Movatterモバイル変換


[0]ホーム

URL:


Skip to main content
Springer Nature Link
Log in

The4He Trimer as an Efimov System

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

We review the results obtained in the last four decades which demonstrate the Efimov nature of the4He three-atomic system.

This is a preview of subscription content,log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bruch L.W., McGee I.J.: Semiempirical helium intermolecular potential. II. Dilute gas properties. J. Chem. Phys.52, 5884 (1970)

    Article ADS  Google Scholar 

  2. Aziz R.A., Nain V.P.S., Carley J.S., Taylor W.L., McConville G.T.: An accurate intermolecular potential for helium. J. Chem. Phys.79, 4330 (1979)

    Article ADS  Google Scholar 

  3. Uang Y.-H., Stwalley W.C.: The possibility of a4He2 bound state, effective range theory, and very low energy He–He scattering. J. Chem. Phys.76, 5069 (1982)

    Article ADS  Google Scholar 

  4. de Boer J.: Contribution to the quantum-mechanical theory of the equation of state and the law of corresponding states. Determination of the law of force of helium. Physica24, S90 (1958)

    Article  Google Scholar 

  5. Beck, D.E.: A new interatomic potential function for helium. Mol. Phys.14, 311 (1968); Errata, Ibid.15, 332 (1968)

    Google Scholar 

  6. Janzen A.R., Aziz R.A.: Modern He–He potentials: another look at binding energy, effective range theory, retardation, and Efimov states. J. Chem. Phys.103, 9626 (1995)

    Article ADS  Google Scholar 

  7. Efimov, V.N.: Weakly-bound states of three resonantly-interacting particles. Sov. J. Nucl. Phys.12, 589 (1971) [Yad. Fiz.12, 1080 (1970)]

    Google Scholar 

  8. Efimov V.: Energy levels arising from resonant two-body forces in a three-body system. Phys. Lett. B33, 563 (1970)

    Article ADS  Google Scholar 

  9. Efimov V.: Energy levels of three resonantly interacting particles. Nucl. Phys. A.210, 157 (1973)

    Article ADS  Google Scholar 

  10. Lim T.K., Duffy S.K., Damert W.C.: Efimov state in the4He trimer. Phys. Rev. Lett.38, 341 (1977)

    Article ADS  Google Scholar 

  11. Anderson J.B., Traynor C.A., Boghosian B.M.: An exact quantum Monte Carlo calculation of the helium–helium intermolecular potential. J. Chem. Phys.99, 345 (1993)

    Article ADS  Google Scholar 

  12. Bishop R.F., Ghassib H.B., Strayer M.R.: Low-energy He–He interactions with phenomenological potentials. J. Low Temp. Phys.26, 669 (1977)

    Article ADS  Google Scholar 

  13. Aziz R.A., McCourt F.R.W., Wong C.C.K.: A new determination of the ground state interatomic potential for He2. Mol. Phys.61, 1487 (1987)

    Article ADS  Google Scholar 

  14. Aziz R.A., Slaman M.J.: An examination of ab initio results for helium potential energy curve. J. Chem. Phys.94, 8047 (1991)

    Article ADS  Google Scholar 

  15. Tang K.T., Toennies J.P., Yiu: Accurate analytical He–He van der Waals potential based on perturbation theory. Phys. Rev. Lett.74, 1546 (1995)

    Article ADS  Google Scholar 

  16. Korona T., Williams H.L., Bokowski R., Jeziorski B., Szalewicz K.: Helium dimer potential from symmetry-adapted perturbation theory calculations using large Gaussian geminal and orbital basis sets. J. Chem. Phys.106, 5109 (1997)

    Article ADS  Google Scholar 

  17. Janzen A.R., Aziz R.A.: An accurate potential energy curve for helium based on ab initio calculations. J. Chem. Phys.107, 914 (1997)

    Article ADS  Google Scholar 

  18. Jeziorska M., Cencek W., Patkowski K., Jeziorski B., Szalewicz K.: Pair potential for helium from symmetry-adapted perturbation theory calculations and from supermolecular data. J. Chem. Phys.127, 124303 (2007)

    Article ADS  Google Scholar 

  19. Motovilov A.K., Sandhas W., Sofianos S.A., Kolganova E.A.: Binding energies and scattering observables in the4He3 atomic system. Eur. Phys. J. D13, 33 (2001)

