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Atom-molecular collisions are studied using the Faddeev differential equations. The results of calculation of the scattering length for the collision of a 4He atom with a 4He7Li dimer are presented. [ABSTRACT FROM AUTHOR]

A symmetry preserving framework for the study of continuum Quantum Chromodynamics (QCD) is obtained from a truncated solution of the QCD equations of motion or QCD's Dyson-Schwinger equations (DSEs). A nonperturbative solution of the DSEs enables the study of, e.g., hadrons as composites of dressed-quarks and dressed-gluons, the phenomena of confinement and dynamical chiral symmetry breaking (DCSB), and therefrom an articulation of any connection between them. It is within this context that we present a unified study of Nucleon, Delta and Roper elastic and transition electromagnetic form factors, and compare predictions made using a framework built upon a Faddeev equation kernel and interaction vertices that possess QCD-like momentum dependence with results obtained using a symmetry-preserving treatment of a vector $$\otimes $$ vector contact-interaction. The comparison emphasises that experiment is sensitive to the momentum dependence of the running coupling and masses in QCD and highlights that the key to describing hadron properties is a veracious expression of DCSB in the bound-state problem. [ABSTRACT FROM AUTHOR]

A symmetry preserving framework for the study of continuum quantum chromodynamics (QCD) is obtained from a truncated solution of the QCD equations of motion or QCD's Dyson-Schwinger equations (DSEs). A nonperturbative solution of the DSEs enables the study of, e.g., hadrons as composites of dressed-quarks and dressed-gluons, the phenomena of confinement and dynamical chiral symmetry breaking, and therefrom an articulation of any connection between them. It is within this context that we present a unified study of Nucleon, Delta and Roper elastic and transition form factors, and compare predictions made using a framework built upon a Faddeev equation kernel and interaction vertices that possess QCD-like momentum dependence with results obtained using a symmetry-preserving treatment of a vector $$\otimes $$ vector contact-interaction. [ABSTRACT FROM AUTHOR]

We present a unified study of nucleon and $${\Delta}$$ elastic and transition form factors, and compare predictions made using a framework built upon a Faddeev equation kernel and interaction vertices that possess QCD-like momentum dependence with results obtained using a symmetry-preserving treatment of a vector $${\otimes}$$ vector contact-interaction. The comparison emphasises that experiments are sensitive to the momentum dependence of the running couplings and masses in the strong interaction sector of the Standard Model and highlights that the key to describing hadron properties is a veracious expression of dynamical chiral symmetry breaking in the bound-state problem. Amongst the results we describe, the following are of particular interest: $${G_{E}^{p}(Q^{2})/G_{M}^{p}(Q^{2})}$$ possesses a zero at Q = 9.5 GeV; any change in the interaction which shifts a zero in the proton ratio to larger Q relocates a zero in $${G_{E}^{n}(Q^{2})/G_M^{n}(Q^{2})}$$ to smaller Q; there is likely a value of momentum transfer above which $${G_{E}^{n} > G_{E}^{p}}$$ ; and the presence of strong diquark correlations within the nucleon is sufficient to understand empirical extractions of the flavour-separated form factors. Regarding the $${\Delta(1232)}$$ -baryon, we find that, inter alia: the electric monopole form factor exhibits a zero; the electric quadrupole form factor is negative, large in magnitude, and sensitive to the nature and strength of correlations in the $${\Delta(1232)}$$ Faddeev amplitude; and the magnetic octupole form factor is negative so long as rest-frame P- and D-wave correlations are included. In connection with the $${N \to \Delta}$$ transition, the momentum-dependence of the magnetic transition form factor, $${G_{M}^{*}}$$ , matches that of $${G_{M}^{n}}$$ once the momentum transfer is high enough to pierce the meson-cloud; and the electric quadrupole ratio is a keen measure of diquark and orbital angular momentum correlations, the zero in which is obscured by meson-cloud effects on the domain currently accessible to experiment. Importantly, within each framework, identical propagators and vertices are sufficient to describe all properties discussed herein. Our analysis and predictions should therefore serve as motivation for measurement of elastic and transition form factors involving the nucleon and its resonances at high photon virtualities using modern electron-beam facilities. [ABSTRACT FROM AUTHOR]

