205Accesses
3Altmetric
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
Subscribe and save
- Get 10 units per month
- Download Article/Chapter or eBook
- 1 Unit = 1 Article or 1 Chapter
- Cancel anytime
Buy Now
Price includes VAT (Japan)
Instant access to the full article PDF.
Similar content being viewed by others
References
Bruch L.W., McGee I.J.: Semiempirical helium intermolecular potential. II. Dilute gas properties. J. Chem. Phys.52, 5884 (1970)
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)
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)
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)
Beck, D.E.: A new interatomic potential function for helium. Mol. Phys.14, 311 (1968); Errata, Ibid.15, 332 (1968)
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)
Efimov, V.N.: Weakly-bound states of three resonantly-interacting particles. Sov. J. Nucl. Phys.12, 589 (1971) [Yad. Fiz.12, 1080 (1970)]
Efimov V.: Energy levels arising from resonant two-body forces in a three-body system. Phys. Lett. B33, 563 (1970)
Efimov V.: Energy levels of three resonantly interacting particles. Nucl. Phys. A.210, 157 (1973)
Lim T.K., Duffy S.K., Damert W.C.: Efimov state in the4He trimer. Phys. Rev. Lett.38, 341 (1977)
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)
Bishop R.F., Ghassib H.B., Strayer M.R.: Low-energy He–He interactions with phenomenological potentials. J. Low Temp. Phys.26, 669 (1977)
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)
Aziz R.A., Slaman M.J.: An examination of ab initio results for helium potential energy curve. J. Chem. Phys.94, 8047 (1991)
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)
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)
Janzen A.R., Aziz R.A.: An accurate potential energy curve for helium based on ab initio calculations. J. Chem. Phys.107, 914 (1997)
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)
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)
Roudnev V., Yakovlev S.: Investigation of4He3 trimer on the base of Faddeev equations in configuration space. Chem. Phys. Lett.328, 97 (2000)
Barletta P., Kievsky A.: Variational description of the helium trimer using correlated hyperspherical harmonic basis functions. Phys. Rev. A64, 042514 (2001)
Blume D., Greene C.H.: Monte Carlo hyperspherical description of helium cluster excited states. J. Chem. Phys.112, 8053 (2000)
Blume D., Greene C.H., Esry B.D.: Comparative study of He3, Ne3, and Ar3 using hyperspherical coordinates. J. Chem. Phys.113, 2145 (2000)
Lazauskas R., Carbonell J.: Description of4He tetramer bound and scattering states. Phys. Rev. A73, 062717 (2006)
Nielsen E., Fedorov D.V., Jensen A.S.: The structure of the atomic helium trimers: Halos and Efimov states. J. Phys. B31, 4085 (1998)
Bressanini D., Zavaglia M., Mella M., Morosi G.: Quantum Monte Carlo investigation of small4He clusters with a3He impurity. J. Chem. Phys.112, 717 (2000)
Salci M., Yarevsky E., Levin S.B., Elander N.: Finite element investigation of the ground states of the helium trimers4He3 and4He2–3He. Int. J. Quant. Chem.107, 464 (2007)
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
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)
Barletta P., Kievsky A.: Scattering states of three-body systems with the hyperspherical adiabatic method. Few-Body Syst.45, 123 (2009)
Kolganova E.A.: Helium trimer in the framework of Faddeev approach. Phys. Part. Nucl.41, 1108 (2010)
Motovilov A.K., Sofianos S.A., Kolganova E.A.: Bound states and scattering processes in the4He3 atomic system. Chem. Phys. Lett.275, 168 (1997)
Kolganova E.A., Motovilov A.K., Sofianos S.A.: Three-body configuration space calculations with hard-core potentials. J. Phys. B31, 1279 (1998)
Roudnev V.: Ultra-low energy elastic scattering in a system of three He atoms. Chem. Phys. Lett.367, 95 (2003)
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)
Kolganova E.A., Motovilov A.K., Sandhas W.: Scattering length of the helium-atom–helium-dimer collision. Phys. Rev. A70, 052711 (2004)
Suno H., Esry B.D.: Adiabatic hyperspherical study of triatomic helium systems. Phys. Rev. A78, 062701 (2008)
Kolganova E.A., Motovilov A.K., Sandhas W.: Ultracold collisions in the system of three helium atoms. Phys. Part. Nucl.40, 206 (2009)
Cornelius T., Glöckle W.: Efimov states for three4He atoms?. J. Chem. Phys85, 3906 (1986)
Esry B.D., Lin C.D., Greene C.H.: Adiabatic hyperspherical study of the helium trimer. Phys. Rev. A54, 394 (1996)
Bedaque P.E., Hammer H.-W., van Kolck U.: The three-boson system with short-range interactions. Nucl. Phys. A646, 444 (1999)
Frederico T., Tomio L., Delfino A., Amorim A.E.A.: Scaling limit of weakly bound triatomic states. Phys. Rev. A60, R9 (1999)
Yamashita M.T., Frederico T., Delfino A., Tomio L.: Scaling limit of virtual states of triatomic systems. Phys. Rev. A66, 052702 (2002)
Braaten E., Hammer H.-W.: Universality in the three-body problem for4He atoms. Phys. Rev. A67, 042706 (2003)
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)
Pen’kov F.M., Sandhas W.: Differential form of the Skornyakov–Ter-Martirosyan equations. Phys. Rev. A72, 060702(R) (2006)
Platter L., Phillips D.R.: The three-boson system at next-to-next-to-leading order. Few-Body Syst.40, 35 (2006)
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)
Braaten E., Hammer H.-W.: Universality in few-body systems with large scattering length. Phys. Rep.428, 259 (2006)