    Article ADS  Google Scholar 

  20. Roudnev V., Yakovlev S.: Investigation of4He3 trimer on the base of Faddeev equations in configuration space. Chem. Phys. Lett.328, 97 (2000)

    Article ADS  Google Scholar 

  21. Barletta P., Kievsky A.: Variational description of the helium trimer using correlated hyperspherical harmonic basis functions. Phys. Rev. A64, 042514 (2001)

    Article ADS  Google Scholar 

  22. Blume D., Greene C.H.: Monte Carlo hyperspherical description of helium cluster excited states. J. Chem. Phys.112, 8053 (2000)

    Article ADS  Google Scholar 

  23. Blume D., Greene C.H., Esry B.D.: Comparative study of He3, Ne3, and Ar3 using hyperspherical coordinates. J. Chem. Phys.113, 2145 (2000)

    Article ADS  Google Scholar 

  24. Lazauskas R., Carbonell J.: Description of4He tetramer bound and scattering states. Phys. Rev. A73, 062717 (2006)

    Article ADS  Google Scholar 

  25. Nielsen E., Fedorov D.V., Jensen A.S.: The structure of the atomic helium trimers: Halos and Efimov states. J. Phys. B31, 4085 (1998)

    Article ADS  Google Scholar 

  26. Bressanini D., Zavaglia M., Mella M., Morosi G.: Quantum Monte Carlo investigation of small4He clusters with a3He impurity. J. Chem. Phys.112, 717 (2000)

    Article ADS  Google Scholar 

  27. Salci M., Yarevsky E., Levin S.B., Elander N.: Finite element investigation of the ground states of the helium trimers4He3 and4He23He. Int. J. Quant. Chem.107, 464 (2007)

    Article ADS  Google Scholar 

  28. Kolganova, E.A., Roudnev, V., Cavagnero, M: Solution of three-dimensional Faddeev equations: ultracold Helium trimer calculations with a public quantum three-body code. E-print arXiv:1010.1404

  29. Orlandini S., Baccarelli I., Gianturco F.A.: Variational calculations of structures and energetics in very floppy trimers: a new computational implementation. Comp. Phys. Comm.180, 384 (2009)

    Article MathSciNet ADS MATH  Google Scholar 

  30. Barletta P., Kievsky A.: Scattering states of three-body systems with the hyperspherical adiabatic method. Few-Body Syst.45, 123 (2009)

    Article ADS  Google Scholar 

  31. Kolganova E.A.: Helium trimer in the framework of Faddeev approach. Phys. Part. Nucl.41, 1108 (2010)

    Article  Google Scholar 

  32. Motovilov A.K., Sofianos S.A., Kolganova E.A.: Bound states and scattering processes in the4He3 atomic system. Chem. Phys. Lett.275, 168 (1997)

    Article ADS  Google Scholar 

  33. Kolganova E.A., Motovilov A.K., Sofianos S.A.: Three-body configuration space calculations with hard-core potentials. J. Phys. B31, 1279 (1998)

    Article ADS  Google Scholar 

  34. Roudnev V.: Ultra-low energy elastic scattering in a system of three He atoms. Chem. Phys. Lett.367, 95 (2003)

    Article ADS  Google Scholar 

  35. Roudnev V.A., Yakovlev S.L., Sofianos S.A.: Bound-state calculations for three atoms without explicit partial wave decomposition. Few-Body Syst.37, 179 (2005)

    Article ADS  Google Scholar 

  36. Kolganova E.A., Motovilov A.K., Sandhas W.: Scattering length of the helium-atom–helium-dimer collision. Phys. Rev. A70, 052711 (2004)

    Article ADS  Google Scholar 

  37. Suno H., Esry B.D.: Adiabatic hyperspherical study of triatomic helium systems. Phys. Rev. A78, 062701 (2008)

    Article ADS  Google Scholar 

  38. Kolganova E.A., Motovilov A.K., Sandhas W.: Ultracold collisions in the system of three helium atoms. Phys. Part. Nucl.40, 206 (2009)

    Article  Google Scholar 

  39. Cornelius T., Glöckle W.: Efimov states for three4He atoms?. J. Chem. Phys85, 3906 (1986)

    Article ADS  Google Scholar 

  40. Esry B.D., Lin C.D., Greene C.H.: Adiabatic hyperspherical study of the helium trimer. Phys. Rev. A54, 394 (1996)

    Article ADS  Google Scholar 

  41. Bedaque P.E., Hammer H.-W., van Kolck U.: The three-boson system with short-range interactions. Nucl. Phys. A646, 444 (1999)

