Few-body Physics Research Articles

Low-energy anti-kaon nucleon and nucleus interaction

Central importance for the physics of strong interaction has the dynamics driven by chiral symmetry breaking in low-energy QCD. Valuable information is provided by high precision x-ray studies of the strong interaction at threshold. In this context precision measurements of the strong interaction induced energy shift and width in kaonic atoms are conducted at LNF/Italy at present and at J-PARC/Japan in the future. New dedicated experimental search for bound systems with anti-kaons are under way at GSI and will be conducted at LNF and J-PARC. These studies will provide urgently needed data for theoretical studies and will open the way to a detailed insight in the low energy regime of the strong force with anti-kaons. Especially interesting are nuclear systems involving strangeness and bound by the strong force, called kaonic nuclear clusters. At present this topic is in intense discussion and the search for these systems is conducted in new experiments (e.g. FOPI at GSI). LEANNIS, an international scientific network in Hadronphysics2 within the European Framework Program FP7, will bring together experimentalists and theorists to perform joint research work on the anti-kaon interaction with nucleons and nuclei. This presentation gives an overview on the open problems and and will present the status and outlook of research activities in this challenging field which is inherently connected with few-body physics.

FAIR - from a few-body perspective

In the next years the Facility for Antiproton and Ion Research FAIR will be constructed at the GSI Helmholtzzentrum fur Schwerionenforschung in Darmstadt, Germany. This new accelerator complex will allow for unprecedented and pathbreaking research in hadronic, nuclear, and atomic physics as well as in applied sciences. This manuscript will discuss some of these research opportunities, with a focus on few-body physics.

Functional renormalization group and conformal invariance in cold atoms

We present an application of a field-theoretic functional renormalization group technique to fewbody (vacuum) physics of nonrelativistic atoms near a Feshbach resonance. We consider and compare a onecomponent bosonic system with a two-component fermionic system, focusing on the scale-free unitarity limit of an infinite scattering length. While the two-body problem is consistent with nonrelativistic conformal symmetry for the two considered systems, a conformal anomaly, manifested through a renormalization group limit cycle with the Efimov parameter s0 ≈ 1.006, is found for bosons in the three-body problem.

More Is Different, Few Is Exotic

As powerful as theoretical physics can be, when it comes to describing the dynamics of several interacting particles, it stumbles at three. This few-body physics is interesting in many contexts, particularly interactions within the nucleus and between atoms and molecules. Although predicted 40 years ago for the special case of resonant interaction, which occurs at the edge of where two-particle bound states start to form, Efimov trimers were only recently observed in ultracold Bose gases. More work followed, revealing evidence of multiple trimer, and even tetramer, states. Now, Pollack et al. (p. [1683][1], published online 19 November; see the Perspective by [Modugno][2] ) observe as many as 11 features near a lithium resonance that can be directly related to different few-body processes. The positions of the features with respect to each other are in excellent agreement with the theoretical prediction, although some deviations, attributed to short-range interactions, present a challenge for a future, more detailed theory. [1]: /lookup/doi/10.1126/science.1182840 [2]: /lookup/doi/10.1126/science.1184235

Universality in Three- and Four-Body Bound States of Ultracold Atoms

Under certain circumstances, three or more interacting particles may form bound states. Although the general few-body problem is not analytically solvable, the so-called Efimov trimers appear for a system of three particles with resonant two-body interactions. The binding energies of these trimers are predicted to be universally connected to each other, independent of the microscopic details of the interaction. By exploiting a Feshbach resonance to widely tune the interactions between trapped ultracold lithium atoms, we find evidence for two universally connected Efimov trimers and their associated four-body bound states. A total of 11 precisely determined three- and four-body features are found in the inelastic-loss spectrum. Their relative locations on either side of the resonance agree well with universal theory, whereas a systematic deviation from universality is found when comparing features across the resonance.

