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The quantum mechanical three-body problem is one of the fundamental challenges of few-body physics. When the two-body interactions become resonant an infinite series of universal three-body bound states is predicted to occur, whose properties are determined by the strength of the two-body interactions. We used radio-frequency fields to associate Efimov trimers consisting of three distinguishable fermions. The measurements of their binding energy are consistent with theoretical predictions that include nonuniversal corrections. [ABSTRACT FROM AUTHOR]

Measurements of the 2H( d, n)3He transverse vector polarization-transfer coefficient $${K^{y'}_{y}}$$ at 0° are reported for 29 outgoing neutron energies between 3.94 and 8.47 MeV. Our new results determine $${K^{y'}_{y}(0^{\circ})}$$ more accurately than previous data, especially for neutron energies below 5 MeV. Low-energy data for this reaction are important both as a high-intensity source of highly polarized neutrons for nuclear physics studies with polarized neutron beams, and as a test of the emerging theoretical descriptions of the four-body system, where recently substantial progress has been made. [ABSTRACT FROM AUTHOR]

The article discusses the universality of few-body physics contributing the interaction of atoms in a quantum gas. It outlines the universal properties of systems with short-range interactions have a connection to the Efimov effect discovered by nuclear theorist Vitaly Efimov. It also explores the observation of successive bound or resonant states separated by the Efimov factor in energy or in scattering length, which is the evidence for universality in a system of three low-energy bosons.

Abstract  A new algorithm is presented for the numerical integration of second-order ordinary differential equations with perturbations that depend on the first derivative of the dependent variables with respect to the independent variable; it is especially designed for few-body problems with velocity-dependent perturbations. The algorithm can be used within extrapolation methods for enhanced accuracy, and it is fully explicit, which makes it a competitive alternative to standard discretization methods. [ABSTRACT FROM AUTHOR]

A procedure to solve few-body problems is developed which is based on an expansion over a small parameter. The parameter is the ratio of potential energy to kinetic energy for states having not small hyperspherical quantum numbers, K> K0. Dynamic equations are reduced perturbatively to equations in the finite-dimension subspace with K ⩽ K0. Contributions from states with K> K0 are taken into account in a closed form, i.e., without an expansion over basis functions. Estimates concerning the efficiency of the approach are presented. [ABSTRACT FROM AUTHOR]

In this article an efficient method to calculate the matrix elements of three-nucleon force is presented. The new method is improved version of partial-wave decomposition of Hüber et al. (Few-Body Syst 22:107, 1997), which simplifies expression to be evaluated as well as permits to reduce computational effort. Proposed method naturally applies to Faddeev-type calculations. [ABSTRACT FROM AUTHOR]

It is well known that the system made up of a fixed proton and antiproton and an electron (or a positron) has no bound states if the internuclear distance R < 0.639 a0. In this paper, I consider the more complicated system in which the electron and the positron are both present and investigate the possibility of obtaining a lower bound on the value of R for which the system has no bound states. I also investigate the implications of the existence of bound states of the simpler, one light particle system regarding bound states of the more complicated system. [ABSTRACT FROM AUTHOR]

A large two-body scattering length leads to universal behavior in few-body systems. In particular, the three-body system displays interesting features such as exact discrete scale invariance in the bound state spectrum in the limit of infinite scattering length. Here, I will discuss how an effective field theory (EFT) can be used to study these features and how the finite range of the underlying interaction impacts the bound state spectrum at first order in the EFT expansion. [ABSTRACT FROM AUTHOR]

It takes two nucleons to bind a Λ hyperon, and perhaps as many as three nucleons to bind two Λ hyperons. Here I review few-body calculations which consider the onset of binding in multi-strange hypernuclei, including $${\Xi}$$ hyperons once the free-space strong-interaction conversion $${\Xi N \to \Lambda \Lambda}$$ becomes Pauli forbidden in Λ-abundant matter. Quasibound states of $${\overline {K}}$$ mesons in few-nucleon systems are also briefly discussed. [ABSTRACT FROM AUTHOR]

