Low-Energy Universality in Atomic and Nuclear Physics

Lucas Platter1
1Department of Physics, Ohio State University, Columbus, USA

Tóm tắt

An effective field theory developed for systems interacting through short-range interactions can be applied to systems of cold atoms with a large scattering length and to nucleons at low energies. It is therefore the ideal tool to analyze the universal properties associated with the Efimov effect in three- and four-body systems. In this progress report, we will discuss recent results obtained within this framework and report on progress regarding the inclusion of higher order corrections associated with the finite range of the underlying interaction.

Từ khóa


Tài liệu tham khảo

Efimov V.: Energy levels arising form the resonant two-body forces in a three-body system. Phys. Lett. 33, 563 (1970) Braaten E., Hammer H.W.: Universality in few-body systems with large scattering length. Phys. Rept. 428, 259 (2006) [arXiv:cond-mat/0410417] Braaten, E., Hammer, H.W.: Efimov Physics in Cold Atoms. Annals Phys. 322, 120 (2007) [arXiv:cond-mat/0612123] Bedaque, P.F., van Kolck, U.: Effective field theory for few nucleon systems. Ann. Rev. Nucl. Part. Sci. 52, 339 (2002) [arXiv:nucl-th/0203055] Epelbaum, E., Hammer, H.W., Meißner, U.G.: Modern Theory of Nuclear Forces. arXiv:0811.1338 [nucl-th] Kaplan, D.B.: Five lectures on effective field theory. arXiv:nucl-th/0510023 Lepage, G.P.: How to renormalize the Schrodinger equation. arXiv:nucl-th/9706029 Polchinski, J.: Effective field theory and the Fermi surface. arXiv:hep-th/9210046 Phillips, D.R.: Building light nuclei from neutrons, protons, and pions. Czech. J. Phys. 52, B49 (2002) [arXiv:nucl-th/0203040] van Kolck, U.: Effective field theory of short range forces. Nucl. Phys. A 645, 273 (1999) [arXiv:nucl-th/9808007] Kaplan, D.B., Savage, M.J., Wise, M.B.: A New expansion for nucleon-nucleon interactions. Phys. Lett. B 424, 390 (1998) [arXiv:nucl-th/9801034] Kaplan, D.B., Savage, M.J., Wise, M.B.: Two nucleon systems from effective field theory. Nucl. Phys. B 534, 329 (1998) [arXiv:nucl-th/9802075] Gegelia J.: EFT and NN Scattering. Phys. Lett. B 429, 227 (1998) Birse, M.C., McGovern, J.A., Richardson, K.G.: A Renormalization group treatment of two-body scattering. PiN Newslett. 15, 280 (1999) [arXiv:nucl-th/9911048] Hammer, H.W., Furnstahl, R.J.: Effective field theory for dilute Fermi systems. Nucl. Phys. A 678, 277 (2000) [arXiv:nucl-th/0004043] Platter, L., Hammer, H.W., Meißner, U.-G.: Quasiparticle properties in effective field theory. Nucl. Phys. A 714, 250 (2003) [arXiv:nucl-th/0208057] Bedaque, P.F., Hammer, H.W., van Kolck, U.: Renormalization of the three-body system with short range interactions. Phys. Rev. Lett. 82, 463 (1999) [arXiv:nucl-th/9809025] Bedaque, P.F., Hammer, H.W., van Kolck, U.: The Three boson system with short range interactions. Nucl. Phys. A 646, 444 (1999) [arXiv:nucl-th/9811046] Skorniakov G.V., Ter-Martirosian K.A.: Three Body Problem for Short Range Forces. 