Small fermionic systems : the common methods and challenges Nuclei Metal clusters (alkalines) Helium 3 droplets Structure and Dynamics Experiments and Theory J. Navarro (Valencia), P. G. Reinhard (Erlangen), ES (Toulouse) + survey (nuclear + He droplets + cluster physicists)

Nuclei, Helium, Metals … Atomic Nuclei Helium droplets Metal clusters Constituents Fermions Neutrons, Protons 3He atoms (2p, 1n, 2e) Ions, Electrons Nucl.-Nucl. Van d. Waals Coulomb Interactions Sizes N < 300 20 < N 3 < N < 105-7 Radius ~ r0,sN1/3 r0 ~ 1fm rs ~ 0.1-0.3 nm r0 ~ 0.25 nm

Some common properties Dense systems with strong Pauli Atomic Nuclei Helium droplets Metal clusters  r0,s provides the relevant length/energy scales Fermi gas estimate r = kF3/ (3p2) = 4/(3p r0,s3)  Inter-constituents distance d ~ 1.5-2 r0,s  Fermi energy eF = h2/2m (3p/4)2/3 1/r0,s2  Long de Broglie wavelength (ground state) lB ~ 2p/ kF ~ p r0,s Quantum mean field

Mean-field : a (possible) common theory Effective mean field theory (1-body : nucleons/electrons/atoms) Nuclei TDHF Density Functional Theory Clusters Helium Foundation of extended mean field theories (VUU)

From one field to the next … Nuclei Structure Dynamics Experim. YES Theory Clusters Structure Dynamics Experim. YES NO  YES Theory Helium Structure Dynamics Experim. NO  YES NO Theory YES Not yet

Multi scale dynamics Nuclei Alkalines (Li, Na, K, Rb, Cs)  Plasmon (collect. oscill. electrons/ions)  Ionic times  Electron-electron collis.  Electron evaporation 1 fs 100 fs 10 fs 10 fm/c 1000 fm/c 100 fm/c Units : microscopic time in rs,0/vF - temperature in eF

from irradiated clusters Electron emission from irradiated clusters ds/dE Electron energy Photoelectrons Yield Laser polarization   Ionization Yield Photon energy 1/ PES: 1-photon then 2-photon processes 2/ ang 3/ Nesc / animation as given + move ions    Ekin s ( w )

Photoelectron spectra (multiphoton) ds/dE Pohl et al, JPB 2004 Exp. Freiburg w = 0.22 Ry FWHM = 34 fs 1s 1p w Electron energy Photoelectrons Yield w  Multiphoton regime  Evolution with laser intensity ?  Towards exponential spectra An exponential spectrum is not necessarily thermal. Caution with temp. HERE: misleading Check multiphoton regime for Freiburg exp + our calculations / check with PG Add schem fig. from slide 3 / multiphoton Role of dissipation ?

from irradiated clusters Electron emission from irradiated clusters ds/dE Photoelectrons Electron energy Yield Laser polarization ds/dW Ionization Yield Angle Angular distrib. Yield 1/ PES: 1-photon then 2-photon processes 2/ ang 3/ Nesc / animation as given + move ions Photon energy s ( w ) Laser

Angular distributions of photoelectrons Laser polarization Laser polar. Directed emission Laser Polarization Na+41  Intensity Isotropic emission Pure mean field: Directed emission Mean-field + colls : Isotropic emission Exp. W4-, Lyon,2001 Giglio et al, PRA 2003

from irradiated clusters Electron emission from irradiated clusters ds/dE Photoelectrons Yield Towards dns/… d2s/dEdW, d2s/dW1dW2 … Electron energy Laser polarization ds/dW Ionization Yield Angular distrib. 1/ PES: 1-photon then 2-photon processes 2/ ang 3/ Nesc / animation as given + move ions Yield Photon energy Angle s ( w ) Laser Laser

Some conclusions and perspectives A few basic questions (inquiry) 1/ Phase transitions in finite systems (thermodynamics, fragmentation) See dedicated talk 2/ Density Functional Theory and Time Dependent DFT, phenomenological vs microscopic models Theoretical methods Many body problem Experimental methods Correlations Multidetetors 3/ Energetic processes (dynamical correlations, Molecular Dynamics) Theoretical methods Correlations Observables Nuclear towards cluster physics

from irradiated clusters Electron emission from irradiated clusters ds/dE Photoelectrons Yield Optical Response Yield Electron energy Laser polarization ds/dW Ionization Yield Angular distrib. 1/ PES: 1-photon then 2-photon processes 2/ ang 3/ Nesc / animation as given + move ions Yield Photon energy Angle s ( w ) Laser Laser

from irradiated clusters Electron emission from irradiated clusters ds/dE Photoelectrons Yield Optical Response Yield w Electron energy w Laser polarization ds/dW Ionization Yield Angular distrib. 1/ PES: 1-photon then 2-photon processes 2/ ang 3/ Nesc / animation as given + move ions Yield Photon energy Angle s ( w ) Laser Laser

from irradiated clusters Electron emission from irradiated clusters ds/dE Photoelectrons Yield w Yield Optical Response Electron energy Laser polarization ds/dW Ionization Yield Angular distrib. 1/ PES: 1-photon then 2-photon processes 2/ ang 3/ Nesc / animation as given + move ions Yield Photon energy Angle s ( w ) Laser Laser

from irradiated clusters Electron emission from irradiated clusters ds/dE Photoelectrons Yield w Yield Optical Response Electron energy Laser polarization ds/dW Ionization Yield Angular distrib. 1/ PES: 1-photon then 2-photon processes 2/ ang 3/ Nesc / animation as given + move ions Yield Photon energy Angle s ( w ) Laser Laser

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

Pump – probe for fission : example Dinh et al, 2004 Na14 + w  Na143+ hn hn Na6+ + Na82+ hn Access to fission time Fission dynamics Viscosity…