We investigate the possibility of calculating the parameters of few-body resonances using the oscillator trap boundary conditions. We place the few-body system in an oscillator trap and calculate the energy spectrum and the strength function of a suitably chosen transition. Broader resonances are identified as Lorentzian peaks in the strength function. Narrower resonances are identified through the pattern of avoided crossings in the spectrum of the system as function of the trap size. As an example we calculate $${0^+_2}$$ and $${0^+_3}$$ resonances in 12C within the 3 α model. [ABSTRACT FROM AUTHOR]

Nuclear reactions involving light nuclei require few-body models to describe the nuclear structure and the reaction mechanism. The production rates for the α+ n+ n → 6 He+ γ and α+ n+ n+ n → 6 He+ n processes are discussed. Typically only very low relative energies are relevant. For environments with a high density, processes involving more particles could dominate. The use of the adiabatic approach as a method to compute cross sections at very low energies is proposed. [ABSTRACT FROM AUTHOR]

The method of screening and renormalization is used to include the Coulomb interaction between the charged particles in the description of few-body nuclear reactions. Calculations are done in the framework of Faddeev-type equations in momentum-space. The reliability of the method is demonstrated. The Coulomb effect on observables is discussed. [ABSTRACT FROM AUTHOR]

Cross section and analyzing power Ay of $^2 {\rm H}(\vec p,p)pn$ reaction at $E_{\vec p} = 247\, {\rm MeV}$ were measured and large disagreements with 3N calculations were found especially at forward angles. Effects of 2π3NF are too small to explain the discrepancy. To microscopically investigate the discrepancy, a 2H(p, pp)n experiment is planned. [ABSTRACT FROM AUTHOR]

One of the methods to obtain a precise solution of a few-body equation is to expand the orbital part of the wave function into the correlated Gaussian with double global vectors. In this contribution, we report our recent studies applying this method to light nuclei, (i) excited states of 4He and (ii) two-nucleon momentum distribution in 6He and 6Li, especially focusing on the importance of the tensor force. [ABSTRACT FROM AUTHOR]

A personal perspective is given on topics which appears to be most promising during the fourth Asia Pacific Conference on Few-Body Problem in Physics 2008. [ABSTRACT FROM AUTHOR]

Abstract: Recent developments on kinematically complete experiments on basic atomic fragmentation processes are reviewed. Comparisons between theoretical and experimental fully differential cross sections for single ionization of light atoms by charged particle impact are analyzed. Furthermore, a method developed very recently, four-particle Dalitz plots, is discussed in context of double ionization. The extraordinary power of these plots is their capability to provide a comprehensive picture of the momentum exchange between all four final-state particles in a single spectrum. [Copyright &y& Elsevier]

At RCNP, there have been intensive experimental studies of few-nucleon systems in the last decade. A variety of spin observables has been measured as well as the cross sections. By comparing data to rigorous calculations, the structure of three-nucleon forces has been discussed. In this contribution, recent results and future perspectives are presented. [ABSTRACT FROM AUTHOR]

Low-energy universality in atomic few-body systems as a result of a large two-body scattering length has gained a lot of attention recently. Here, I discuss recent progress in describing the three-body recombination of cold atoms in terms of a finite set of universal scaling functions and review results for the recombination length of 133Cs atoms obtained with these functions. Furthermore, I will consider the inclusion of effective range corrections and the relevance for further calculations in atomic and nuclear physics. [ABSTRACT FROM AUTHOR]

A general approach for a consistent and unified description of the possible reactions on few-nucleon systems up to the first resonance region is presented. It is based on one unique Hamiltonian which considers nucleonic, mesonic and isobaric degrees of freedom. The model has already been applied to several reactions in the two-nucleon sector and is presently extended to the three-nucleon sector. [ABSTRACT FROM AUTHOR]