Quantum scattering theory on the momentum lattice

A new approach based on the wave-packet continuum discretization method recently developed by the present authors for solving quantum-mechanical scattering problems for atomic and nuclear scattering processes and few-body physics is described. The formalism uses the complete continuum discretization scheme in terms of the momentum stationary wave-packet basis, which leads to formulation of the scattering problem on a lattice in the momentum space. The solution of the few-body scattering problem can be found in the approach from linear matrix equations with nonsingular matrix elements, averaged on energy over lattice cells. The developed approach is illustrated by the solution of numerous two- and three-body scattering problems with local and nonlocal potentials below and well above the three-body breakup threshold.

Cold and ultracold molecules: science, technology and applications

This paper presents a review of the current state of the art in the research field of cold and ultracold molecules. It serves as an introduction to the focus issue of New Journal of Physics on Cold and Ultracold Molecules and describes new prospects for fundamental research and technological development. Cold and ultracold molecules may revolutionize physical chemistry and few-body physics, provide techniques for probing new states of quantum matter, allow for precision measurements of both fundamental and applied interest, and enable quantum simulations of condensed-matter phenomena. Ultracold molecules offer promising applications such as new platforms for quantum computing, precise control of molecular dynamics, nanolithography and Bose-enhanced chemistry. The discussion is based on recent experimental and theoretical work and concludes with a summary of anticipated future directions and open questions in this rapidly expanding research field.

Efimov effect from functional renormalization

We apply a field-theoretic functional renormalization-group technique to the few-body (vacuum) physics of nonrelativistic atoms near a Feshbach resonance. Three systems are considered: one-component bosons with a U(1) symmetry, two-component fermions with a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{SU}(2)$ symmetry, and three-component fermions with a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{SU}(3)$ symmetry. We focus on the scale-invariant unitarity limit of an infinite scattering length. The exact solution for the two-body sector is consistent with the unitary fixed-point behavior of the considered systems. Nevertheless, the numerical three-body solution in the $s$-wave sector develops a limit cycle scaling in case of U(1) bosons and SU(3) fermions. The Efimov parameter for the one-component bosons and the three-component fermions is found to be $s\ensuremath{\approx}1.006$, consistent with the result of Efimov.

Observation of an Efimov-like trimer resonance in ultracold atom–dimer scattering

The observation of a trimer resonance in an ultracold mixture of caesium atoms and dimers confirms one of the key predictions of three-body physics in the limit of resonant two-body interactions, with possible implications for understanding few-body states in nuclear matter. The field of few-body physics has originally been motivated by understanding nuclear matter, but in the past few years ultracold gases with tunable interactions have emerged as model systems to experimentally explore few-body quantum systems1,2,3. Even though the energy scales involved are vastly different for ultracold and nuclear matter (picoelectronvolt as compared with megaelectronvolt), few-body phenomena acquire universal properties for near-resonant two-body interactions2. So-called Efimov states represent a paradigm for universal quantum states in the three-body sector4. After decades of theoretical work, a first experimental signature of such a weakly bound trimer state was recently found under conditions where a weakly bound dimer state is absent5,6,7. Here, we report on a trimer state in the opposite regime, where such a dimer state exists. The trimer state manifests itself in a resonant enhancement of inelastic collisions in a mixture of atoms and dimers. Our observation is closely related to an atom–dimer resonance as predicted by Efimov8,9,10, but occurs in the theoretically challenging regime where the trimer spectrum reveals effects beyond the universal limit.

Experiments on few-nucleon systems at MAMI

The experimental effort at the Mainz Microtron with respect to few-body physics is focused on a number of selected topics. The structure of 3He has been studied in the reactions \(^3\vec{{\rm H}}{\rm e}(\vec{e},e{\prime}n)\) and \(^3\vec{{\rm H}}{\rm e}(\vec{e},e{\prime}p)\) with large (transversal) missing momenta and in quasi-elastic electron scattering. Experiments to determine the neutron electric form factor G en have been performed – a measurement at a four-momentum transfer Q 2 ∼ 1.5(GeV/c)2 took place in July 2007. Electromagnetically induced two-nucleon knockout has been investigated in order to study the role of correlated nucleon-nucleon motion in the nucleus. Measurements of the (e,e′ pn) reaction on 3He and 16O were performed for the first time. A triple-polarization experiment of type \(^3\vec{{\rm H}}{\rm e}(\vec{e},e{\prime}\vec{p})d\) has been performed in August 2007, where, in addition, the spin of the knocked-out proton is analyzed. This measurement provides information on the spin-dependent momentum distribution of proton-deuteron clusters in the 3He nucleus. By using this deuteron-tagging method spin-polarized 3He might also serve as an effective polarized proton target for electron scattering experiments.

