lecture 5: helium droplets grebenev, toennies & vilesov science 279, 2083 (1998)
TRANSCRIPT
Lecture 5: Helium Droplets
Grebenev, Toennies & VilesovScience 279, 2083 (1998)
Helium Droplets
T0 ≤ 35 KP0 ≥ 20 bar
Droplets are cooledby evaporation to=0.38 K (4He),=0.15 K (3He)
Brink and Stringari,Z. Phys. D 15, 257 (1990)
Some Microscopic Manifestations of Superfluidity
1. Free Rotations of Molecules
2. The Roton Gap (Phonon Wing)
3. Anomalously Small Moments of Inertia
How many atoms are needed for superfluidity?
How will this number depend on the observed property?
2002-03-01-T3a-Ka
Low temp.nozzle
Scatteringchamber
Photon absorptionand
Evaporation
Ionizer
Massspectrometer
Mirror
La
ser
be
am
T0
0
-
-
v
v
20 K
20 bar
d=5 mm
P
Apparatus for Laser Depletion Spectoscopy
Mass.Spect.Signal
Laser Frequency n
none IR photon evaporates
4
DN ~ ~~ ~h
7.2K-7%
400 atoms
For an N=6000 He dropletthis leads to a 7%signal depletion
+
Laser Depletion Spectroscopy
Sharp spectral features indicate that the molecule rotates without friction
The closer spacing of the lines indicates a factor 2.7 largermoment of inertia
Is this a new microscopic manifestation of superfluidity?
OCS
Since IR absorption lines are so sharp, what about electronic transitions?
The Phase Diagram and Phonons in Liquid 4He
The experimental sideband reflects the DOS of Elementary Excitations
rotational lines
Large 4He Clusters: 100< N< 5000
Small 4He Clusters: N< 100
Two Methods Used to Produce Mixed 4He/3He Droplets
Aggregation of 4He Atoms Around an OCS Molecule Inside a 3He Droplet
3He
OCS surrounded by a cage of 4He
IR Spectra of OCS in 3He Droplets
with Increasing Numbers of 4He
Atoms
~ 60 He atoms are needed to restore free rotations:
Number needed for superfluidity? Grebenev Toennies and Vilesov Science, 279, 2083 (1998)
Wavenumber [cm-1]
Rel
ativ
e D
eple
tion
[%]
The Appearance of a Phonon Wing Heralds the Opening up of the Roton Gap
Pörtner, Toennies and Vilesov, in preparation
According to this Criterium 90 4He Atoms are needed for Superfluidity!
maxon
roton
rotons: in 4He only
maxons: in both 4He and 3He
SEARCH FOR SUPERFLUIDITY INPARA- H ( pH ) CLUSTERS2 2
(Ginzburg and Sobyanin, JETP Lett. , 242 (1972))15
pH has no total nuclear spin, I = 0at T = 0 all molecules are in j = 0
pH are spinless Bosons like He indistinguishable
The superfluid transition temperature is given by
T = n 3.31 g Mk
c
T = 6.0 K c
22/3
2/3B
for pH g = 12
but H solidifies at
T = 13.8 K !m
2
2
2
T = 1.4 K
For ortho - H (oH ), I = 1 and j = 1, g = 9. 2 2
c
Para-Hydrogen Has Long Been A Candidate for Superfluidity
Bose condensed
Non-condensed
The reduced coordinationIn small droplets favorssuperfluid response
Decrease in the moment of inertia indicatessuperfluidity
5.
24 3
2001-06-13-t2-kus
4.
3.
2.
