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

p E

Polarizability of metal clusters exceeds that of a sphere of bulk metal

0 10 20 30 40

Cluster size (N)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

NaN

0/R

3

R3

A point charge near an isolated cluster polarizes it, and is then attracted to the resulting dipole

2cluster e

ep E

r

12

12 2

2

42

dipolee clusterV e

p

r re

e

“Polarization potential” [e- attracted by its own image charge]

-e

-e

N a n

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

2 22L

e

E

Particle will “fall to the center” when E exceeds the height of the effective barrier.

Result:

For clusters

Quantum-mechanical treatment

/ /( )~ iqz A iqr A

r

fe e

r

incoming + spherical wave

/

0~ ( )iA r

re g

sink at origin

(0)

2

capture

L

E

( several meV)capture LE

[V.Kasperovich et al. (1999,2000)]

0.0 0.5 1.0 1.5 2.0 2.5 3.0Adjusted Electron Energy (eV)

0.0

0.4

0.8

1.2

Nor

mal

ized

Cro

ss S

ectio

n

ExperimentLangevin Capture

Tota

l ani

on y

ield

2 22( )

eE

E

Langevin

Low-energy capture data are in goodagreement with the Langevin picture

High polarizabilities large cross sections

Cro

ss s

ectio

n (Å

2 )(Fullerenes are a case of a “rigid” system with state-specific sticking probabilities)

polarizationselection rules

[R.Abouaf et al. (1997), V.Kasperovich et al. (2001), M. Lezius (2003)]

0 40 80 120 Na n Cluster Size

40

58

92

138

8

20

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” –- -

20 40(Na ,Na ,...)

or will they somehow reorganize into the shell sequence ? - -19 39(Na ,Na ,...)

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 (Ee=0.1 eV)

(1) An approaching electron polarizes the cluster…

(2) … is captured…

-e

-e

Na n

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

- / NN BN

D k Tr A e

No adjustable parameters

The measured NaN- abundance distribution is a

product of evaporation cascades from clusters “reheated” by the energy deposited by the e-.

[R.Rabinovitch et al. (2008,2010)]

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Intensity

Cluster anion size, N

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.]

243[1 ln ]k k k

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 C60 (below the Langevin regime)

[L.-S.Wang et al. (1991)]

A A+ e-

E E-IP-+

Thermionic emission: electron evaporation

/( )( ) captukT

reW e

Electron emission by hot WN- clusters

/( ) kTW e Langevin :Polarizable cluster:

/( ) kTW e

Bulk surface: sticking coefficient=1

[J. C. Pinaré et al. (1988)]

/( ) kTW e Simple Boltzmann:

However: more recent WN- thermionic emission data

/kinetic energy ( ) Bk TW e γ

[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 [H2O=1.85 D]

There are a number of observations of “dipole-bound states”

capture

d

E

[D.C.Clary, I.I.Fabrikant]

… but no direct measurements of capture cross sections

[K. Bowen et al.]

~

R

Long-range (van der Waals)potential: -C6/r

6

Origin of van der Waals force: attraction between virtual dipoles

Long-range forces between neutral particles - van der Waals interaction

From 2nd order perturbation theory one finds that the zero-point energy of the system is lowered by

66

" "CU

r

632

A BAB A B

A BC

If the dipole strengths of A and B lie within a narrowrange, this simplifies to the “London dispersion formula”

This attraction is a purely quantum effect

Interaction coefficient

()=dipole dynamic polarizability.

[Fritz London,1930] “London forces”“Dispersion forces”

…and yet…

pressure

ln(b

ea

m in

ten

sity

)

slope cross section C6

Nan + C60

[V.K. et al., 1998]0 10 20 30 40

Cluster size (N)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 /

R3

NaN

1.9 2.2 2.5 2.8

Photon Energy (eV)

0

4

8

12

16

Cro

ss S

ectio

n (Å

2)

Na8

80 Å3

60

60

606

3

2n

n

n

Na C

Na CNa CC

0 2 4 6 8 10 12 14 16 18 20

Nan cluster size

0

50 000

100 000

150 000

200 000

C6

coef

ficie

nt (

a.u.

)Dispersion TheoryFrom measured c ross sec t ions

0 2 4 6 8 10 12 14 16 18 20

Nan cluster size

0

1000

2000

3000

4000

5000

6000

7000

Ce

nte

r-o

f-m

ass

cro

ss s

ect

ion

(Å

2 ) Nan+C60

Hard-sphere cross section

Rydberg atoms α~n7 !

Retarded interactions - Casimir forces

Large distance between particles: propagation time of electromagnetic signals between particles > charge oscillation period

r/c > ν-1

r > λ

23

4

A BAB

rcV

r

7

A

B

- A pronounced relativistic effect even when A and B are not moving at relativistic speeds.

- An “everyday” manifestation of QED.

e-

211

4rem

eV

rc

5

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.