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Scales of critically stable few-body halo system

FB18, Santos, Aug.21-26, 2006. Collaborators. Marcelo T. Yamashita – Itapeva /Unesp Lauro Tomio – IFT/Unesp/São Paulo Antonio Delfino – UFF/Niterói Sadhan K. Adhikari - IFT/Unesp/São Paulo. Scales of critically stable few-body halo system. Tobias Frederico

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Scales of critically stable few-body halo system

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  1. FB18, Santos, Aug.21-26, 2006 • Collaborators • Marcelo T. Yamashita – Itapeva /Unesp • Lauro Tomio – IFT/Unesp/São Paulo • Antonio Delfino – UFF/Niterói • Sadhan K. Adhikari - IFT/Unesp/São Paulo Scales of critically stable few-body halo system Tobias Frederico Instituto Tecnológico de Aeronáutica São José dos Campos - Brazil

  2. OUTLINE Nuclear and Atomic weakly bound three-body halo systems How to study weakly bound three-body systems? Thomas-Efimov effect Scaling limit & limit cycle, scaling functions and correlations between observables General classification scheme: n-n-c or A-A-B Threshold conditions for an excited N+1Efimov state Three-bosons: analytic structure & Efimov state trajectory Root mean square radii Four boson systems: new scale? Summary and perspectives

  3. First observation 6He T. Bjerge, Nature138, 400 (1936) growth of the cross section 11Li colliding with some targets Tanihata et al., Phys. Rev. Lett. 55, 2676 (1985) neutrons T. Kobayashi et al. Phys. Lett. B 232, 51 (1989) Two-neutron halo nucleus

  4. Nuclear weakly bound three-body halo systems core-neutron-neutron halo nuclei 11Li 14Be 20C Binding energy ~ MeV or < MeV Rnn(Exp) ~ 6 - 8 fm (11Li) F. M. Marqués et al. Phys. Rev. C 64, 061301 (2001) M. Petrascu et al. Nucl. Phys. A 738, 503 (2004) core n n

  5. Atomic weakly bound three-body systems A o dimer R4He-4He~ 50 A B B A-B-B weakly bound molecules ultra-low binding ~ mK or < mK 133Cs3 (trapped ultracold gas near a Feshbach resonance) 4He3 4He2 – 7Li 4He2 – 6Li 4He2 – 23Na R4He-4He~ 10 A o

  6. How to study weakly bound three-body systems? Use a realistic interaction and calculate the Hamiltonian eigenstates.... What details of the interaction are important for the results? Large systems are peculiar: size >> interaction range! ....and the eigenfunction of the Hamiltonian satisfies a free Schrödinger equation almost everywhere for nonzero interparticle distances! Zero-range interaction asymptotic wf behaviour & universality

  7. How to study weakly bound three-body systems? Charateristic phenomena: Thomas collapse (1935) and Efimov effect (1970) ro 0 |a|  ??? infinitely many weakly bound states |a|/ro Thomas-Efimov effect! 8 8

  8. How to study weakly bound three-body systems? Thomas-Efimov effect Skorniakov and Ter-Martirosian equations (1956) = / / = 3 3 Adhikari,TF,Goldman, PRL74 (1995) 487 8  Thomas collapse: = /  0 Efimov effect:  0

  9. Scaling limit & limit cycle Efimov 1970 Scaling function Scaling limit: Frederico et al PRA60 (1999)R9 Yamashita et al PRA66(2003)052702 Limit cycle: Mohr et al Ann.Phys. 321 (2006)225

  10. Scaling functions: Correlation between observables Correlation between S-wave observables Phillips plot: triton B.E. X doublet scattering length 2nd order neutron-deuteron polarization observables X triton B.E. Trapped atomic trimer B.E. X recombination rate

  11. Weakly bound system wave function & contact interaction Three-boson wave function: (1) q1 (2) (3) R1 + (12) + (13)

  12. BORROMEAN TANGO bound state virtual state SAMBA ALL-BOUND General classification scheme: n-n-c or A-A-B Yamashita, Tomio and T. F. Nucl. Phys. A 735, 40 (2004)

  13. General classification scheme: n-n-c or A-A-B Scales: Energy of the bound/virtual nn system Energy of the bound/virtual nc system Energy of the Nth state of the nnc system A = mass of the core

  14. Halo-nuclei: Threshold for an excited N+1Efimov state Amorim,TF,Tomio PRC56(1997)2378 All-bound nc bound Samba Knn=(Bnn)1/2 Knc=(Bnc)1/2 nc virtual Tango Borromean nn bound nn virtual