1.OCS in largemixed droplet
Capture of firstH molecule2
Capture of secondH molecule2
H molecule movesfreely in liq. He andbinds at OCS replacinga He atom
24
After many H capturesOCS is surrounded by rings of H
2
2
H2
Aggregation of p-H2 molecules around an OCS molecule inside a
mixed 4He/3He droplet
(5-6 H2)
(3-4 H2)
(5-6 H2)
Average Moments of Inertia
Ia Ib Ic
840 1590 1590
55 1590 1590
880 2500 2500
This is the first evidencefor superfluidity of p-H2
In 1959 Migdal applied BCS theory (1957) to explain superfluidity in nuclei
end of lecture 5
Lecture 6: Helium clusters
he-he pot
The large zero point energy also affects the dimer
The large zero-point energy makes liquid Helium the most tenuous of all liquids
About 10 years ago it was not known whether the He dimer had a bound state
The diffraction angle is inversely prop. to N
Low temp.cluster source
T0
0
-
-
v
v
40 K
1 barP
Non - destructive Diffraction Grating “Mass Spectrometer”
Previous: Na atoms, Pritchard et al (1988); He*, Mlynek et al (1991)
m m 5 5slit slit
80 cm
Mass spectrometerdetector
m 20~~slit +
detect
He atoms at mass 4 4
2003-01-24-T1-Ka
J
He clusters at mass 8 4
Can discriminate against atoms with mass spectrometer set at mass 8 and larger from J. P. Toennies
Electron Microscope Picture of the SiNx Transmission Gratings
Courtesy of Prof. H. Smith and Dr. Tim Savas, M. I. T.
2002-07-24-T2-WK
He Atom Diffraction Pattern for 300 K Beam
22 22
n=
15 15
8 8
5 5
105
10 4
10 3
102
10 1
Mas
s 4
Io
n S
ign
al [
cts/
sec]
-12 -8 -4 0 4 8 12
Deflection Angle [mrad]
T = 294 K0
P = 140 bar0
= 0.56 A°
-1 1
Bragg: A°0.561000 A°
nd
= (n=1) = 0.56 10-3 rad..
= 150 radmDJ
from J. P. Toennies
At Low Source Temperatures New Diffraction Peaks Appear
Measure Size of Dimer from Cross Sectionon Scattering from Grating Bars
<R>2
s0 seff- :
s0 seff
He (1s)2
He<R>
Break-up reduces effective slit width
Hegerfeldt and Köhler, PRL 84 (2000)
2003-07-10-T1-Schr.
from J. P. Toennies
n=-1
n=-2
n=+1
n=+2
2003-07-17-T1-Schr.
n=0
Single Slit Diffraction is Envelope of Grating Diffraction
Single slit:
Grating:
p-
p+
p
p
Matter Waves: Feynmann: Lecture Notes in Physics
Dps-~
eff
Slit function
from J. P. Toennies
0 500 1000 1500 200056
57
58
59
60
61
62
63
64
Effe
ctiv
e S
l it W
idth
s
[nm
]e
ff
Particle Velocity v [m/s]
Effective Slit Widths vs Particle VelocityHe Atom versus He Dimer
Scattering length a = 2 <R> = 97 A
C =0.12 meV nm33
He
He2
Grisenti, Schöllkopf, Toennies Hegerfeldt, Köhler and StollPhys. Rev. Lett. 85 2284 (2000)
=2.5nm
SeffD
oo
V (particle-wall) = 33C
X-
<R> = 52.0 +
Eb -~4m 2
2
<R>
=1.2 10 K-3.1 10-3 K
104 A°
=1.1 10-3 K
0.4 A
Grisenti; Schöllkopf, Toennies, Hegerfeldt, Köhler and Stoll, Phys. Rev. Lett. 85 2284 (2000)
Since <R> is much greater than Rout the dimeris a classically forbidden molecule
<R>
The 4He dimer: the world‘s weakest bound and largest ground state molecule
A frail GIANT!
from J. P. Toennies
He
He
He
2
23
+
He, He ,He
Cluster beam
Kr
l
3
n
Cluster Size Resolved Integral Cross Sections
0 2.0 4.0 6.0 8.0 10.0103
104
Pea
k A
rea
[arb
. uni
ts]
He4
He3
He2
12.0
Pressure Krypton Gas [10 mbar]-5
He
7 10 4.
2003-06-26-T1-Schr.
I=I exp (- n l)s. .o
See Monday poster No 172
of He Clusters in Scattering from Kr Atoms
A.Kalinin, O. Kornilov, L. Rusin, J. P. Toennies, and G. Vladimirov, Phys. Rev. Lett. 93, 163402 (2004)
To Further Study the Dimer it is Interestingto Scatter from an Object Smaller than the Dimer: An Atom!
