vitaly kresin university of southern california los angeles long-range polarization interactions
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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.