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Helium Trimer in the Framework of Faddeev Approach

Helium Trimer in the Framework of Faddeev Approach. Elena Kolganova BLTP JINR, Dubna , Russia. In collaboration with A.K.Motovilov (JINR Dubna) W.Sandhas (PI Bonn). Two-body and three-body, experiment. 4 He - 4 He.

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Helium Trimer in the Framework of Faddeev Approach

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  1. Helium Trimer in the Framework of Faddeev Approach Elena Kolganova BLTP JINR, Dubna, Russia In collaboration with A.K.Motovilov (JINR Dubna) W.Sandhas (PI Bonn) Few-Body Conference, August 31, 2009 Elena Kolganova (JINR, Dubna)

  2. Two-body and three-body, experiment 4He - 4He • 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 4He- 4He - 4He Experiment – Toennies et al. JCP 104, 1155 (1996), JCP 117, 1544 (2002) Trimer pair distance Theory – variational, hyperspherical, Faddeev equations (integral, differential) Few-Body Conference, August 31, 2009 Elena Kolganova (JINR, Dubna)

  3. 4He2 Two-body, theory • Potential models: Aziz et al. – HFD-B (1987), LM2M2 (1991),Tang et al. – TTY (1995) where 4He – 4He potential (LM2M2) Few-Body Conference, August 31, 2009 Elena Kolganova (JINR, Dubna)

  4. Two-body, theory 4He - 4He • Potential models: Aziz et al. – HFD-B (1987), LM2M2 (1991) Tang et al. – TTY (1995) Few-Body Conference, August 31, 2009 Elena Kolganova (JINR, Dubna)

  5. Three-body, theory formalism Faddeev differential equations for hard-core potentials Few-Body Conference, August 31, 2009 Elena Kolganova (JINR, Dubna)

  6. Three-body, theory formalism Faddeev differential equations for hard-core potentials Boundary condition model is mathematically rigorous ! Merkuriev, Motovilov, LMP 7 (1983) 497; Motovilov, VLU 22 (1983) 76; Merkuriev, Motovilov, Yakovlev, TMP 94(1993)306 JPB 31(1998) 1279 Few-Body Conference, August 31, 2009 Elena Kolganova (JINR, Dubna)

  7. When the total angular momentum L of the system is fixed, the three-body dynamics is constrained onto three-dimensional internal space [5], which can be parametrized by coordinates For zero angular momentum the Faddeev equations in internal space are given by the set of three coupled three-dimensional equations or in hyperspherical coordinates [5] - V.V.Kostrykin,A.A.Kvitsinsky,S.P.Merkuriev, Few-Body Syst. 6 (1989) 97 Few-Body Conference, August 31, 2009 Elena Kolganova (JINR, Dubna) 7 E.Kolganova (Dubna)

  8. For computational purposes, one can reduce the dimension by expanding the Faddeev components into an auxiliary basis, at the expense of dealing with an infinite number of partial equations. Expanding the function Fain a series of bispherical harmonics One can obtain the partial equation The asymptotic boundary conditions for the partial-wave Faddeev components of the 2’2,3 scattering wave function for and/or reads r’ and/or y’ reads Where p is the relative moment conjugate to Jacoby variable y, E is the scattering energy, stand for the spherical Bessel and Hankel functions Few-Body Conference, August 31, 2009 Elena Kolganova (JINR, Dubna) 8 E.Kolganova (Dubna)

  9. Three-body, theorybound states and scattering 4He3 and 3He 4He2 Bogolyubov Conference, August 24, 2009 Elena Kolganova (JINR, Dubna) Few-Body Conference, August 31, 2009 Elena Kolganova (JINR, Dubna) 9

  10. Three-body, theory bound states 4He3 V. Kolontsov Bogolyubov Conference, August 24, 2009 Elena Kolganova (JINR, Dubna) Few-Body Conference, August 31, 2009 Elena Kolganova (JINR, Dubna) 10

  11. Outgoing results and future directions • Scattering calculations, especially, above three-body threshold • Resonances calculations, • to see the influence of applying 3D eq. to their values and positions • Kolganova E.A. and Motovilov A.K. Mechanism of the Emergence of Efimov States in the 4He Trimer Yad. Fiz. 1999. V. 62. P. 1253–1267 [Phys. At. Nucl. 62, 1179 (1999)]. Acknowledgements • My collaborators - Prof. A.K.Motovilov and Prof. W.Sandhas • Diploma student – V.Kolontsov • Alexander von Humboldt foundation • Heisenberg-Landau Program Thank you! Few-Body Conference, August 31, 2009 Elena Kolganova (JINR, Dubna)

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