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

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

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.

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.

Result: For clusters Quantum- mechanical treatment

[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)]

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 ?

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)

(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

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)]

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.]

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)]

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:

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

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.] ~

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

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…

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

Rydberg atoms α~n 7 !

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-

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.