1. Scattering of Low Energy Neutrons by Deuterons. Sov. Phys. JETP 4, 648 (1957) Danilov, G.S.: On The Three-Body Problem with Short-Range Forces. Sov. Phys. JETP 13, 349 (1961) [J. Exptl. Theoret. Phys. (USSR) 40, 498 (1961)] Kharchenko, V.F.: Solution of the Skornyakov-Ter-Martirosian Equations for Three Nucleons with Cutoff at Large Momenta. Sov. J. Nucl. Phys. 16, 173 (1973) [Yad. Fiz. 16, 310 (1972)] Nielsen E., Fedorov D.V., Jensen A.S., Garrido E.: The three-body problem with short-range interactions. Phys. Rep. 347, 373 (2001) Wilson K.G.: Renormalization Group and Strong Interactions. Phys. Rev. D 3, 1818 (1971) Efimov V.: Force-range correction in the three-body problem: Application to three-nucleon systems. Phys. Rev. C 44, 2303 (1991) Efimov V.: Effective interaction of three resonantly interacting particles and the force range. Phys. Rev. C 47, 1876 (1993) Hammer, H.W., Mehen, T.: Range corrections to doublet S wave neutron deuteron scattering. Phys. Lett. B 516, 353 (2001) [arXiv:nucl-th/0105072] Platter, L., Ji, C., Phillips, D.R.: Range Corrections to Three-Body Observables near a Feshbach Resonance. Phys. Rev. A 79, 022702 (2009) [arXiv:0808.1230 [cond-mat.other]] Thøgersen M., Fedorov D.V., Jensen A.S.: Universal properties of Efimov physics beyond the scattering length approximation. Phys. Rev. A 78, 020501 (2008) Ji, C., Phillips, D.R., Platter, L.: in preparation Bedaque, P.F., Rupak, G., Griesshammer, H.W., Hammer, H.W.: Low-energy expansion in the three-body system to all orders and the triton channel. Nucl. Phys. A 714, 589 (2003) [arXiv:nucl-th/0207034] Gabbiani, F.: Effective range in doublet S-wave neutron deuteron scattering. arXiv:nucl-th/0104088 Platter, L., Phillips, D.R.: The Three-Boson System at Next-To-Next-To-Leading Order. Few Body Syst. 40, 35 (2006) [arXiv:cond-mat/0604255] Platter, L.: The Three-nucleon system at next-to-next-to-leading order. Phys. Rev. C 74, 037001 (2006) [arXiv:nucl-th/0606006] Hammer, H.W., Phillips, D.R., Platter, L.: Pion-mass dependence of three-nucleon observables. Eur. Phys. J. A 32, 335 (2007) [arXiv:0704.3726 [nucl-th]] Griesshammer, H.W.: Naive dimensional analysis for three-body forces without pions. Nucl. Phys. A 760, 110 (2005) [arXiv:nucl-th/0502039] Gasaneo G., Macek J.H.: Hyperspherical adiabatic eigenvalues for zero-range potentials. J. Phys. B 35, 2239 (2002) Platter, L., Hammer, H.W., Meißner, U.G.: The Four boson system with short range interactions. Phys. Rev. A 70, 052101 (2004) [arXiv:cond-mat/0404313] Glöckle W.: The quantum mechanical few-body problem. Springer, Heidelberg (1983) Schmid E.W., Ziegelmann H.: The quantum mechanical three-body problem. Vieweg, Wiesbaden (1971) Hammer, H.W., Platter, L.: Universal Properties of the Four-Body System with Large Scattering Length. Eur. Phys. J. A 32, 113 (2007) [arXiv:nucl-th/0610105] Schöllkopf W., Toennies J.P.: The nondestructive detection of the helium dimer and trimer. J. Chem. Phys. 104, 1155 (1996) Roudnev V., Yakovlev S.: Investigation of 4He3 trimer on the base of Faddeev equations in configuration space. Chem. Phys. Lett. 328, 97 (2000) Roudnev V.: Ultra-low energy elastic scattering in a system of three He atoms. Chem. Phys. Lett. 367, 95 (2003) Motovilov A.K., Sandhas W., Sofianos S.A., Kolganova E.A.: Binding energies and scattering observables in the 4He3 atomic system. Eur. Phys. J. D 13, 33 (2001) Kolganova E.A., Motovilov A.K., Sandhas W.: Scattering length of the helium-atom-helium-dimer collision. Phys. Rev. A 70, 052711 (2004) Blume D., Greene C.H.: Monte Carlo hyperspherical description of helium cluster excited states. J. Chem. Phys. 112, 8053 (2000) Lewerenz M.: Structure and energetics of small helium clusters: Quantum simulations using a recent perturbational pair potential. J. Chem. Phys. 106, 4596 (1997) Nakaichi-Maeda S., Lim T.K.: Zero-energy scattering and bound states in the 4He trimer and tetramer. Phys. Rev. A 28, 692 (1983) von Stecher, J., D’Incao, J.P., Greene, C.H.: Four-body legacy of the Efimov effect. Nat. Phys. 5, 417–421 (2009) [arXiv:0810.3876] Kraemer T., Mark M., Waldburger P., Danzl J.G., Chin C., Engeser B., Lange A.D., Pilch K., Jaakkola A., Nägerl H.