    Article ADS  Google Scholar 

  42. Frederico T., Tomio L., Delfino A., Amorim A.E.A.: Scaling limit of weakly bound triatomic states. Phys. Rev. A60, R9 (1999)

    Article ADS  Google Scholar 

  43. Yamashita M.T., Frederico T., Delfino A., Tomio L.: Scaling limit of virtual states of triatomic systems. Phys. Rev. A66, 052702 (2002)

    Article ADS  Google Scholar 

  44. Braaten E., Hammer H.-W.: Universality in the three-body problem for4He atoms. Phys. Rev. A67, 042706 (2003)

    Article ADS  Google Scholar 

  45. Pen’kov F.M.: One-parametric dependences of spectra, scattering lengths and recombination coefficients for a system of three bosons. J. Exp. Theor. Phys.97, 485 (2003)

    Article ADS  Google Scholar 

  46. Pen’kov F.M., Sandhas W.: Differential form of the Skornyakov–Ter-Martirosyan equations. Phys. Rev. A72, 060702(R) (2006)

    Google Scholar 

  47. Platter L., Phillips D.R.: The three-boson system at next-to-next-to-leading order. Few-Body Syst.40, 35 (2006)

    Article ADS  Google Scholar 

  48. Shepard J.R.: Calculations of recombination rates for cold4He atoms from atom-dimer phase shifts and determination of universal scaling functions. Phys. Rev. A75, 062713 (2007)

    Article ADS  Google Scholar 

  49. Braaten E., Hammer H.-W.: Universality in few-body systems with large scattering length. Phys. Rep.428, 259 (2006)

    Article MathSciNet ADS  Google Scholar 

  50. Luo F., McBane G.C., Kim G., Giese C.F., Gentry W.R.: The weakest bond: experimental observation of helium dimer. J. Chem. Phys.98, 3564 (1993)

    Article ADS  Google Scholar 

  51. Schöllkopf W., Toennies J.P.: Nondestructive mass selection of small van der Waals clusters. Science266, 1345 (1994)

    Article ADS  Google Scholar 

  52. Luo F., Giese C.F., Gentry W.R.: Direct measurement of the size of the helium dimer. J. Chem. Phys.104, 1151 (1996)

    Article ADS  Google Scholar 

  53. Grisenti R., Schöllkopf W., Toennies J.P., Hegerfeld G.C., Köhler T., Stoll M.: Determination of the bond length and binding energy of the helium dimer by diffraction from a transmission grating. Phys. Rev. Lett.85, 2284 (2000)

    Article ADS  Google Scholar 

  54. Hegerfeldt G.C., Köhler T.: How to study the elusive Efimov state of the4He3 molecule through a new atom-optical state-selection technique. Phys. Rev. Lett.84, 3215 (2000)

    Article ADS  Google Scholar 

  55. Brühl R., Kalinin A., Kornilov O., Toennies J.P., Hegerfeld G.C., Stoll M.: Matter wave diffraction from an inclined transmission grating: searching for the elusive4He trimer Efimov state. Phys. Rev. Lett.95, 06002 (2005)

    Article  Google Scholar 

  56. Lewerenz M.: Structure and energetics of small helium clusters: quantum simulations using a recent perturbational pair potential. J. Chem. Phys.106, 4596 (1997)

    Article ADS  Google Scholar 

  57. Kolganova E.A., Motovilov A.K., Sandhas W.: Ultracold scattering processes in three-atomic helium systems. Nucl. Phys. A790, 752c (2007)

    Article ADS  Google Scholar 

  58. Kolganova E.A., Motovilov A.K.: Mechanism of the emergence of Efimov states in the4He trimer. Phys. At. Nucl.62, 1179 (1999)

    Google Scholar 

  59. Reed M., Simon B.: Methods of Modern Mathematical Physics. IV: Analysis of Operators. Academic, New York (1978)

    MATH  Google Scholar 

  60. Tamura H.: The Efimov effect of three-body Schrödinger operators: asymptotics for the number of negative eigenvalues. Nagoya Math. J.130, 55 (1993)