Cold-atom systems and the scaling limit

With perspective to applications of cold-atom systems, some aspects of few-body physics at very low energies will be reviewed. By exploring the possibilities of varying the two-body interaction via the Feshbach resonance mechanism, some recent results are reported for condensed systems in optical lattices.

Vijay Pandharipande and Few-Body Physics

We briefly review the contributions of Vijay Pandharipande to Few-Body Physics. Vijay made many crucial contributions to few-nucleon physics; we can only touch upon some, from the spectra of light nuclei, to low- and high-energy reactions revealing their structure, and studies of the nuclear interaction. We briefly trace the beginnings of Vijay's work in few-nucleon physics, present a few of the highlights during his work, and briefly comment on the future of the line of theoretical work Vijay instigated.

Relativistic aspects of few-body physics

After a brief review of alternative approaches to the relativistic treatment of few-body problems, I discuss (i) recent progress in the study of NN and NNN systems, (ii) a new method for solving the Bethe-Salpeter equation in Minkowski space, (iii) new relativistic treatment of spin 3/2 fields, and (iv) construction of conserved electromagnetic currents in a relativistic optical model.

Facets of charge-exchange reactions — from astrophysics to double beta decay

In this paper we present recent results on the (d, 2He) charge exchange reaction at intermediate energies. We show that the (d, 2He) reaction has evolved to a powerful spectroscopic tool capable of providing new and sometimes unexpected insight into nuclear structure phenomena. The key issue here is the high resolution of order 100 keV, which can now routinely be obtained. The program has been launched at the AGOR Superconducting Cyclotron Facility at the KVI Groningen. By now, it covers a wide field of physics questions ranging from few-body physics, the structure of halo-nuclei to questions pertaining to the dynamics of supernova explosions and nuclear synthesis, and more recently to the measurements of double-beta ( β β ) decay matrix elements and the determination of half-lives of β β decaying nuclei.

Evidence for Efimov quantum states in an ultracold gas of caesium atoms

Systems of three interacting particles are notorious for their complex physical behaviour. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of bound trimer states appearing for three identical bosons with a resonant two-body interaction. Counterintuitively, these states even exist in the absence of a corresponding two-body bound state. Since the formulation of Efimov's problem in the context of nuclear physics 35 years ago, it has attracted great interest in many areas of physics. However, the observation of Efimov quantum states has remained an elusive goal. Here we report the observation of an Efimov resonance in an ultracold gas of caesium atoms. The resonance occurs in the range of large negative two-body scattering lengths, arising from the coupling of three free atoms to an Efimov trimer. Experimentally, we observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied. We also detect a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point with which to explore the universal properties of resonantly interacting few-body systems. While Feshbach resonances have provided the key to control quantum-mechanical interactions on the two-body level, Efimov resonances connect ultracold matter to the world of few-body quantum phenomena.

Few-body physics in effective field theory

Effective field theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with short-range interactions and large two-body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three-body force with limit cycle behaviour is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms and nuclear physics. In particular, we will discuss the possibility of an infrared limit cycle in QCD. Recent extensions of the EFT approach to the four-body system and N-boson droplets in two spatial dimensions will also be addressed.