  15. Weakly bound molecules: Threshold for an excited N+1Efimov state All-bound Samba Kaa=(Baa)1/2 Kab=(Bab)1/2 Tango Borromean Delfino,TF,Tomio JCP 113 (2000) 7874

  16. Three-bosons: analytic structure & Efimov state trajectory Bound 3-body state Bound 2-body state x x -E3 -E2 Three-body cut Two-body cut Virtual 3-body state -E3 (N+1) x x x -E3(N) -E2 Three-body cut Virtual 3-body state

  17. Efimov state trajectory: 2-body bound

  18. Three-bosons: analytic structure & Efimov state trajectory Bound 3-body state Virtual 2-body state x -E3 Three-body cut x 3-body Resonance -E3 (N+1) x x -E3(N) Three-body cut x 3-body Resonance

  19. Efimov state trajectory: 2-body virtual S-wave three-boson resonance Evidence of continuum resonances in recombination of ultracold Cs atoms

  20. Evidence of continuum resonances in ultracold cesium gas M.T. Yamashita, “Triatomic states in ultracold gases” Parallel session R6-16, Friday

  21. Threshold for an excited N+1Efimov state Arora, Mazumdar, Bhasin, PRC69(2004)061301(R) Mazuumdar, Rao, Bhasin, PRL97(2006)062503 Resonance in n+19C

  22. A <r2A> <r2AB> CM <r2B> B B <r2BB> Root mean square radii

  23. Scaling functions for the radii + two-body bound state - two-body virtual state g = A or B Root mean square radii

  24. Root mean square radii Core Yamashita, Tomio and T. F. Nucl. Phys. A 735, 40 (2004) Exp:

  25. nA bound nA bound nA virtual nA virtual Root mean square radii

  26. For a fixed E3 bound state ALL-BOUND > virtual state SAMBA > TANGO > BORROMEAN Root mean square radii

  27. Radii are experimentally extracted from R. Hanbury-Brown and R. Q. Twiss (HBT) - NATURE 177, 27 (1956) 178, 1046 (1956) 178, 1447 (1956) correlation function First used in astrophysics Nuclear Physics Neutron-neutron correlation function

  28. qA One-body density A pA Breakup amplitude including the FSI between the neutrons Y is the three-body wave function n n' Neutron-neutron correlation function

  29. F. M. Marqués et al. Phys. Rev. C 64, 061301 (2001) x1.425 F. M. Marqués et al. Phys. Lett. B 476, 219 (2000) E3 = 1.337 MeV EnA = 0.2 MeV Enn = 0.143 MeV asymptotic region ? Neutron-neutron correlation function M. T. Yamashita, T. Frederico and L. Tomio Phys. Rev. C 72, 011601(R) (2005)

  30. F. M. Marqués et al. Phys. Rev. C 64, 061301 (2001) x2.5 M. Petrascu et al. Nucl. Phys. A 738, 503 (2004) E3 = 0.29 MeV EnA = 0.05 MeV E3 = 0.37 MeV EnA = 0.8 MeV E3 = 0.37 MeV EnA = 0.05 MeV Enn = 0.143 MeV Neutron-neutron correlation function

  31. F. M. Marqués et al. Phys. Rev. C 64, 061301 (2001) E3 = 0.973 MeV EnA = 4 MeV x1.12 E3 = 0.973 MeV EnA = 0 Enn = 0.143 MeV Neutron-neutron correlation function

  32. Results for different radii of the molecular system ABB Radii for weakly bound molecules Yamashita, Marques de Carvalho, Tomio , T. F., Phys. Rev. A 68, 012506 (2003)

  33. Ground First excited Symbols from P. Barletta and A. Kievsky Phys. Rev. A 64, 042514 (2001) squares - Ground state circles - First excited state Weakly bound molecules

  34. Four-boson system: new scale? no new scale new scale

  35. Four-boson system: a new scale?

  36. Four-boson system: a new scale? MeV Tjon line:

  37. Zero-range model: classification of weakly-bound systems threshold conditions for excited states and resonances ( evidence of the trajectory of resonance in ultra-cold atoms) 6He, 11Li, 14Be, 20C 4He-4He-(4He, 6Li, 7Li, 23Na) Neutron-neutron correlation function Summary and perspectives Weakly bound & large systems: few scales regime Flexibility: Evidence for a four-boson scale Next: Exploration of the different possibilities of threshold conditions for resonances Scattering, breakup of halo nuclei and weakly bound molecules: universal properties Four-boson excited states, resonances & scattering

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