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)
Schöllkopf W., Toennies J.P.: Nondestructive mass selection of small van der Waals clusters. Science266, 1345 (1994)
Luo F., Giese C.F., Gentry W.R.: Direct measurement of the size of the helium dimer. J. Chem. Phys.104, 1151 (1996)
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)
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)
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)
Lewerenz M.: Structure and energetics of small helium clusters: quantum simulations using a recent perturbational pair potential. J. Chem. Phys.106, 4596 (1997)
Kolganova E.A., Motovilov A.K., Sandhas W.: Ultracold scattering processes in three-atomic helium systems. Nucl. Phys. A790, 752c (2007)
Kolganova E.A., Motovilov A.K.: Mechanism of the emergence of Efimov states in the4He trimer. Phys. At. Nucl.62, 1179 (1999)
Reed M., Simon B.: Methods of Modern Mathematical Physics. IV: Analysis of Operators. Academic, New York (1978)
Tamura H.: The Efimov effect of three-body Schrödinger operators: asymptotics for the number of negative eigenvalues. Nagoya Math. J.130, 55 (1993)
Sobolev A.V.: The Efimov effect. Discrete spectrum asymptotics. Commun. Math. Phys.156, 101 (1993)
Danilov G.S.: On the three-body problem with short-range forces. Sov. Phys. JETP13, 349 (1961)
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)
Albeverio S., Lakaev S., Makarov K.A.: The Efimov effect and an extended Szegö-Kac limit theorem. Lett. Math. Phys.43, 73 (1998)
Faddeev L.D.: Integral Equations Method in Scattering Theory for Three and More Particles. Mosk. Inzh. Fiz. Inst., Moscow (1971) (in Russian)
Amado R.D., Noble J.V.: On Efimov’s effect: a new pathology of three-particle systems. Phys. Lett. B35, 25 (1971)
Amado R.D., Noble J.V.: Efimov’s effect: a new pathology of three-particle systems. II. Phys. Rev. D5, 1992 (1971)
Merkuriev S.P., Faddeev L.D.: Quantum Scattering Theory for Several-Particle Systems. Nauka, Moscow (1985) (in Russian)
Jafaev D.R.: On the theory of the discrete spectrum of the three-particle Schrödinger operator. Math. USSR Sb.23, 535 (1974)
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)
Wang X.P.: On the existence of theN-body Efimov effect. J. Funct. Anal.209, 137 (2004)
Wang X.P., Wang Y.: Existence of two-cluster threshold resonances and theN-body Efimov effect. J. Math. Phys.46, 112106 (2005)
Phillips A.C.: Three-body systems in nuclear physics. Rep. Prog. Phys.40, 905 (1977)
Thomas L.H.: The interaction between a neutron and a proton and the structure ofH3. Phys. Rev.47, 903 (1935)
Minlos R.A., Faddeev L.D.: On the point interaction for a three-particle system in quantum mechanics. Sov. Phys. Dokl.6, 1072 (1961)
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)
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)
Nielsen E., Fedorov D.V., Jensen A.S., Garrido E.: The three-body problem with short-range interactions. Phys. Rep.347, 373 (2001)
Lee M.D., Köhler T., Julienne P.S.: Excited Thomas–Efimov levels in ultracold gases. Phys. Rev. A.76, 012720 (2007)
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)
Stoll M., Köhler T.: Production of three-body Efimov molecules in an optical lattice. Phys. Rev. A72, 022714 (2005)
Jonsell S.: Efimov states for systems with negative scattering lengths. Europhys. Lett.76, 8 (2006)
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)
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)
Moerdijk A.J., Verhaar B.J., Axelsson A.: Resonances in ultracold collisions of6Li,7Li, and23Na. Phys. Rev. A.51, 4852 (1995)
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)
Esry B.D., Greene C.H.: A ménage à trois laid bare. Nature440, 289 (2006)
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)
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)
Kolganova E.A., Motovilov A.K., Sandhas W.: Ultracold helium trimers. Few-Body Syst.44, 233 (2008)
Kolganova E.A., Motovilov A.K.: Scattering and resonances in the4He three-atomic system. Comp. Phys. Comm.126, 88 (2000)
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)
Motovilov A.K.: Representations for the three-bodyT-matrix, scattering matrices and resolvent on unphysical energy sheets. Math. Nachr.187, 147 (1997)
von Stecher J.: Weakly bound cluster states of Efimov character. J. Phys. B43, 101002 (2010)
Esry B.D.: Ultracold experiments strike universal physics—again. Physics2, 26 (2009)
Wang Y., Esry B.D.: Efimov trimer formation via ultracold four-body recombination. Phys. Rev. Lett.102, 133201 (2009)
Ferlaino F., Grimm R.G.: Forty years of Efimov physics: How a bizarre prediction turned into a hot topic. Physics3, 9 (2010)
Author information
Authors and Affiliations
Bogoliubov Laboratory of Theoretical Physics, JINR, Joliot-Curie 6, 141980, Dubna, Moscow Region, Russia
E. A. Kolganova & A. K. Motovilov
Physikalisches Institut, Universität Bonn, Endenicher Allee 11-13, 53115, Bonn, Germany
W. Sandhas
- E. A. Kolganova
You can also search for this author inPubMed Google Scholar
- A. K. Motovilov
You can also search for this author inPubMed Google Scholar
- 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
Cite this article
Kolganova, E.A., Motovilov, A.K. & Sandhas, W. The4He Trimer as an Efimov System.Few-Body Syst51, 249–257 (2011). https://doi.org/10.1007/s00601-011-0233-x
Received:
Accepted:
Published:
Issue Date:
Share this article
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt content-sharing initiative