Time-resolved analysis of large amplitude collective motion in metal 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 experiments Optical response as preferred tool of analysis Pump probe scenarios

Coulomb repulsion Neutrons Scission Collective variable Potential Time resolved nuclear fission Fission of a hot nucleus 1 source2 sources Measure i) number of emitted neutrons ii) angular distribution 1 nucleus : « isotropic » 2 nuclei : « anisotropic » i ) Fission time  ~ s ii) Nuclear viscosity

Neutrons, Protons Ions, Electrons Atomic Nuclei Metal clusters SizesN < 3003 < N < Constituents Fermions Nuclei and metal clusters Radius ~ r 0,s N 1/3 r 0 ~ 1fmr s ~ nm  r 0,s relevant length/energy scales  Inter-constituents distance d ~ r 0,s  Fermi energy  F = h 2 /2m (3  ) 2/3 1/r 0,s 2  ~ 2  / k F ~  r 0,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 … atoms MEANFIELDMEANFIELD Shells, collective motion (resonances, fission…) … … Free nucleonsNucleons IN nucleusNucleus ClusterAtom IN cluster Free 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 potentialIons + 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 r s,0 /v F - 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 from metal clusters Laser polarization Electron energy Photoelectrons Yield  (  ) d  /dE Photoabsorption Yield Photon energy Optical response Deformations Abundances Magic numbers Ionization potentials Single particle energies Mass spectrum Yield Ion « mass » (m/q)  h electrons cluster

Experimental signals from metal clusters Laser polarization Electron energy Photoelectrons Yield  (  ) d  /dE Photoabsorption Yield Photon energy Optical response Deformations Abundances Magic numbers Ionization potentials Single particle energies Mass spectrum Yield 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 K  K K 9 + What about fission ? 

Experimental signals from metal clusters Laser polarization Electron energy Photoelectrons Yield  (  ) d  /dE Photoabsorption Yield Photon energy Optical response Deformations Abundances Magic numbers Ionization potentials Single particle energies Mass spectrum Yield Ion « mass » (m/q)  h electrons cluster

Experimental signals from metal clusters Laser polarization Electron energy Photoelectrons Yield d  /dE Photoabsorption Yield Photon energy Abundances Magic numbers Ionization potentials Single particle energies Mass spectrum Yield Ion « mass » (m/q)  h electrons cluster Ionization Yield Photon energy

Experimental signals from metal clusters Laser polarization Electron energy Photoelectrons Yield d  /dE Photoabsorption Yield Photon energy Abundances Magic numbers Ionization potentials Single particle energies Mass spectrum Yield Ion « mass » (m/q)  h electrons cluster Ionization Yield Photon energy  

Experimental signals from metal clusters Laser polarization Electron energy Photoelectrons Yield d  /dE Photoabsorption Yield Photon energy Abundances Magic numbers Ionization potentials Single particle energies Mass spectrum Yield Ion « mass » (m/q)  h electrons cluster Ionization Yield Photon energy 

Experimental signals from metal clusters Laser polarization Electron energy Photoelectrons Yield d  /dE Photoabsorption Yield Photon energy Abundances Magic numbers Ionization potentials Single particle energies Mass spectrum Yield Ion « mass » (m/q)  h electrons cluster Ionization Yield Photon energy 

Pump – probe for fission : principle Probe ⃕ Ionization Pump Time / Delay Plasmon high  low  2 parameters : delay AND frequency  / Ioniz. Mie

Dinh et al, 2004 Pump – probe for fission : example Na 14 +   Na    Na Na 8 2+ 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