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Quantum Monte Carlo Simulations of Mixed 3 He/ 4 He Clusters

Universita’ degli Studi dell’Insubria . Quantum Monte Carlo Simulations of Mixed 3 He/ 4 He Clusters. Dario Bressanini. dario.bressanini@uninsubria.it http://www.unico.it/ ~ dario. Trento 2 Sep 2003. Helium. A helium atom is an elementary particle. A weakly interacting hard sphere.

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Quantum Monte Carlo Simulations of Mixed 3 He/ 4 He Clusters

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  1. Universita’ degli Studi dell’Insubria Quantum Monte CarloSimulations of Mixed3He/4He Clusters Dario Bressanini dario.bressanini@uninsubria.ithttp://www.unico.it/~dario Trento 2 Sep 2003

  2. 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

  3. 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

  4. 4Hen 4He2dimer exists All clusters bound Liquid: stable 4Hen Clusters Stability • 4He3 bound. Efimov effect?

  5. 3He2dimer unbound Liquid: stable 3Hen Clusters Stability • Even less is known for mixed clusters. Is 3Hem4Hen stable ? • What is the smallest 3Hem stable cluster ? 3Hem m = ? 20 < m < 35 critically bound

  6. Bonding interaction Non-bonding interaction 3He4Hedimer unbound 3He4He2Trimer bound 3He4HenAll clusters up bound 3He4Hen Clusters Stability 3He4He2E = -0.00984(5) cm-1 4He3 E = -0.08784(7) cm-1

  7. 3He24HeTrimer unbound 3He24He2Tetramer bound5 out of 6 unbound pairs 3He24HenAll clusters up bound 4He4 E = -0.3886(1) cm-1 3He4He3E = -0.2062(1) cm-1 3He24He2E = -0.071(1) cm-1 3He24Hen Clusters Stability • Now put two 3He. Singlet state. Y is positive everywhere

  8. Evidence of 3He24He2 Kalinin, Kornilov and Toennies

  9. 3He34Hen Clusters Stability • Adding a third fermionic helium, introduces a nodalsurface into the wave function that destabilizes the system • What is the smallest 3He34Hen stable cluster ? • For L=0 n = 9, for L=1 n = 4

  10. Evidence of 4He43He3 Kalinin, Kornilov and Toennies

  11. Mixed He clusters: 3Hem4Hen 4Hen 3Hem 0 1 2 3 4 5 6 7 8 9 10 11 Bound L=0 0 1 2 3 4 5 Unbound Unknown Maybe L=1 S=1/2 L=1 S=1 35 3He34He4 L=0 S=1/2 3He24He2 L=0 S=0 3He34He4 L=1 S=1/2 3He24He2 L=1 S=1

  12. 3He4He10 c.o.m 3He24He10 3He34He10 3Hem4He10 m = 0,1,2,3 L=0 3He distribution with respect to the center of mass r(3He-C.O.M.)

  13. b a aoutside b outside on opposite sides 4He10 a aoutside a inside boutside a inside 3Hem4He10 m = 0,1,2,3 L=0 3He- 3He distributions r(3He- 3He) The (tentative) picture: two 3He outside (a, b) and one ainside, pushed away from the other a3He

  14. b a 4He10 a a a b 3He34He10 L=0 Why ? It is a Nodal Effect.The wave function is zero if the two a3He are at the same distance from the b3He. 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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