Quantum Monte Carlo Simulations of Mixed 3He4He Clusters

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Quantum Monte Carlo Simulations of Mixed 3He/4He
Clusters
Universita degli Studi dellInsubria
Dario Bressanini
dario.bressanini_at_uninsubria.ithttp//www.unico.it
/dario
Trento 2 Sep 2003
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Helium

• A helium atom is an elementary particle. A weakly
  interacting hard sphere.
• Interatomic potential is known more accurately
  than any other atom.

• Two isotopes
• 3He (fermion antisymmetric trial function, spin
  1/2)
• 4He (boson symmetric trial function, spin zero)
• The interaction potential is the same

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Experiment on He droplets
Toennies and Vilesov, Ann. Rev. Phys. Chem. 49,
1 (1998)

• Adiabatic expansion cools helium to below the
  critical point, forming droplets.
• The droplets are sent through a scattering
  chamber to pick up impurities, and are detected
  with a mass spectrometer

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Helium Clusters

• Small mass of helium atom
• Very weak He-He interaction

0.02 Kcal/mol0.9 10-3 cm-10.4 10-8
hartree10-7 eV
Highly non-classical systems. No equilibrium
structure. ab-initio methods and normal mode
analysis useless
High resolution spectroscopy
Superfluidity
Low temperature chemistry
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4Hen Clusters Stability

• 4He3 bound. Efimov effect?

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3Hen Clusters Stability

• What is the smallest 3Hem stable cluster ?

3Hem
m ? 20 lt m lt 35 critically bound

• Even less is known for mixed clusters. Is
  3Hem4Hen stable ?

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3He4Hen Clusters Stability
3He4He2 E -0.00984(5) cm-1
4He3 E -0.08784(7) cm-1
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3He24Hen Clusters Stability

• Now put two 3He. Singlet state. Y is positive
  everywhere

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Evidence of 3He24He2 Kalinin, Kornilov and
Toennies
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3He34Hen Clusters Stability

• Adding a third fermionic helium, introduces a
  nodal surface into the wave function that
  destabilizes the system
• What is the smallest 3He34Hen stable cluster ?
• For L0 n 9, for L1 n 4

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Evidence of 4He43He3 Kalinin, Kornilov and
Toennies
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Mixed He clusters 3Hem4Hen
4Hen
3Hem
0 1 2 3 4 5 6 7 8 9
10 11
Bound L0
0 1 2 3 4 5
Unbound
Unknown
Maybe
L1 S1/2
L1 S1
35
3He34He4 L0 S1/2
3He24He2 L0 S0
3He34He4 L1 S1/2
3He24He2 L1 S1
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3Hem4He10 m 0,1,2,3 L0
3He distribution with respect to the center of
mass
r(3He-C.O.M.)
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3Hem4He10 m 0,1,2,3 L0
3He- 3He distributions
r(3He- 3He)
The (tentative) picture two 3He outside (a, b)
and one a inside, pushed away from the other a 3He
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3He34He10 L0
Why ?
It is a Nodal Effect.The wave function is zero
if the two a 3He are at the same distance from
the b 3He. For this reason the three atoms are
not free to move on the surface of the cluster.
One is pushed inside to avoid the wave function
node.
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Nodes?

• To be continued....
• more on Nodes this afternoon
• Stay tuned...