    MathSciNet MATH  Google Scholar 

  61. Sobolev A.V.: The Efimov effect. Discrete spectrum asymptotics. Commun. Math. Phys.156, 101 (1993)

    Article MathSciNet ADS MATH  Google Scholar 

  62. Danilov G.S.: On the three-body problem with short-range forces. Sov. Phys. JETP13, 349 (1961)

    MathSciNet MATH  Google Scholar 

  63. Skornyakov G.V., Ter-Martirosyan K.A.: Three body problem for short-range forces. Low energy neutron scattering by deuterons. Sov. Phys. JETP4, 648 (1956)

    MATH  Google Scholar 

  64. Albeverio S., Lakaev S., Makarov K.A.: The Efimov effect and an extended Szegö-Kac limit theorem. Lett. Math. Phys.43, 73 (1998)

    Article MathSciNet MATH  Google Scholar 

  65. Faddeev L.D.: Integral Equations Method in Scattering Theory for Three and More Particles. Mosk. Inzh. Fiz. Inst., Moscow (1971) (in Russian)

    Google Scholar 

  66. Amado R.D., Noble J.V.: On Efimov’s effect: a new pathology of three-particle systems. Phys. Lett. B35, 25 (1971)

    Article ADS  Google Scholar 

  67. Amado R.D., Noble J.V.: Efimov’s effect: a new pathology of three-particle systems. II. Phys. Rev. D5, 1992 (1971)

    Article ADS  Google Scholar 

  68. Merkuriev S.P., Faddeev L.D.: Quantum Scattering Theory for Several-Particle Systems. Nauka, Moscow (1985) (in Russian)

    Google Scholar 

  69. Jafaev D.R.: On the theory of the discrete spectrum of the three-particle Schrödinger operator. Math. USSR Sb.23, 535 (1974)

    Article  Google Scholar 

  70. Vugal’ter S.A., Zhislin G.M.: On the discrete spectrum of Schrod̈inger operators of multiparticle systems with two-particle virtual levels. Dokl. Akad. Nauk SSSR267, 784 (1982)

    MathSciNet  Google Scholar 

  71. Wang X.P.: On the existence of theN-body Efimov effect. J. Funct. Anal.209, 137 (2004)

    Article MathSciNet MATH  Google Scholar 

  72. Wang X.P., Wang Y.: Existence of two-cluster threshold resonances and theN-body Efimov effect. J. Math. Phys.46, 112106 (2005)

    Article MathSciNet ADS  Google Scholar 

  73. Phillips A.C.: Three-body systems in nuclear physics. Rep. Prog. Phys.40, 905 (1977)

    Article ADS  Google Scholar 

  74. Thomas L.H.: The interaction between a neutron and a proton and the structure ofH3. Phys. Rev.47, 903 (1935)

    Article ADS MATH  Google Scholar 

  75. Minlos R.A., Faddeev L.D.: On the point interaction for a three-particle system in quantum mechanics. Sov. Phys. Dokl.6, 1072 (1961)

    MathSciNet ADS  Google Scholar 

  76. Albeverio S., Høegh-Krohn R., Wu T.T.: A class of exactly solvable three-body quantum mechanical problems and the universal low energy behavior. Phys. Lett. A.83, 105 (1981)

    Article MathSciNet ADS  Google Scholar 

  77. Makarov K.A., Melezhik V.V.: Two sides of a coin: the Efimov effect and collapse in a three-body system with point interactions. I. Theor. Math. Phys.107, 755 (1996)

    Article MathSciNet MATH  Google Scholar 

  78. Nielsen E., Fedorov D.V., Jensen A.S., Garrido E.: The three-body problem with short-range interactions. Phys. Rep.347, 373 (2001)

    Article MathSciNet ADS MATH  Google Scholar 

  79. Lee M.D., Köhler T., Julienne P.S.: Excited Thomas–Efimov levels in ultracold gases. Phys. Rev. A.76, 012720 (2007)

    Article ADS  Google Scholar 

  80. Bedaque P.F., Braaten E., Hammer H.-W.: Three-body recombination in Bose gases with the large scattering length. Phys. Rev. Lett.85, 908 (2000)