We briefly review to what extent the relativistic approaches have brought some light in clarifying some discrepancies in the few-nucleon problem. [ABSTRACT FROM AUTHOR]

The history of the three-nucleon analyzing power puzzle is described by an experimentalist who has been collaborating with few-body theoreticians in trying to unravel the physics of this long-standing phenomenon. Although surprising effects have been discovered along the way, the puzzle is still unexplained. Hopefully, some of the long-range three-nucleon force terms predicted by chiral effective field theory in N3LO will eventually solve the puzzle. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: Recent progress on the solution of ab initio three- and four-nucleon scattering equations in momentum space that include the correct treatment of the Coulomb interaction is reviewed; results for specific observables in reactions initiated by , and are shown. In addition three-body calculations of reactions are compared with equivalent CDCC calculations. [Copyright &y& Elsevier]

Abstract: A simple class of unitary renormalization group transformations that force Hamiltonians towards a band-diagonal form produce few-body interactions in which low- and high-energy states are decoupled, which can greatly simplify many-body calculations. One such transformation has been applied to phenomenological and effective field theory nucleon–nucleon interactions with success, but further progress requires consistent treatment of at least the three-nucleon interaction. In this paper we demonstrate in an extremely simple model how these renormalization group transformations consistently evolve two- and three-body interactions towards band-diagonal form, and introduce a diagrammatic approach that generalizes to the realistic nuclear problem. [Copyright &y& Elsevier]

The effect of screened Coulomb (Yukawa) potentials on the photodetachment cross sections of the positronium negative ion is investigated by using the asymptotic form of the bound-state wave function and a plane wave form for the final-state wave function. The required normalization constant is determined from highly accurate, completely non-adiabatic wave functions for the three-particle systems. Photodetachment cross sections for the Ps− ion are calculated for different Debye shielding lengths ( D) ranging from infinite (pure Coulomb) to D = 1.81. [ABSTRACT FROM AUTHOR]

To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we propose a novel method related to the use of hyperspherical harmonics. We suggest an appropriate extension to form a new basis of spin-angular harmonics that is suitable for a representation of the vertex functions. We present a numerical algorithm to solve the Bethe-Salpeter equation and investigate in detail the properties of the solution for the scalar, pseudoscalar and vector meson exchange kernels including the stability of bound states. We also compare our results to the nonrelativistic ones and to the results given by light-front dynamics. [ABSTRACT FROM AUTHOR]

A calculation of the current quark-mass dependence of nucleon static electromagnetic properties is necessary in order to use observational data as a means to place constraints on the variation of Nature’s fundamental parameters. A Poincaré-covariant Faddeev equation, which describes baryons as composites of confined quarks and nonpointlike diquarks, is used to calculate this dependence. The results indicate that, like observables dependent on the nucleons’ magnetic moments, quantities sensitive to their magnetic and charge radii, such as the energy levels and transition frequencies in hydrogen and deuterium, might also provide a tool with which to place limits on the allowed variation in Nature’s constants. [ABSTRACT FROM AUTHOR]

The angular motion of a few-body system is described with global vectors which depend on the positions of the particles. The previous study using a single global vector is extended to make it possible to describe both natural and unnatural parity states. Numerical examples include three- and four-nucleon systems interacting via nucleon-nucleon potentials of AV8 type and a 3α system with a nonlocal αα potential. The results using the explicitly correlated Gaussian basis with the global vectors are shown to be in good agreement with those of other methods. A unique role of the unnatural parity component, caused by the tensor force, is clarified in the 0− 1 state of 4He. The two-particle correlation function is calculated in the coordinate and momentum spaces to show different characteristics of the interactions employed. [ABSTRACT FROM AUTHOR]