-C., Grimm R.: Evidence for Efimov quantum states in an ultracold gas of cesium atoms. Nature 440, 315 (2006) Ottenstein, T.B., Lompe, T., Kohnen, M., Wenz, A.N., Jochim, S.: Collisional stability of a three-component degenerate Fermi gas. Phys. Rev. Lett. 101, 203202 (2008) [arXiv:0806.0587] Huckans, J.H., Williams, J.R., Hazlett, E.L., Stites, R.W., O’Hara, K.M.: Three-body recombination in a three-state Fermi gas with widely tunable interactions. Phys. Rev. Lett. 102, 165302 (2009) [arXiv:0810.3288] Zaccanti, M., Modugno, G., D’Erico, C., Farroti, M., Roati, G., Inguscio, M.: talk at DAMOP 2008, State College, Pennsylvania, USA Thalhammer, G., Barontini, G., Catani, J., Rabatti, F., Weber, C., Simoni, A., Minardi, F., Inguscio, M.: Collisional and molecular spectroscopy in an ultracold Bose-Bose mixture. arXiv:0903.0976 Ferlaino, F., Knoop, S., Berninger, M., Harm, W., D’Incao, J.P., Nägerl, H.-C., Grimm, R.: Evidence for Universal Four-Body States Tied to an Efimov Trimer. arXiv:0903.1276 Bedaque, P.F., Braaten, E., Hammer, H.W.: Three body recombination in Bose gases with large scattering length. Phys. Rev. Lett. 85, 908 (2000) [arXiv:cond-mat/0002365] Esry B.D., Greene C.H., Suno H.: Threshold laws for three-body recombination. Phys. Rev. A 65, 010705 (2001) Macek J.H., Ovchinnikov S., Gasaneo G.: Solution for boson-diboson elastic scattering at zero energy in the shape-independent model. Phys. Rev. A 72, 032709 (2005) Macek J.H., Ovchinnikov S., Gasaneo G.: Exact solution for three particles interacting via zero-range potentials. Phys. Rev. A 73, 032704 (2006) Petrov, D.: talk at the Workshop on Strongly Interacting Quantum Gases, Ohio State University, April (2005) Nielsen E., Macek J.H.: Low-Energy Recombination of Identical Bosons by Three-Body Collisions. Phys. Rev. Lett. 83, 1566 (1999) Esry B.D., Greene C.H., Burke J.P.: Recombination of Three Atoms in the Ultracold Limit. Phys. Rev. Lett. 83, 1751 (1999) Braaten, E. Hammer, H.W.: Enhanced dimer deactivation in an atomic/molecular BEC. Phys. Rev. A 70, 042706 (2004) [arXiv:cond-mat/0303249] Braaten, E., Hammer, H.W.: Three body recombination into deep bound states in a Bose gas with large scattering length. Phys. Rev. Lett. 87, 160407 (2001) [arXiv:cond-mat/0103331] Efimov, V.: Low-Energy Properties Of Three Resonantly Interacting Particles. Sov. J. Nucl. Phys. 29, 546 (1979) [Yad. Fiz. 29, 1058 (1979)] Braaten, E., Hammer, H.W., Kang, D., Platter, L.: Three-Body Recombination of Identical Bosons with a Large Positive Scattering Length at Nonzero Temperature. Phys. Rev. A 78, 043605 (2008) [arXiv:0801.1732 [cond-mat.other]] Hammer, H.W., Lahde, T.A., Platter, L.: Effective range corrections to three-body recombination for atoms with large scattering length. Phys. Rev. A 75, 032715 (2007) [arXiv:cond-mat/0611769] Braaten, E., Hammer, H.W., Kang, D., Platter, L.: Three-body Recombination