1. Vitaly Kresin University of Southern California Los Angeles Long-range polarization interactions

2. Induced electric dipole moment Thanks to their mobile electrons, metal clusters respond to an external field with a high polarizability Polarizability of metal clusters exceeds that of a sphere of bulk metal R3R3

3. A point charge near an isolated cluster polarizes it, and is then attracted to the resulting dipole “Polarization potential”  [e - attracted by its own image charge] The electron may even be captured by this field.

4. Centrifugal barrier Classical trajectory Particles with impact parameters below a certain value spiral into the center of force and are captured.  Langevin [1905] capture cross section Particle will “fall to the center” when E exceeds the height of the effective barrier.

5. Result: For clusters Quantum- mechanical treatment

7. [V.Kasperovich et al. (1999,2000)] Total anion yield Low-energy capture data are in good agreement with the Langevin picture High polarizabilities  large cross sections Cross section (Å 2 ) (Fullerenes are a case of a “rigid” system with state- specific sticking probabilities) polarization selection rules [R.Abouaf et al. (1997), V.Kasperovich et al. (2001), M. Lezius (2003)]

8. What is the fate of the electron after it enters the cluster? Will the anions have maximal intensities at the magic numbers of the neutral beam – since there is a large population of these “parents” – or will they somehow reorganize into the shell sequence ?

9. The magic numbers are lowered by one; the change of intensity patterns in between shell closings is not a simple shift by one electron number Experimental results (  E e  =0.1 eV)

10. (1) An approaching electron polarizes the cluster… (2) … is captured… Steps involved in anion formation (3) … and deposits E= KE + EA into the cluster This energy is rapidly randomized → the cluster heats up (4) Hot clusters evaporate atoms and dimers The evaporation rate is exponentially sensitive to the cluster temperature and dissociation energy

11. No adjustable parameters The measured Na N - abundance distribution is a product of evaporation cascades from clusters “reheated” by the energy deposited by the e -. [R.Rabinovitch et al. (2008,2010)]

12. Multiple electron attachment: “Electron bath” in a Penning trap ClusterTrap experimental arrangement (1) cluster source, (2) transfer section, (3) electron gun, (4) superconducting magnet with Penning trap, (5) ToF drift section, and (6) ion detector. [L. Schweikhard et al.]

13. Photoionization, evaporation, fission: The long-range polarization potential modifies the energy barriers and affects the final state of the emitted particle. E.Wigner(1948) T.F.O’Malley(1965) Inverse effects: Polarization forces in emission processes Example: Threshold photodetachment of cold C 60 (below the Langevin regime) [L.-S.Wang et al. (1991)]

14. A A+A+ e-e- E E-IP-   + Thermionic emission: electron evaporation Electron emission by hot W N - clusters Polarizable cluster: Bulk surface: sticking coefficient=1 [J. C. Pinaré et al. (1988)] Simple Boltzmann:

15. However: more recent W N - thermionic emission data [B.Concina et al. (2010)] Sticking coefficients << 1? Shape effects?

16. Electron capture by a permanent electric dipole A permanent dipole can support a bound state only if d>1.635 Debye [H 2 O=1.85 D] There are a number of observations of “dipole-bound states” [D.C.Clary, I.I.Fabrikant] … but no direct measurements of capture cross sections [K. Bowen et al.] ~

17. Origin of van der Waals force: attraction between virtual dipoles Long-range forces between neutral particles - van der Waals interaction From 2 nd order perturbation theory one finds that the zero-point energy of the system is lowered by

18. If the dipole strengths of A and B lie within a narrow range, this simplifies to the “London dispersion formula” This attraction is a purely quantum effect [Science, June 2000] Interaction coefficient  (  )=dipole dynamic polarizability. [Fritz London,1930] “London forces” “Dispersion forces” …and yet…

20. pressure ln(beam intensity) slope  cross section  C 6 Na n + C 60 [V.K. et al., 1998]  80 Å 3

22. Rydberg atoms α~n 7 !

23. Retarded interactions - Casimir forces Large distance between particles: propagation time of electromagnetic signals between particles > charge oscillation period r/c > ν -1 r > λ AB -A pronounced relativistic effect even when A and B are not moving at relativistic speeds. - An “everyday” manifestation of QED. e-e-

24. Summary Polarizable particles exhibit strong long-range interactions: polarization (image charge) van der Waals (virtual dipole-dipole, quantum effect) Casimir (retardation: finite speed of light) These interactions can be studied by beam scattering experiments (as well as using scanning microscopy, cantilevers, etc.) There is a bridge between spectroscopic data and the study of long-range forces The long-range potentials have a strong influence on capture, emission, and evaporation phenomena.