Doerte Blume
Washington State University

Hans-Werner Hammer
HISKP (Theorie), Universität Bonn

Shina Tan
Georgia Institute of Technology,

Program Coordinator:
Inge Dolan
(206) 685-4286

Application form
Deadline September 30, 2013

Seminar Schedules:

  • Week 1 (March 10-14)
  • Week 2 (March 17-21)
  • Week 3 (March 24-28)
  • Week 4 (March 31-April 4)
  • Week 5 (April 7-11)
  • Week 6 (April 14-18)
  • Week 7 (April 21-25)
  • Week 8 (April 28-May 2)
  • Week 9 (May 5-9)
  • Talks online

    Exit report

    Friends of the INT

    Obtain an INT preprint number

    INT homepage

    This program will be accompanied by a five-day workshop entitled: "Few-body Universality in Atomic and Nuclear Physics: Recent Experimental and Theoretical Advances".


    Workshop dates:
    May 12, 2014 - May 16, 2014

    Workshop Organizers:
    Doerte Blume
    Washington State University

    Francesca Ferlaino
    Institut für Experimentalphysik
    Universität Innsbruck

    Chris Greene
    Purdue University

    Daniel Phillips
    Ohio University

    There is a registration fee of $35 to attend this workshop. Please make this payment when you arrive at the INT. You may pay in cash - exact change preferred! - or by a check drawn on a U.S. bank. Sorry, we cannot accept credit cards.

    INT Program INT-14-1

    Universality in few-body systems: Theoretical challenges
    and new directions

    March 10, 2014 - May 16, 2014


    The program will focus on the universality in few-body systems relevant to atomic and nuclear physics. Theoretical challenges and new directions will be discussed and identified, and confronted with experimental results where possible. The program will be capped by a five-day workshop, which will bring together theorists and experimentalists from both atomic and nuclear physics.

    The universality of few-body systems is currently a hot topic, with many new and exciting directions. Theoretical predictions related to systems with resonant s-wave interactions can now be tested experimentally, and universal behavior has been found to extend beyond the two- and three-body problems. An equally important emerging frontier in this area is the fact that cold atomic gases can be used to engineer not only systems with resonant s-wave interactions, but also a variety of other systems, e.g. in lower dimensions or with p-wave-interactions. Gases composed of unequal-mass fermions, and where dipolar interactions are present, may also soon be realized in the strongly-interacting, low-energy regime. They, too, provide new frontiers for the investigation of universality.

    These experimental developments go hand-in-hand with rapid theoretical break-throughs. A full understanding of universal features of these more complex systems will emerge by applying a variety of theoretical techniques. While much has been achieved, many open questions remain (see below). And these questions give insight not just into atom-atom interactions, but also to systems bound by the strong nuclear force, such as halo nuclei and hadronic molecules.

    For halo nuclei, the question of universality in higher partial waves is particularly relevant, as many such systems have resonant p-wave interactions. Perhaps because of this, there is no consensus on which properties of halo nuclei are universal. In particular, a universal binding mechanism for higher-partial-wave states is missing. Meanwhile, electromagnetic observables, such as Coulomb dissociation, provide an alternative view on such systems. A universal treatment of this process is now available for one-neutron halo nuclei, but the extension to more complex systems may reveal further universal correlations. It will also provide a link to atomic-physics observables like the radio-frequency response of the gas. The program will facilitate interactions and cross fertilization in order to address such questions and so, we hope, answer some of the key questions in the field:

