quantum monte carlo simulations of mixed 3 he/ 4 he clusters
DESCRIPTION
Universita’ degli Studi dell’Insubria . Quantum Monte Carlo Simulations of Mixed 3 He/ 4 He Clusters. Dario Bressanini. [email protected] http://www.unico.it/ ~ dario. Trento 2 Sep 2003. Helium. A helium atom is an elementary particle. A weakly interacting hard sphere. - PowerPoint PPT PresentationTRANSCRIPT
Quantum Monte Quantum Monte CarloCarlo Simulations Simulations of Mixedof Mixed 33He/He/44He He
ClustersClusters
[email protected]@uninsubria.ithttp://www.unico.it/http://www.unico.it/~~dariodario
Dario Dario BressaniniBressanini
Universita’ degli Studi dell’Insubria
Trento 2 Sep 2003Trento 2 Sep 2003
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HeliumHelium A helium atom is an A helium atom is an
elementary particle. A weakly elementary particle. A weakly interacting hard sphere.interacting hard sphere.
Interatomic potential is Interatomic potential is known more accurately than known more accurately than any other atom. any other atom.
Two isotopes: Two isotopes: • 33He (fermion: antisymmetric trial function, spin 1/2) He (fermion: antisymmetric trial function, spin 1/2) • 44He (boson: symmetric trial function, spin zero)He (boson: symmetric trial function, spin zero)• The interaction potential is the sameThe interaction potential is the same
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Helium ClustersHelium Clusters1.1. Small mass of helium atomSmall mass of helium atom
2.2. Very weak He-He interactionVery weak He-He interaction
0.02 Kcal/mol0.9 * 10-3 cm-1
0.4 * 10-8 hartree10-7 eV
Highly non-classical systems. No equilibrium structure.Highly non-classical systems. No equilibrium structure.ab-initio methods and normal mode ab-initio methods and normal mode analysisanalysis useless useless
SuperfluiditySuperfluidityHigh resolution High resolution spectroscopyspectroscopy
Low temperature Low temperature chemistrychemistry
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44HeHenn Cluster Clusterss Stability Stability
44HeHe33 bound. Efimov effect? bound. Efimov effect?
Liquid: stableLiquid: stable
44HeHe22 dimer existsdimer exists
44HeHenn
All clusters All clusters boundbound
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33HeHenn Cluster Clusterss Stability Stability
Even less is known for mixed clusters. Even less is known for mixed clusters. Is Is 33HeHemm
44HeHenn stable ? stable ?
What is the smallest What is the smallest 33HeHemm stable cluster ? stable cluster ?
Liquid: stableLiquid: stable
33HeHe22
dimer dimer unboundunbound
33HeHemm
m = ?m = ? 20 < 20 < mm < 35 < 35critically boundcritically bound
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33HeHe44HeHenn Cluster Clusterss Stability Stability
33HeHe44HeHedimer dimer unboundunbound
33HeHe44HeHe22
Trimer boundTrimer bound33HeHe44HeHenn
All clusters All clusters up boundup bound
44HeHe3 3 E = E = -0.08784(7)-0.08784(7) cm cm-1-1
33HeHe44HeHe22 E = E = -0.00984(5)-0.00984(5) cm cm-1-1
Bonding Bonding interactioninteractionNon-bonding Non-bonding interactioninteraction
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33HeHe2244HeHenn Cluster Clusterss StabilityStability
Now put two Now put two 33HeHe. Singlet state. . Singlet state. is positive everywhere is positive everywhere
33HeHe2244HeHenn
All clusters All clusters up boundup bound
33HeHe2244HeHe
Trimer Trimer unboundunbound
33HeHe2244HeHe22
Tetramer boundTetramer bound5 out of 6 unbound pairs5 out of 6 unbound pairs
44HeHe4 4 E = E = -0.-0.33888866((11)) cm cm-1-1
33HeHe44HeHe33 E = E = -0.-0.20622062((11)) cm cm-1-1
33HeHe2244HeHe22 E = E = -0.-0.071071((11)) cm cm-1-1
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Evidence of Evidence of 33HeHe2244HeHe2 2 Kalinin, Kornilov Kalinin, Kornilov
and Toenniesand Toennies
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33HeHe3344HeHenn Cluster Clusterss StabilityStability
Adding a third fermionic helium, introduces a Adding a third fermionic helium, introduces a nodalnodal surfacesurface into the wave function that destabilizes the system into the wave function that destabilizes the system
What is the smallest What is the smallest 33HeHe3344HeHenn stable cluster ? stable cluster ?
For L=0 n = 9, for L=1 n = 4For L=0 n = 9, for L=1 n = 4
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Evidence of Evidence of 44HeHe4433HeHe3 3 Kalinin, Kornilov Kalinin, Kornilov
and Toenniesand Toennies
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Mixed He clusters: Mixed He clusters: 33HeHemm
44HeHenn 44HeHenn 33HeHemm 0 1 2 3 4 5 6 70 1 2 3 4 5 6 7 8 9 10 11 8 9 10 1100
11
22
33
44
55
3535
33HeHe2244HeHe22 L=0 S=0 L=0 S=0
Bound L=0Bound L=0
UnboundUnbound
UnknownUnknown
MaybeMaybe
L=1 S=1/2L=1 S=1/2
33HeHe3344HeHe44 L=1 S=1/2 L=1 S=1/233HeHe22
44HeHe22 L=1 S=1 L=1 S=1
33HeHe3344HeHe44 L=0 S=1/2 L=0 S=1/2
L=1 S=1L=1 S=1
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33HeHemm44HeHe1010 m = 0,1,2,3 m = 0,1,2,3
L=0L=033HeHe d distribution with respect to the center of massistribution with respect to the center of mass
((33He-He-C.O.M.C.O.M.))
c.o.mc.o.m
5 10 15 20 25 300
0.002
0.004
0.006
0.008
0.01
33HeHe44HeHe1010
5 10 15 20 25 300
0.002
0.004
0.006
0.008
0.0133HeHe22
44HeHe1010
5 10 15 20 25 300
0.002
0.004
0.006
0.008
0.01
0.012
33HeHe3344HeHe1010
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33HeHemm44HeHe1010 m = 0,1,2,3 m = 0,1,2,3
L=0L=033HeHe- - 33HeHe d distributionistributionss ((33He- He- 33He)He)
5 10 15 20 25 30 35 400
0.0025
0.005
0.0075
0.01
0.0125
0.015
The The (tentative)(tentative) picture: two picture: two 33HeHe outside outside ((, , ) and one ) and one inside, pushed away inside, pushed away from the other from the other 33HeHe
44HeHe1010
outside outside inside inside
outside outside inside inside
outside outside outside outside on opposite sideson opposite sides
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33HeHe3344HeHe1010 L=0 L=0
Why ?Why ?
44HeHe1010
It is a It is a Nodal EffectNodal Effect..The wave function is zero if the two The wave function is zero if the two 33HeHe are at the same distance from the are at the same distance from the 33HeHe. For . For this reason the three atoms are not free to this reason the three atoms are not free to move on the surface of the cluster. One is move on the surface of the cluster. One is pushed inside to avoid the wave function pushed inside to avoid the wave function node. node.