We present predictions for the binding energies of the light hypernuclei $${^3_\Lambda{\rm H},\, ^4_\Lambda{\rm He}}$$ and $${^4_\Lambda{\rm H}}$$ based on Faddeev- and Yakubovsky equations in momentum space. We discuss how such results can help to test the existing hyperon-nucleon ( Y N) potential models and effective field theory based Y N interactions. Especially, we show results for the chiral interactions at next-to-leading order. [ABSTRACT FROM AUTHOR]

A variational-bound formulation of the N-particle scattering problem has been developed based on the Yakubovskii-Faddeev chain-of-partition equations. It is shown that the scattering amplitude for the elastic, rearrangement or break-up processes satisfies a Lippmann-Schwinger type integral equation in which the kernel integration is over the open channels and the closed channels enter through the effective potential. In the case where only two (three)-cluster open channels are allowed, the integral equation for the transition amplitude involves integration over only one (two) momentum vector(s). A variational estimate for the effective potential input to the integral equation is obtained when the closed channel partition Green's functions are estimated variationally. It is shown that the variational estimates for the closed-channel Green's function also provide upper and lower bounds that can be used as a subsidiary extremum principle to determine optimum parameters in the trial function. Several methods are provided for simplifying the determination of the effective potential. The inclusion of Coulomb potentials in the Yakubovskii-Faddeev (YF) chain-of-partition formalism is also described. In this approach the inter-particle potential is not assumed to be separable as in typical quasi-particle schemes. The many-body dependence of the effective potential is included via expectation values involving an inter-particle potential and spatially decaying trial functions. The N-body scattering problem is therefore reduced to: (a) solving a two-body scattering problem (three-body in the case of break-up) and (b) a bound-state type calculation to determine the effective potential. As an initial application, the method is applied to the case of low-energy elastic deuteron-deuteron scattering (including the Coulomb force) and compared to a recent cluster-reduction calculation. [ABSTRACT FROM AUTHOR]

Recently a formalism for a direct treatment of the Faddeev equation for the three-nucleon bound state in three dimensions has been proposed. It relies on an operator representation of the Faddeev component in the momentum space and leads to a finite set of coupled equations for scalar functions which depend only on three variables. In this paper we provide further elements of this formalism and show the first numerical results for chiral NNLO nuclear forces. [ABSTRACT FROM AUTHOR]

Neutron spectra from the reaction $${K^- + d \rightarrow \pi + \Sigma + n}$$ were calculated in the energy range $${E^{cm}_{K^-} = }$$ 0–50 MeV using coupled channel Faddeev equations for the description of the $${\bar{K} N N - \pi\Sigma N}$$ three-body system. The aim was to trace the signature of the Λ(1405) resonance in the spectra. We found, that while in the direct spectra kinematic effects mask completely the peak corresponding to the resonance, the deviation spectrum method of Esmaili et al. (Phys. Rev. C 83:055207, 2011 ) is able to eliminate kinematics and differentiate between different models of Λ(1405). Four different phenomenological $${\bar{K} N - \pi\Sigma}$$ interactions were used in order to study the effect of their pole positions on the neutron spectra. [ABSTRACT FROM AUTHOR]

Observables in proton-deuteron scattering are sensitive probes of the nucleon-nucleon interaction and three-nucleon force effects (3NF). Several facilities in the world, including Kernfysisch Versneller Instituut (KVI), allow a detailed study a few-nucleon interaction below the pion-production threshold exploiting polarized proton and deuteron beams. In this contribution we explored 3NF effects in the break-up scattering process by performing a measurement of differential cross section and the analyzing power, especially the x component of the analyzing power, using a 135 MeV polarized-proton beam impinging on a liquid-deuteron target. The proton-deuteron breakup reaction leads to a final state with three free particles and a rich phase space that allows us to study observables for continuous set of kinematical configurations of the outgoing nucleons. The results are interpreted with the help of state-of-the-art Faddeev calculations. [ABSTRACT FROM AUTHOR]