    • For which systems is the three-body Efimov parameter determined by two-body physics such as the van der Waals length or two-body effective range? What determines whether or not the three-body parameter is determined predominantly by two-body physics? Does the evidence for universality of the three-body parameter, recently found in atomic systems near broad resonances, carry over to narrow resonances or nuclear systems?
    • What does the Efimov scenario look like for four, five, and more particles? What are the differences between systems with bosonic and mixed symmetry? How many, and which, parameters are needed to fully determine the properties of few-body systems with Efimov character? Does the Efimov scenario change for highly mass-imbalanced systems?
    • How are universal properties modified by external confinement, e.g., in a narrow trap?
    • Which aspects of Borromean states are universal?
    • Which aspects of halo nuclei are universal and which ones are non-universal? Is there a universal binding mechanism?
    • How can the deviations from the Tjon line be parametrized?
    • Which properties of few-dipole systems, which interact through non-central long-range forces, are universal? Recent work extended the Efimov scenario to bosonic three-dipole systems and predicted a universal bound state for fermionic three-dipole systems. Can these studies be extended to larger dipolar systems? How can universal aspects of these non-s-wave interacting systems be observed in an ultracold gas composed of dipolar molecules? What can few-dipole systems teach us about the tensor force, which plays an important role in nuclear physics?
    • What is the proper classification scheme for universal and non-universal aspects of p-wave and higher-partial-wave resonances? How can strongly-interacting p-wave few-body systems be stabilized in experiments? Are these systems realized in halo nuclei? If so, where?
    • Which aspects of non-s-wave resonance states and interactions are universal? What are the limitations of universality in higher partial waves?
    • What are the analytical and numerical tools which we have available to study universal aspects of few-body systems?
    • Which observables---that are accessible in cold atomic gases---reveal universal features of few-atom systems. How are they correlated? Which of them have analogs that can be used to examine universality in the context of nuclear few-body systems?
    • Which classes of states do few-fermion systems with unequal masses support? Do they support four- and five-body states that are fully determined by the s-wave scattering length?
    • How does universality of low-dimensional systems differ from that of three-dimensional systems? Are there new universal effects for few-body systems in mixed spatial dimensions? Can mixed dimensional effects help to deepen our understanding of three-dimensional few-body physics?
    • Can few-nucleon systems be simulated by a few-atom system? In particular, can the scattering length and the effective range be tuned simultaneously? What questions could be addressed if a cold-atom realization of four species of fermions with resonant interactions could be attained?
    • What signatures of universality can be revealed using electromagnetic fields (e.g. radio-frequency response in cold atomic gases and Coulomb dissociation in halo nuclei)? Which of these are experimentally realizable in nuclei?
    • Which aspects of spin-orbit coupled atomic few-body systems are universal? What can spin-orbit coupled atomic systems teach us about the properties of nuclei and vice versa?
    Target group:

    The program seeks to bring together researchers with diverse backgrounds from the atomic and nuclear physics communities. Hence we wish to attract scientists with different strengths: researchers who are well-versed in the intricacies of multi-channel atom-atom scattering or the two- and three-body nuclear interactions; experts on connecting the few- and many-body problems; scientists who have strong analytical expertise; scientists with knowledge of diverse numerical approaches to few-body calculations (e.g. in coordinate or momentum space, for bound-state and scattering states), and people with a strong background in effective field theory. The program will have around 10 to 15 participants at any given time. Participants will be invited to present their work during informal morning talks (at a rate of about one talk per day). In addition, we will organize two weekly afternoon discussions on topics of common interest. We will particularly encourage discussions that aim at identifying and defining new frontiers within the area of universal few-body physics, and which aim at establishing concrete connections between theoretical predictions and experimental observables.

    The program will be accompanied by a five-day workshop entitled: "Few-body Universality in Atomic and Nuclear Physics: Recent Experimental and Theoretical Advances".

    Workshop dates: May 12, 2014 - May 16, 2014
      Monday, May 12: 8am registration, 9am first talk
      Friday, May 16: workshop ends at 12.30pm
    There is a registration fee of $35 to attend this workshop. Please make this payment when you arrive at the INT. You may pay in cash - exact change preferred! - or by a check drawn on a U.S. bank. Sorry, we cannot accept credit cards.


    Workshop organizers:

    Doerte Blume
    Department of Physics and Astronomy,
    Washington State University, Pullman, WA 99164-2814
    Phone: +1-509-335-2412, email:

    Francesca Ferlaino
    Institut für Experimentalphysik
    Universität Innsbruck,
    Technikerstrasse 25,
    6020 Innsbruck, Austria
    Phone: +43-512-507-6340, email:

    Chris Greene
    Department of Physics, Purdue University,
    West Lafayette, IN 47907
    phone: +1-765-496-1859, email:

    Daniel Phillips
    Department of Physics and Astronomy, Ohio University
    Athens, OH 45701
    phone: +1-740-593-1698, email:

    More background:

    Few-body physics has played a prominent role in atomic, molecular and nuclear physics since the early days of quantum mechanics. One of the most prominent examples of this is the three-body Efimov effect, which was predicted in the early seventies by Vitaly Efimov, a nuclear theorist. Motivated by the large scattering lengths in the two-nucleon system, Efimov considered the---at the time hypothetical---three-body system with resonant two-body interactions. He predicted that this system would have an infinite geometric sequence of bound states, with successive binding energies in the ratio 515:1. Despite concerted theoretical and experimental efforts, it was not until 2006 that Efimov's rather counterintuitive prediction was confirmed in cold-atom experiments. Since then, there has been an explosion of interest and effort focused on the physics of few-body systems which have features in common with Efimov's original scenario. On the theory side the effective hyperspherical potential curves that underlie Efimov's analysis have been found to be an elegant way of understanding universal aspects of low-energy three-body collisions, while an expansion around the "unitary limit" of resonant interactions provides the basis for an effective field theory within which generic properties of strongly interacting quantum systems can be derived. These methods have led to intriguing extensions of Efimov's result to four-, and higher-, body systems, as well as hypotheses regarding the implications of "Efimov physics" for phases of many-body quantum systems with resonant two-body interactions. Several of the theoretical results produced in this direction since 2006 have stimulated, and ultimately been confirmed in, experiments with cold atomic gases. Thus, in this area of few-body physics theory and experiment are both developing rapidly, in a mutually beneficial fashion. In so doing they inform our understanding of systems ranging from cold gases of atoms, to few-hadron systems, to halo nuclei.

    The program aims to seize this opportunity by bringing together leading theorists working on aspects of few-body systems which, like the Efimov effect, are universal. Throughout, the term "universal" is used quite broadly. It indicates that a certain observable or phenomenon can be described by a finite and well-defined parameter or set of parameters, e.g. an observable which depends only on the s-wave scattering length, or on that observable and the so-called three-body phase which determines the particular energies of three-body bound states in Efimov's problem.

    A major boost for theorists working on questions related to universal few-body physics has come from the tremendous progress made in cold-atom experiments. The ability to manipulate samples of atoms at cold or ultracold temperatures, and to measure observables such as trap losses, yields information on two-, three- and four-atom processes. This, combined with the experimental tunability of scattering parameters (e.g. the two-body scattering length), has driven many of the advances in this area.

    These advances have significant implications for systems bound by the strong interaction. Such systems are to be understood as providing "effective" few-body problems, e.g. few-nucleon systems at energies such that their quark substructure is not resolved, and halo nuclei examined in the regime where a treatment in terms of a small number of clustered degrees of freedom is appropriate. In a similar vein, hadronic molecules can also be treated as few-body systems (e.g., the X(3872) as a D* D molecule) in a low-energy regime where the substructure of the clusters making up the bound states is not resolved.

    The Efimov effect is then (approximately) realized already in the three-nucleon problem---a fact that we now understand is associated with the "universal" correlations in these systems, such as the Phillips line (correlation of triton binding and doublet neutron-deuteron scattering length) and the Tjon line (correlation of three- and four-body binding energies). Similar correlations are being discovered in more complex effective few-body problems, e.g. some halo systems. Few-body universality thus complements ab initio approaches to these nuclei by providing a way to understand and predict correlations between different observables in loosely-bound nuclear systems. This, in turn, opens the possibility to look for universal aspects of nuclear systems close to the driplines. These nuclei will be investigated at present and future radioactive beam facilities, and provide another arena for universal phenomena in nuclear physics.

    The ten-week program will identify key problems and challenges in the investigation of universal aspects of these few-body systems. With the Efimov effect now well established for three equal-mass particles interacting via resonant s-wave interactions in three dimensions, we want our program to identify and characterize universal physics in four- and higher-body systems and determine universal aspects of non-central interactions. We want to discuss and develop the theoretical tools that will permit a rigorous treatment of these highly non-trivial problems, where dynamics occurring at scales differing by several orders of magnitude can affect the final result. And we want to determine which experimental signatures theorists can predict, and which observables are sufficiently sensitive to discriminate between different hypotheses regarding universality in these emerging contexts.