of Fermionic Atoms with Large Scattering Lengths. arXiv:0811.3578 [cond-mat.other] Naidon, P., Ueda, M.: A possible Efimov trimer state in 3-component lithium 6. arXiv:0811.4086 Schmidt, R., Floerchinger, S., Wetterich, C.: Three-body loss in lithium from functional renormalization. Phys. Rev. A 79, 053633 (2009) [arXiv:0812.1191] Braaten, E., Hammer, H.W.: Resonant dimer relaxation in cold atoms with a large scattering length. Phys. Rev. A 75, 052710 (2007) [arXiv:cond-mat/0610116] Helfrich, K., Hammer, H.W.: Resonant Atom-Dimer Relaxation in Ultracold Atoms. Europhys. Lett. 86, 53003 (2009) [arXiv:0902.3410 [cond-mat.other]] Knoop, S., et al.: Observation of an Efimov-like resonance in ultracold atom-dimer scattering. Nat. Phys. 5, 227 (2009) [arXiv:0807.3306 [cond-mat]] von Stecher, J., D’Incao, J.P., Greene, C.H.: Universal Four-Boson States in Ultracold Molecular Gases: Resonant Effects in Dimer-Dimer Collisions. Phys. Rev. Lett. 103, 033004 (2009) [arXiv:0903.3348] Epelbaum, E.: Few-nucleon forces and systems in chiral effective field theory. Prog. Part. Nucl. Phys. 57, 654 (2006) [arXiv:nucl-th/0509032] Kong, X., Ravndal, F.: Proton proton fusion in effective field theory. Phys. Rev. C 64, 044002 (2001) [arXiv:nucl-th/0004038] Christlmeier, S., Griesshammer, H.W.: Pion-less Effective Field Theory on Low-Energy Deuteron Electro-Disintegration. Phys. Rev. C 77, 064001 (2008) [arXiv:0803.1307 [nucl-th]] Arenhövel, H., Leidemann, W., Tomusiak, E.L.: General survey of polarization observables in deuteron electrodisintegration. Eur. Phys. J. A 23, 147 (2005) [arXiv:nucl-th/0407053] Tamae T. et al.: Out-of-Plane Measurement of the D(e, e′ p) Coincidence Cross Section. Phys. Rev. Lett. 59, 2919 (1987) von Neumann-Cosel P. et al.: Deuteron Breakup in the 2H(e, e′ p) Reaction at Low Momentum Transfer and Close to Threshold. Phys. Rev. Lett. 88, 202304 (2002) Ryezayeva N. et al.: Measurement of the Reaction 2H(e, e′) at 180° Close to the Deuteron Breakup Threshold. Phys. Rev. Lett. 100, 172501 (2008) Ando, S.I.: \({pp \rightarrow pp \pi_0}\) near threshold in pionless effective theory. Eur. Phys. J. A 33, 185 (2007) [arXiv:0707.2157[nucl-th]] Phillips, D.R., Schindler, M.R., Springer, R.P.: An Effective-field-theory analysis of low-energy parity-violation in nucleon-nucleon scattering. arXiv:0812.2073 [nucl-th] Bedaque, P.F., Hammer, H.W., van Kolck, U.: Effective theory for neutron deuteron scattering: Energy dependence. Phys. Rev. C 58, 641 (1998) [arXiv:nucl-th/9802057] Bedaque, P.F., Hammer, H.W., van Kolck, U.: Effective theory of the triton. Nucl. Phys. A 676, 357 (2000) [arXiv:nucl-th/9906032] Platter, L., Hammer, H.W.: Universality in the triton charge form-factor. Nucl. Phys. A 766, 132 (2006) [arXiv:nucl-th/0509045] Friar J.L., Gibson B.F., Tomusiak E.L., Payne G.L.: Configuration space Faddeev calculations. IV. Trinucleon charge density. Phys. Rev. C 24, 665 (1981) Friar J.L., Gibson B.F., Chen C.R., Payne G.L.: Scaling relations for triton ground-state observables. Phys. Lett. 161, 241 (1985) Chen C.R., Payne G.L., Friar J.L., Gibson B.F.: Convergence of Faddeev partial-wave series for triton ground state. Phys. Rev. C 31, 2266 (1985) Sadeghi H., Bayegan S., Grießhammer H.W.: Effective field theory calculation of thermal energies and radiative capture cross-section. Phys. Lett. B 643, 263 (2006) Sadeghi