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