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Ultracold Scattering Processes in Three-Atomic Helium Systems

Ultracold Scattering Processes in Three-Atomic Helium Systems. W.Sandhas (Bonn). E.A. Kolganova (JINR Dubna) A.K. Motovilov (JINR Dubna). Outline. Overview - experiment and theory (two-body, three-body) Formalism (Faddeev equations, Hard-Core model) Results

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Ultracold Scattering Processes in Three-Atomic Helium Systems

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  1. Ultracold Scattering Processes in Three-Atomic Helium Systems W.Sandhas(Bonn) E.A. Kolganova(JINR Dubna) A.K. Motovilov(JINR Dubna)

  2. Outline • Overview - experiment and theory (two-body, three-body) • Formalism (Faddeev equations, Hard-Core model) • Results • three-body bound states (4He3 and 3He4He2) • scattering (phase shifts and scattering length) • Conclusion FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  3. 4He - 4He Two-body, experiment • First observation by Luo et al. (1993) and Schöllkopf, Toennies (1994) • First measurement of the bond length by Grisenti et al.(2000) • Estimation of the binding energy and scattering length FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  4. 4He2 Two-body, theory • Potential models: Aziz et al. – HFD-B (1987), LM2M2 (1991),Tang et al. – TTY (1995) where and 4He – 4He potential (TTY) FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  5. Two-body, theory 4He - 4He • Potential models: Aziz et al. – HFD-B (1987), LM2M2 (1991) Tang et al. – TTY (1995) FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  6. Three-body, experiment and theory bound states 4He- 4He - 4He Experiment – Toennies et al. JCP 104, 1155 (1996), JCP 117, 1544 (2002) Theory – Variational methods Hyperspherical approach Faddeev equations Egs  126 mK Eex  2.28 mK FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  7. Three-body, theory formalism [4] - L.D.Faddeev,S.P.Merkuriev, 1993, Quantum scattering theory for several particles FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  8. Three-body, theory formalism 4He2 - 4He Faddeev integro-differential equationsafter angular partial-wave analysis At L=0 the partial angular momentum corresponds both to the dimer and an additional atom. stand to the standard Jacobi variables. The kernel depend only on hyperangles - see L.D.Faddeev,S.P.Merkuriev, 1993. FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  9. Three-body, theory formalism 4He2 - 4He Boundary conditions Hard-core boundary conditions: The asymptotic condition for the helium trimer bound states Here, is the dimer wave function, stands for the dimer energy, FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  10. Three-body, theory formalism 4He2 - 4He Boundary conditions The asymptotic condition for the partial-wave Faddeev components of the (2 + 1  2 + 1 ; 1 + 1 + 1) scattering wave function reads, FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  11. Three-body, theory bound state 4He3 Bound state calculations Roudnev, Yakovlev (1999) Panharipande et al. (1983) Cornelius, Gloeckle (1986) Barnett, Walley (1993) Carbonell,Gignoux, Merkuriev (1993) Lewerenz (1997) Nielsen,Fedorov,Jensen (1998) Esry,Lin,Greene (1996) Motovilov,Kolganova, Sandhas,Sofianos (1997,2001) FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  12. Three-body, theory bound state 4He3 Bound state calculations Roudnev, Yakovlev (2000) Cornelius, Gloeckle (1986) Nakaichi-Maeda, Lim (1983) Esry,Lin,Greene (1996) Nielsen,Fedorov,Jensen (1998) Blume,Greene (2000) Barletta, Kievsky (2001) Motovilov,Kolganova, Sandhas,Sofianos (1997,2001) FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  13. 4He - 4He2 Three-body, theory scattering Scattering Length calculations Roudnev (2003) Blume,Greene (2000) Penkov (2003) Braaten,Hammer (2003) 2004,2005 1998 Motovilov,Kolganova,Sandhas FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  14. Three-body, theory scattering state 4He4He2 FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  15. Three-body, theory scattering state 4He4He2 FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  16. Three-body, theory bound state 3He4He2 FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  17. Three-body, theory scattering 3He -4He2 FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  18. Three-body, theory scattering 4He - 4He2 Phase shifts calculations usingFaddeev differential equations Roudnev (2003) Kolganova,Motovilov(1998,2001) Zero-range model - Hammer et al. (1999,2003), Penkov(2003) FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  19. 3He - 4He2 Three-body, theory scattering FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  20. Three-body, theory scattering 4He2 - 4He Partial wave-function for HFD-B potential at E=1.4mK FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

  21. Conclusions • We employed formalism which is suitable for three-body atomic systems interacting via hard-core potentials. This method lets us calculate bound states and scattering observables. • Scattering length and phase shifts for the helium three-atomic systems have been calculated. • It was demonstrated how the Efimov states emerge from the virtual ones when decreasing the strength of the interaction. FB18, Santos, Brazil, August 25, 2006 Werner Sandhas (Bonn)

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