The contribution of the K +Λ channel to the Gerasimov-Drell-Hearn (GDH) sum rule has been calculated by using the models that fit the recent SAPHIR or CLAS differential cross-section data. It is shown that the two data sets yield quite different contributions. The contribution of this channel to the forward spin polarizability of the proton also has been calculated. It is shown too that the inclusion of the recent CLAS C x and C z data in the fitting data base does not significantly change the result of the present calculation. Results of the fit, however, reveal the role of the S 11(1650), P 11(1710), P 13(1720), and P 13(1900) resonances for the description of the C x and C z data. A brief discussion on the importance of these resonances is given. Measurements of the polarized total cross section σ TT′ by the CLAS, LEPS, and MAMI collaborations are expected to verify this finding. [ABSTRACT FROM AUTHOR]

The hyperspherical method is a widely used and successful approach for the quantum treatment of elementary chemical processes. It has been mostly applied to three-atomic systems, and current progress is here outlined concerning the basic theoretical framework for the extension to four-body bound state and reactive scattering problems. Although most applications only exploit the advantages of the hyperspherical coordinate systems for the formulation of the few-body problem, the full power of the technique implies representations explicitly involving quantum hyperangular momentum operators as dynamical quantities and hyperspherical harmonics as basis functions. In terms of discrete analogues of these harmonics one has a universal representation for the kinetic energy and a diagonal representation for the potential (hyperquantization algorithm). Very recently, advances have been made on the use of the approach in classical dynamics, provided that a hyperspherical formulation is given based on “classical” definitions of the hyperangular momenta and related quantities. The aim of the present paper is to offer a retrospective and prospective view of the hyperspherical methods both in quantum and classical dynamics. Specifically, regarding the general quantum hyperspherical approaches for three- and four-body systems, we first focus on the basis set issue, and then we present developments on the classical formulation that has led to applications involving the implementations of hyperspherical techniques for classical molecular dynamics simulations of simple nanoaggregates. [ABSTRACT FROM AUTHOR]

We present a practical method to solve Faddeev three-body equations at energies above the three-body breakup threshold as integral equations in coordinate space. This is an extension of a previously used method for bound states and scattering states below three-body breakup threshold energy. We show that breakup components in three-body reactions produce long-range effects on Faddeev integral kernels in coordinate space, and propose numerical procedures to treat these effects. Using these techniques, we solve Faddeev equations for neutron-deuteron scattering to compare with benchmark solutions. [ABSTRACT FROM AUTHOR]

We consider a two-centre regularization procedure in order to study mainly a one-dimensional restricted four-body problem for charge dynamics. Our particular system is the hydrogen molecule, which is a mixed chaotic system. Several types of periodic orbits of that two-fixed-centre system were found for one-dimensional medial and axial configurations. [ABSTRACT FROM AUTHOR]

We examine the applicability and viability of methods to obtain knowledge about bound states from information provided solely in Euclidean space. Rudimentary methods can be adequate if one only requires information about the ground and first excited state and assumptions made about analytic properties are valid. However, to obtain information from Schwinger functions about higher mass states, something more sophisticated is necessary. A method based on the correlator matrix can be dependable when operators are carefully tuned and errors are small. This method is nevertheless not competitive when an unambiguous analytic continuation of even a single Schwinger function to complex momenta is available. [ABSTRACT FROM AUTHOR]

It is shown that in the framework of an analytical confinement, when quark and gluon propagators are induced by a vacuum self-dual gluon field with constant strength, the masses of mesons with quantum numbers Q = ( J P , n), where n is the radial quantum number, and quark constituents m 1, m 2 are described with reasonable accuracy by the formula $$M_Q(m_1,m_2)=(m_1+m_2)\left[1+\frac{A_Q}{(m_1+m_2)^{1.23}}\right].$$ The positive parameter A Q is unique for all mesons with a fixed quantum number Q. Sets of mesons J P = 1−, 0+, 1+, 2+, 3− for n = 0 and 1− , 2+ for n > 0 and different flavor constituent quarks ( u = d, s, c, b) are considered. [ABSTRACT FROM AUTHOR]

