Diapositiva 1

1
Cluster Magic Numbers
2
Recent highly accurate diffusion Monte Carlo
(T0) calculation rules out existence of magic
numbers due to stabilities
Cluster Number Size N
R. Guardiola,O. Kornilov, J. Navarro and J. P.
Toennies, J. Chem Phys, 2006
3
HeN
from J. P. Toennies
He2
4
Magic Numbers in Large 4He Clusters
2nd cl
5
26
Bruehl et al Phys. Rev. Lett. 92 185301 (2004)
6
To explain Magic numbers recall that clusters are
formed in early hot stages of the expansion
The K have sharp peaks whenever the N cluster has
a new excited state. Then both ? and K will
increase. But for the N1 cluster both ? will be
about the same and K will fall back.
from J. P. Toennies
7
Single-particle excitation theory of evaporation
and cluster stability
evaporation probability
Magic numbers!
8
Thermalization via evaporation (DFT)
2006
9
Binding energy per atom
Barranco et al (2006)
10
Atomic radial distributions
4Hen
3Hen
Barranco et al (2006)
11
one-particle states
Barranco et al (2006)
12
3He in 4Hen
l
Barranco et al (2006)
13
4He / 3He phase separation
Barranco et al (2006)
14
Stable 4He 3He mixed clusters
Barranco et al (2006)
15
Electron bubbles in 4He droplets

• R ? 1.7 nm
• ? ? 0.48 dyn/cm
• E ? 0.26 eV

dynamics?
end of lecture 7
16
In quest of 4He supersolid
a work with J. Peter Toennies (MPI-DSO
Göttingen), Franco Dalfovo (Uni Trento), Robert
Grisenti Manuel Käsz (Uni Frankfurt), Pablo
Nieto (Automoma Madrid)
? History of a conjecture BEC in a quantum
solid ?
? 4He vacuum expansion from low -T sources
? The Geyser effect in solid 4He vacuum
expansion
? Vacancy diffusivity and solid 4He Poisson
ratio
? Bernoulli flow of a nominal 4He solid
? Suppression of flow anomalies by 1 3He
Firenze 2005 - 1
17
History of a conjecture BEC in a quantum solid?
1969 Andreev Lifshitz
1970 Chester ? Leggett
1977 Greywall
2004 Kim Chan
2004 Ceperley Bernu
Firenze 2005 - 2
18
Kim Chan 2004
measurements of non-classical rotational inertia
Firenze 2005 - 3
19
Kim Chan
no trend ?
Firenze 2005 - 4
20
Galli Reatto 2001
(a) no ground state vacancies but only thermal
vacancies
(b-d) ground state thermal vacancies (for
different vacancy formation energies)
what about injected (non-equilibrium) vacancies?
Firenze 2005 - 5
21
Vacuum expansion of solid 4He
Firenze 2005 - 6
22
continuity
Bernoulli
Firenze 2005 - 7
23
4He phase diagram
Firenze 2005 - 8
24
The Geyser effect
25
Period vs. T at constant pressure
40.7 bar
35.0 bar
32.0 bar
26
Period versus P0 at constant temperature
Bernoulli ?
Firenze 2005 - 11
27
?P? ? information on Poisson ratio of solid 4He
Ps/l ? information on dynamical processes
inside solid 4He
Firenze 2005 - 12
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(No Transcript)
29
(No Transcript)
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Poisson ratio of solid 4He
Firenze 2005 - 13
31
Firenze 2005 - 14
motion of dislocation motion of vacancies
Plastic flow
dominant in solid He (high diffusivity!)
vacancy injection at s/l interface sweeping by
pressure gradient
Polturak et al experiment (PRL 1998)
32
Vacancy drift
solid 4He ? p-type SC
Firenze 2005 - 15
33
The vacancy mechanism
A0
L
As/l
Virtual volume to be filled by vacancies in the
time L/u0
u0
?Va V - Va Va 35.15 Å3 (atomic
volume) V ? 0.45Va (vacancy isobaric
formation volume)
Firenze 2005 - 16
34
Geyser mechanism
accumulation of vacancies up to a critical
concentration Xc
diffusion
COLLAPSE!
drift diffusion
Pressure
0
L
distance from s/l interface
vacancy bleaching resetting of initial
conditions
35
Data on vacancy diffusivity and concentration in
4He
36
Firenze 2005 - 18
Transport theory
Generation function
surface generation velocity
37
Firenze 2005 - 19
Solution for L??
Excess vacancies
Current at the s/l interface (x 0) due to
excess vacancies
? surface depletion layer thickness
38
reduced form

• the shape of the current depends on 2 parameters
  (?, ?)
• the time scale implies another parameter (?v)
• the ratio of the oscillation amplitude to the
  constant
• background is measured by X0Vauv/u0 and is of
  the order
• of a few percent (as seen in experiment)
• fitting ?

39
Dv 1.310-5 cm2/s ?v 5.41010 s/g uv
2.010-3 cm/s us 2uv ?s 60 s ?v 13
s ? 10.7 s ?0 82 s
Theory vs. experiment
P0 31 bar T0 1.74 K best fit with ? 4
? 1.214
40
large ? means fast recombination
better fits are obtained with finite L (one more
parameter)
41
Period ?0 vs. diffusivity
finite L ? approximate solution by Greens
function method
Xc critical concentration
Firenze 2005 - 23
42
Firenze 2005 - 24
43
Anomalies below the ? point!
44
a sharp transition in the flow regime at 1.58 K !
45
Effects of 3He on the anomalies
from R. Richardson et al
Firenze 2005 - 27
46
small amounts of 3He remove the anomaly!
47
normal behaviour induced by less than 1 3He !
48
normal behaviour induced by less than 1 3He !
49
CONCLUSIONS

• The geyser effect indicates (via Bernoullis law)
  an oscillation of the s/l (quasi-)equilibrium
  pressure at a given T vacancy concentration
  appears to be the only system variable which can
  give such effect.

2. Below the ? temperature flow anomalies are
observed (a) The most dramatic one is
the occurrence of a Bernoulli flow
corresponding to pressures gt Pm, at which
4He should be solid. (b) Below 1.58 K a
sharp drop of the geyser period signals a
dramatic change in the flow
properties of solid 4He. These
anomalies, suggesting superflow conditions, are
attributed to injected excess vacancies,
and agree with Galli and Reatto predictions
for a vacancy-induced (Andreev-Lifshitz)
supersolid phase.

• A 3He concentration of 0.1 is shown to suppress
  the flow anomalies, suggesting a quantum nature
  of the superflow.

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There is no end to this wonderful world
of experimental discovery and
mental constructions of
reality as new facts become known.
That is why physicists have more fun
than most people
Miklos Gyulassy, 2004
end of lecture 8