Systematic investigation of three-nucleon force effects in elastic scattering of polarized protons from deuterons at intermediate energies

The question, whether the high-quality nucleon-nucleon potentials can successfully describe the three-nucleon system, and to what extent three-nucleon forces (3NFs) play a role, has become very important in nuclear few-body physics. One kinematic region where effects because of 3NFs show up is in the minimum of the differential cross section of elastic nucleon-deuteron scattering. Another observable, which could give an indication about the contribution of the spin to 3NFs, is the vector analyzing power. To investigate the importance of 3NFs systematically over a broad range of intermediate energies, both observables of elastic proton-deuteron scattering have been measured at proton bombarding energies of 108, 120, 135, 150, 170, and 190 MeV, covering an angular range in the center-of-mass system between ${30}^{\ifmmode^\circ\else\textdegree\fi{}}$ and ${170}^{\ifmmode^\circ\else\textdegree\fi{}}$. The results show unambiguously the shortcomings of calculations employing only two-body forces and the necessity of the inclusion of 3NFs. They also show the limitations of the results of the present day models for few-nucleon systems at backward angles, especially at higher beam energies. New calculations based on chiral perturbation theory are also presented and compared with the data at the lowest energy.

Light-Front Field Theory of Hot and Dense Quark Matter

Extending the concepts of light-front field theory to quantum statistics provides a novel approach towards nuclear matter under extreme conditions. Such conditions exist, e.g., in neutron stars or in the early stage of our universe. They are experimentally expected to occur in heavy ion collisions, e.g., at RHIC and accelerators to be build at GSI and CERN. Light-front field theory is particularly suited, since it is based on a relativistic Hamiltonian approach. It allows us to treat the perturbative as well as the nonperturbative regime of QCD and also correlations that emerge as a field of few-body physics and is important for hadronization. Last but not least the Hamiltonian approach is useful for nonequilibrium processes by utilizing, e.g., the formalism of nonequilibrium statistical operators.

Weak interaction processes in supernovae: New probes using charge exchange reaction at intermediate energies

Spin-isospin-flip excitations in nuclei at vanishing momentum transfer are generally referred to as Gamov-Teller (GT) transitions. They are being studied because the simplicity of the excitation makes them an ideal probe for testing nuclear structure models. In astrophysics, GT transitions provide an important input for model calculations and element formation during the explosive phase of a massive star at the end of its life-time. GT transitions in the β − direction (also referred to as isospin lowering T < transitions) have extensively been studied through (p,n) and ( 3 He,t) charge-exchange reactions [B.D. Anderson et al., Phys. Rev. C 36 (1987) 2195, B.D. Anderson et al., Phys. Rev. C 43 (1991) 50, J. Rapaport et al., Phys. Rev. C 24 (1981) 335, H. Akimune et al., Nucl. Phys. A 569 (1994) 245c, Y. Fujita et al., Phys. Lett. B 365 (1996) 29]. The generally good resolution allows easy extraction of the GT distribution and the total B(GT − ) strength in the final nucleus. On the other hand, determination of B(GT + ) strength through a charge-exchange reaction in the T > direction were mostly done with secondary neutron beams, and as such, they come with significant experimental difficulties. TRIUMF has pioneered this field in the late 80's and early 90's with a rich and highly successful (n,p) program using a several hundred MeV neutron beam from a 7 Li(p,n) 7 Be reaction [R. Helmer, Can. J. Phys. 65 (1987) 588]. In this paper we present the ( d , 2 He) reaction at intermediate energies as another and potentially even more powerful tool for charge-exchange reactions in the T > , resp. β + direction. The key issue here will be the high resolution of order 100 keV, which provides new and sometimes unexpected insight into nuclear structure phenomena. This program has been launched at the AGOR Superconducting Cyclotron Facility at the KVI Groningen. By now, it covers a wide field of physics questions ranging from few-body physics, the structure of halo-nuclei, to questions pertaining to the dynamics of supernova explosions and nuclear synthesis, and more recently to the measurements of ( ββ ) decay matrix elements and the determination of half-lives of ( ββ ) decaying nuclei.

Two Interacting Electrons in a Spherical Gaussian Confining Potential Quantum Well**The project supported by National Natural Science Foundation of China under Grant No. 10275014

Two-electron states of a three-dimensional spherical GaAs quantum dot (QD) with a Gaussian confining potential confinement are studied. Calculations are made by using the method of few-body physics within the effective-mass approximation. We have calculated the energy levels of single and triplet states as functions of the range and depth of the confining potential well in the spherical QDs. The same calculations performed with the parabolic approximation of the Gaussian potential lead to the results, which are qualitatively and quantitatively different.