Finite Fermi liquid droplets, mean-field approaches …
Collective modes
Optical response as a tool of analysis of structure and dynamics
Pump probe analysis of fission