H., Bayegan S.: \({Nd \rightarrow ^3}\) H γ with effective field theory. Nucl. Phys. A 753, 291 (2005) Rupak, G., Kong, X.W.: Quartet S-wave p d scattering in EFT. Nucl. Phys. A 717, 73 (2003) [arXiv:nucl-th/0108059] Platter, L., Hammer, H.W., Meißner, U.G.: On the correlation between the binding energies of the triton and the alpha-particle. Phys. Lett. B 607, 254 (2005) [arXiv:nucl-th/0409040] Nogga, A., Kamada, H., Glöckle, W.: Modern nuclear force predictions for the alpha particle. Phys. Rev. Lett. 85, 944 (2000) [arXiv:nucl-th/0004023] Epelbaum, E., Kamada, H., Nogga, A., Witała, H., Glöckle, W., Meißner, U.-G.: The Three nucleon and four nucleon systems from chiral effective field theory. Phys. Rev. Lett. 86, 4787 (2001) [arXiv:nucl-th/0007057] Epelbaum, E., Nogga, A., Glöckle, W., Kamada, H., Meißner, U.-G., Witała, H.: Three nucleon forces from chiral effective field theory. Phys. Rev. C 66, 064001 (2002) [arXiv:nucl-th/0208023] Beck D.H. et al.: Tritium form factors at low q. Phys. Rev. C 30, 1403 (1984) Beck D. et al.: Isoscalar and isovector form factors of 3H and 3He for Q below 2.9 fm−1 from electron-scattering measurements. Phys. Rev. Lett. 59, 1537 (1987) Nogga, A., Bogner, S.K., Schwenk, A.: Low-momentum interaction in few-nucleon systems. Phys. Rev. C 70, 061002 (2004) [arXiv:nucl-th/0405016] Stetcu, I., Barrett, B.R., van Kolck, U.: No-core shell model in an effective-field-theory framework. Phys. Lett. B 653, 358 (2007) [arXiv:nucl-th/0609023] Bacca, S., Schwenk, A., Hagen, G., Papenbrock, T.: Helium halo nuclei from low-momentum interactions. arXiv:0902.1696 [nucl-th] Riisager K.: Nuclear halo states. Rev. Mod. Phys. 66, 1105 (1994) Zhukov M.V., Danilin B.V., Fedorov D.V., Bang J.M., Thompson I.J., Vaagen J.S.: Bound state properties of Borromean Halo nuclei: He-6 and Li-11. Phys. Rep. 231, 151 (1993) Hansen P.G., Jensen A.S., Jonson B.: Nuclear halos. Ann. Rev. Nucl. Part. Sci. 45, 591 (1995) Tanihata I.: Neutron halo nuclei. J. Phys. G 22, 157 (1996) Jensen A.S., Riisager K., Fedorov D.V., Garrido E.: Structure and reactions of quantum halos. Rev. Mod. Phys. 76, 215 (2004) Yamashita M.T., Frederico T., Tomio L.: Trajectory of neutron-neutron-18C excited three-body state. Phys. Lett. B 660, 339 (2008) Yamashita, M.T., Frederico, T., Tomio, L.: Neutron-19C scattering near an Efimov state. Phys. Lett. B 670, 49 (2008) [arXiv:0808.3113 [nucl-th]] Bertulani, C.A., Hammer, H.W., Van Kolck, U.: Effective field theory for halo nuclei. Nucl. Phys. A 712, 37 (2002) [arXiv:nucl-th/0205063] Bedaque, P.F., Hammer, H.W., van Kolck, U.: Narrow resonances in effective field theory. Phys. Lett. B 569, 159 (2003) [arXiv:nucl-th/0304007] Higa, R., Hammer, H.W., van Kolck, U.: alpha alpha Scattering in Halo Effective Field Theory. Nucl. Phys. A 809, 171 (2008) [arXiv:0802.3426 [nucl-th]] Canham, D.L., Hammer, H.W.: Universal properties and structure of halo nuclei. Eur. Phys. J. A 37, 367 (2008) [ar-Xiv:0807.3258 [nucl-th]] TUNL nuclear data evaluation project, http://www.tunl.duke.edu/NuclData/ Kirscher, J., Griesshammer, H.W., Shukla, D., Hofmann, H.M.: Universality in Pion-less EFT with the Resonating Group Model: Three and Four Nucleons. arXiv:0903.5538 [nucl-th] Deltuva, A., Fonseca, A.C.: Four-nucleon scattering: Ab initio calculations in momentum space. Phys. Rev. C 75, 014005 (2007) [arXiv:nucl-th/0611029]