The four-body bound state with two-body interactions is formulated in three-dimensional approach, a recently developed momentum-space representation which greatly simplifies the numerical calculations of few-body systems without performing the partial wave decomposition. The obtained three-dimensional Faddeev-Yakubovsky integral equations are solved with two-body spin-independent and spin-averaged potentials. This is the first step toward the calculations of the four-nucleon bound-state problem in three-dimensional approach. Results for four-body binding energies are in good agreement with achievements of the other methods. [ABSTRACT FROM AUTHOR]

We compare the efficiency of two Faddeev-type approaches for the nuclear three-body Coulomb problem. The first one is a modification of Noble’s approach, the second one is due to Sasakawa and Sawada. In an integral-equation formulation both of these methods rely on the same Green’s operators and driving terms. The differences lie in the treatment of the long-range Coulomb potentials. Numerical examples show that the modified Faddeev-Noble approach provides for faster convergence. [ABSTRACT FROM AUTHOR]

Recently there has been developed a new approach to the study of critical quantum systems in 1+1 dimensions which reduces them to problems in one-dimensional Brownian motion. This goes under the name of stochastic, or Schramm, Loewner Evolution (SLE). I review some of the recent progress in this area, from the point of view of many-body theory. Connections to random matrices also emerge. [ABSTRACT FROM AUTHOR]

Fully differential studies of single ionization of neutral atoms by charged particle impact have proven to be extremely powerful to advance our understanding of the few-body dynamics in atomic processes. Until a few years ago, such data were only available for electron impact and were mostly limited to electrons ejected into the scattering plane. When fully differential data were finally obtained for ion impact covering the entire three-dimensional space, very surprising features were observed. It then became clear that our understanding of ionization processes in atomic collisions is not nearly as complete as previously assumed. Here, we review the development of experimental and theoretical studies of three-dimensional fully differential single ionization cross-sections since then. [ABSTRACT FROM AUTHOR]

Few-body systems provide a testing ground for models of the NN interaction, reaction mechanisms and for models of nuclei. An overview of results of coincidence experiments on the deuteron, 3He and 4He obtained in the last 20 years at MAMI and at other facilities, covering a wide range of momentum and energy transfers, is presented. [ABSTRACT FROM AUTHOR]

An overview over present achievements and future challenges in the field of few-nucleon systems is presented. Special emphasis is laid on the construction of a unified approach to hadronic and electromagnetic reactions on few-nucleon systems, necessary for studying the borderline between quark-gluon and effective descriptions. [ABSTRACT FROM AUTHOR]

Within the ( α, n, p) three-body model, the s-wave 6Li → α + d vertex constant G 01 and the asymptotic normalization coefficient C 01 (these two quantities are proportional to each other) for the wave function describing the 6Li nucleus in the α + d channel are calculated by solving Faddeev equations for various sets of nucleon-nucleon and α N potentials. The resulting values of G 01 and C 01 are used to calculate the astrophysical factor S(E) for the radiative-capture reaction d( α, γ)6Li at energies in the range E = 0–600 keV. The calculated values of G 01 and C 01 appear to be sensitive to the form of the pair potentials used. It is shown that, upon correctly taking into account the contributions of the E2 and E1 multipolarities, the values of S(E) in the region E < 150 keV are determined primarily by the values of C 01 and of the 6Li binding energy in the α + d channel. [ABSTRACT FROM AUTHOR]

We consider the uniqueness of the solution to a three-body problem with zero-range Skyrme interactions in configuration space. With the lowest, k 0, two-body term alone the problem is known to have no unique solution as the system collapses – the variational estimate of the energy tends towards negative infinity, the size of the system towards zero. We argue that the next, k 2, two-body term removes the collapse and the three-body system acquires finite ground-state energy and size. The three-body interaction term is thus not necessary to provide a unique solution to the problem. [ABSTRACT FROM AUTHOR]

The complex dilated Mittag-Leffler, the T-matrix, and the Siegert pseudostate methods are briefly reviewed. Their respective strengths and weaknesses and some recent results are discussed. [ABSTRACT FROM AUTHOR]