The Kr atom can pass through the middle of the molecule without its being affected
The dimer is nearly invisible:
magic!
from J. P. Toennies
end of lecture 6
2003-06-23-T2a-Schr.
Cluster Magic Numbers
Geometrical Electronic
Metal clusters
Fermi Level
Do liquid He clusters have magic numbers?
R. Melzer and J.G. Zabolitzky say No!
Ar55 C60
J. Phys. A: Math. Gen. 17 L565 (1984)
Cluster Magic Numbers
Det
achm
ent E
nerg
y [K
]
2004-08-16-T1-Schr.
Ground State Energies of He Clusters
Guardiola and Navarro, priv. comm.
Monte Carlo Calculations: Diffusion
0
1
2
3
4
5
0
0
10
10
20
20
30
30
40
40
50
50-150
-100
-50
0
Binding Energies
Bin
ding
Ene
rgy
E
[K]
b
Atom DetachmentEnergies
m = EN
DD
Recent highly accurate diffusion Monte Carlo (T=0) calculationrules out existence of magic numbers due to stabilities:
R. Guardiola,O. Kornilov, J. Navarro and J. P. Toennies, J. Chem Phys, 2006
Cluster Number Size N
He
He
2
3
4 5678
He
N=
Deflection Angle [mrad]
-4 -3 -2 -1 00
5
10
15
20
He
Sig
nal [
cts/
sec]
+
T =6.7 KoP =1.5 bar
=4.0 Alo
Magic Numbers in He Clusters: He4 4N
Angular resolution 20 10 rad.-6DJ .
x0.03
2003-08-11-T1a-Schr.
Searching for Large 4He Clusters: 4HeN
He2+
from J. P. Toennies
Magic Numbers in Large 4He Clusters
10-4
10-3
10-2
10-1
100
G(N
)
Cluster Size Distributions G(N), N < 100
0 10 20 30 40 50 60 70 80 90 100Cluster Number Size N
0
1
2
3
4
5
Ge
xp(N
) / G
fit(N
)P0 = 1.33 bar
1.28 bar
1.22 bar
1.16 bar
1.10 bar
P0 = 1.33 bar
1.28 bar
1.22 bar
1.16 bar
1.10 bar
Brühl et al. Phys. Rev. Lett. 92 185301-1 (2004)
42
23
13,149,10
2004-01-21-T6-Schr.
T =6.7 K0
G (N) = I J( ) N
G (N) = I J J( ) ddN
-2
J N-1
26
2003-06-26-T1-Fu
C lus tergro wth
Evapo ra tive Co oling
d= 5 mm
Clusters Reach Final Sizes in Early,“ Hot “ Stage of Expansion
Growth reaction
Equilibrium constant
Abrupt changes in equilibrium constants areknown to affect size distributions
He + He HeN-1
N-1 1
N
NNK =
X
X
X X
S g j e-E j /kT
j
Where are partition functionsX
The K have sharp peaks whenever the N cluster has a new excited state. Then both Ξ and K will increase.
But for the N+1 cluster both Ξ will be about the same and K will fall back.
To explain Magic numbers recall that clusters
are formed in early „hot“ stages of the expansion
fro
m J
. P
. T
oe
nn
ies
0n 0)( ,01 ndRkj
)()()0(
2
)12(
)(
,,02
,
2
,
ndndnd
nd
RIRkjR
n
dS
Rd
P
)/(
,)()(
22
0
22
dB
xd
TRMk
dxxxjeRI
Single-particle excitation theory of evaporation and cluster stability
Magic numbers!
evaporation probability
200 /2 MVk
2006
Thermalization via evaporation (DFT)
Binding energy per atom
Barranco et al (2006)
Atomic radial distributions
3Hen
4Hen
Barranco et al (2006)
Barranco et al (2006)
one-particle states
3He in 4Hen
Barranco et al (2006)
4He / 3He phase separation
Barranco et al (2006)
Stable 4He + 3He mixed clusters
Barranco et al (2006)
Electron bubbles in 4He droplets
R 1.7 nm
0.48 dyn/cm
E 0.26 eV
322
22
3
44
2PRR
RmE
e