    Article ADS  Google Scholar 

  81. Stoll M., Köhler T.: Production of three-body Efimov molecules in an optical lattice. Phys. Rev. A72, 022714 (2005)

    Article ADS  Google Scholar 

  82. Jonsell S.: Efimov states for systems with negative scattering lengths. Europhys. Lett.76, 8 (2006)

    Article ADS  Google Scholar 

  83. Kraemer T., Mark M., Waldburger P., Danzl J.G., Chin C., Engeser B., Lange A.D., Pilch K., Jaakkola A., Nag̈erl H.-C., Grimm R.: Evidence for Efimov quantum states in an ultracold gas of caesium atoms. Nature440, 315 (2006)

    Article ADS  Google Scholar 

  84. Thøgersen M., Fedorov D.V., Jensen A.S., Esry B.D., Wang Y.: Conditions for Efimov physics for finite-range potentials. Phys. Rev. A80, 013608 (2009)

    Article ADS  Google Scholar 

  85. Moerdijk A.J., Verhaar B.J., Axelsson A.: Resonances in ultracold collisions of6Li,7Li, and23Na. Phys. Rev. A.51, 4852 (1995)

    Article ADS  Google Scholar 

  86. Nag̈erl H.-C., Kraemer T., Mark M., Waldburger P., Danzl J.G., Engeser B., Lange A.D., Pilch K., Jaakkola A., Chin C., Grimm R.: Experimental evidence for Efimov quantum states. AIP Conf. Proc.869, 269 (2006)

    Article ADS  Google Scholar 

  87. Esry B.D., Greene C.H.: A ménage à trois laid bare. Nature440, 289 (2006)

    Article ADS  Google Scholar 

  88. Barontini, G., Weber, C., Rabatti, F., Catani, J., Thalhammer, G., Inguscio, M., Minardi, F.: Observation of heteronuclear atomic Efimov resonances. Phys. Rev. Lett.103, 043201 (2009); Erratum, Ibid.104, 059901 (2010)

    Google Scholar 

  89. Lompe T., Ottenstein T.B., Serwane F., Viering K., Wenz A.N., Zürn G., Jochim S.: Atom–dimer scattering in a three-component fermi gas. Phys. Rev. Lett.105, 103201 (2010)

    Article ADS  Google Scholar 

  90. Kolganova E.A., Motovilov A.K., Sandhas W.: Ultracold helium trimers. Few-Body Syst.44, 233 (2008)

    Article ADS  Google Scholar 

  91. Kolganova E.A., Motovilov A.K.: Scattering and resonances in the4He three-atomic system. Comp. Phys. Comm.126, 88 (2000)

    Article ADS MATH  Google Scholar 

  92. Motovilov A.K., Kolganova E.A.: Structure ofT- andS-matrices in unphysical sheets and resonances in three-body systems. Few-Body Syst. Suppl.10, 75 (1999)

    Article  Google Scholar 

  93. Motovilov A.K.: Representations for the three-bodyT-matrix, scattering matrices and resolvent on unphysical energy sheets. Math. Nachr.187, 147 (1997)

    Article MathSciNet MATH  Google Scholar 

  94. von Stecher J.: Weakly bound cluster states of Efimov character. J. Phys. B43, 101002 (2010)

    Article ADS  Google Scholar 

  95. Esry B.D.: Ultracold experiments strike universal physics—again. Physics2, 26 (2009)

    Article  Google Scholar 

  96. Wang Y., Esry B.D.: Efimov trimer formation via ultracold four-body recombination. Phys. Rev. Lett.102, 133201 (2009)

    Article ADS  Google Scholar 

  97. Ferlaino F., Grimm R.G.: Forty years of Efimov physics: How a bizarre prediction turned into a hot topic. Physics3, 9 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, JINR, Joliot-Curie 6, 141980, Dubna, Moscow Region, Russia

    E. A. Kolganova & A. K. Motovilov

  2. Physikalisches Institut, Universität Bonn, Endenicher Allee 11-13, 53115, Bonn, Germany

    W. Sandhas

Authors
  1. E. A. Kolganova

    You can also search for this author inPubMed Google Scholar

  2. A. K. Motovilov

    You can also search for this author inPubMed Google Scholar

  3. W. Sandhas

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence toA. K. Motovilov.

Additional information

Dedicated to the 40th anniversary of the Efimov effect

Special issue devoted to Efimov physics.

This work was supported by the Deutsche Forschungsgemeinschaft (DFG), the Heisenberg-Landau Program, the Alexander von Humboldt Foundation, and the Russian Foundation for Basic Research.

Rights and permissions

About this article

Access this article

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Advertisement


[8]ページ先頭

©2009-2025 Movatter.jp