Abstract: We investigate and compare two asymptotic wave functions for atomic double ionization in the region where the distance between the escaping electrons is small when compared to the distance from the nucleus. The first of the forms was derived by Alt and Mukhamedzhanov and solves the three body Schrodinger equation to an order of 1/r 2. The second wave function was derived by Engelns, Klar and Malcherek for use in all asymptotic regimes. These forms will be compared numerically and analytically. [Copyright &y& Elsevier]

By expanding the wave function in terms of the translationally invariant basis of harmonic oscillator functions, we calculate the converging upper (variational) bound for the energy. It is shown that one can construct lower bounds using the reduced density matrix that corresponds to the upper bound. These lower bounds converge to an exact value with the expansion of the basis. We perform the calculations of both bounds with realistic nucleon-nucleon potential for ground states of the triton and the alpha-particle. [ABSTRACT FROM AUTHOR]

Based on the investigation of the asymptotic behaviour of the polarization loop function for scalar charged particles in an external gauge field we determine the interaction Hamiltonian including the nonperturbative corrections of the relativistic character of motion and the large coupling constant. The mass spectrum of the bound state is analytically derived. The mechanism for arising of the constituent mass of the bound-state forming particles is explained. The change of the bound-state mass and of the constituent mass of particles is analyzed by varying the coupling constant. The mass spectrum of the two-gluon glueball is calculated taking into account spin-orbit and spin-spin interactions. [ABSTRACT FROM AUTHOR]

It is shown that an ensemble of particles with tripolar (colour) charges will necessarily cohere in a hierarchy of structures, from simple clusters and strings to complex aggregates and cyclic molecule-like structures. The basic combinatoric rule remains essentially the same on different levels of the hierarchy, thus leading to a pattern of resemblance between different levels. The number of primitive charges in each structure is determined by the symmetry of the combined effective potential of this structure. The outlined scheme can serve as a framework for building a model of composite fundamental fermions. [ABSTRACT FROM AUTHOR]

The exact solution for the two-particle spectrum of the Heisenberg-Peierls one-dimensional spin chain is given by working in the fermionic representation. The resulting equations for the eigenvalues are, in some sense, similar to those of the BCS model and must be solved numerically. [ABSTRACT FROM AUTHOR]

A Poincaré-covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain masses and Faddeev amplitudes for the nucleon and Δ. The amplitudes are a component of a nucleon-photon vertex that automatically fulfills the Ward-Takahashi identity for on-shell nucleons. These elements are sufficient for the calculation of a quark core contribution to the nucleons’ electromagnetic form factors. An accurate description of the static properties is not possible with the core alone but the error is uniformly reduced by the incorporation of meson-loop contributions. Such contributions to form factors are noticeable for Q2 ≲ 2 GeV2 but vanish with increasing momentum transfer. Hence, larger Q2 experiments probe the quark core. The calculated behaviour of G E p( Q2)/ G M p( Q2) on Q2 ∈ [2,6] GeV2 agrees with that inferred from polarization transfer data. Moreover, $\sqrt{Q^2} F_2(Q^2)/F_1(Q^2)\hskip-1pt\approx $ constant on this domain. These outcomes result from correlations in the proton’s amplitude. [ABSTRACT FROM AUTHOR]

It is a well-known feature of odd space-time dimensions d that there exist two inequivalent fundamental representations A and B of the Dirac gamma matrices. Moreover, the parity transformation swaps the fermion fields living in A and B. As a consequence, a parity-invariant Lagrangian can only be constructed by incorporating both the representations. Based upon these ideas and contrary to long-held belief, we show that in addition to a discrete exchange symmetry for the massless case, we can also define chiral symmetry provided the Lagrangian contains fields corresponding to both the inequivalent representations. We also study the transformation properties of the corresponding chiral currents under parity and charge-conjugation operations. We work explicitly in 2 + 1 dimensions and later show how some of these ideas generalize to an arbitrary number of odd dimensions. [ABSTRACT FROM AUTHOR]