We report on a recent calculation of the properties of the DNN system, a charmed meson with two nucleons. The system is analogous to the $${{\bar {K}}NN}$$ system substituting a strange quark by a charm quark. Two different methods are used to evaluate the binding and width, the Fixed Center approximation to the Faddeev equations and a variational calculation. In both methods we find that the system is bound by about 200 MeV and the width is smaller than 40 MeV, a situation opposite to the one of the $${{\bar {K}}NN}$$ system and which makes this state well suited for experimental observation. [ABSTRACT FROM AUTHOR]

We have measured all deuteron analyzing powers $${(A_{y}^{d}, A_{yy}, A_{xx}, A_{xz})}$$ for deuteron-proton elastic scattering at 294 MeV/nucleon in order to study the properties of three nucleon forces (3 NFs). Measurement was made at in an angular range of $${\theta_{{\rm c.m.}} = 35.6^{\circ} - 163.0^{\circ}}$$. Obtained data were compared with Faddeev calculations with and without the 3 NFs. At $${\theta_{{\rm c.m.}}\lesssim 120^{\circ}}$$ all the data have general agreement with the calculations, while the measured data at $${\theta_{{\rm c.m.}} \gtrsim 120^{\circ}}$$ are not explained by any theoretical calculations. These results were consistent with those at 250 MeV/nucleon. [ABSTRACT FROM AUTHOR]

A field-theoretical description of the photoproduction of two pions off the nucleon is presented that applies to real as well as virtual photons in the one-photon approximation. The Lorentz-covariant theory is complete at the level of all explicit Faddeev-type three-body final-state mechanisms of dressed interacting hadrons, including those of the nonlinear Dyson-Schwinger type. All electromagnetic currents are constructed to satisfy their respective (generalized) Ward-Takahashi identities and thus satisfy local gauge invariance as a matter of course. The Faddeev-type ordering structure results in a natural expansion of the full two-pion photoproduction current $${M^\mu_{\pi \pi}}$$ in terms of multiple loops that preserve gauge invariance order by order in the number of loops, which in turn lends itself naturally to practical applications of increasing sophistication with increasing number of loops. [ABSTRACT FROM AUTHOR]

As a first step toward clarifying whether the strange dibaryon resonances in the $${\bar{K}NN-\pi YN}$$ system can emerge with a physical significance in the nuclear-reaction observables, we compute the break-up probability of $${Y_K + N \to \pi +\Sigma + N}$$ at real scattering energies by solving $${\bar{K}NN-\pi YN}$$ coupled-channel Alt-Grassberger-Sandhas equations. We examine how the signature of the dibaryon resonance shows up in the probability, and also discuss the possibility for a use of strange dibaryon production reactions to distinguish two-body-interaction models with Λ(1405). [ABSTRACT FROM AUTHOR]

A simple method to calculate ground state energies for a typical condensates containing up to A ~ 10 atoms is presented. The method, based on the expansion of the wave function in terms of the Faddeev components, which in turn are expanded in terms of potential harmonics is numerically efficient. We obtain ground state results for condensates of Rb containing up to A → 10 atoms. The results agree very well with other methods in regions where the other methods are valid. [ABSTRACT FROM AUTHOR]

Recent achievements in three nucleon force study via three nucleon scattering at intermediate energies ( $${E \gtrsim 100 \,\,{\rm MeV/nucleon}}$$) are discussed. [ABSTRACT FROM AUTHOR]

For the Σ-Σ- α system we theoretically look into the possible existence of a quasi-bound state in the framework of Faddeev calculations. We are particularly interested in the state of total iso-spin T=2, because there is no strong conversion between Ξ-N- α and $${\Lambda-\Lambda-\alpha}$$ . An analytic continuation using the point method is applied to search the eigenvalue in the complex energy plane. In our results the Σ-Σ- α three-body system has two quasi-bound states ( J = 0) where, depending on the potential parameters in the Nijmegen NSC97 model potential, the energy ranges between −1.4 and −2.4 MeV and the level width is about 0.4 MeV for the ground state. In addition, we obtained the excited state at −0.15 MeV (width 4 MeV). [ABSTRACT FROM AUTHOR]

In the first part of the contribution, we discuss the results of a recent benchmark calculation of n − H and p − He phase-shifts below the trinucleon disintegration thresholds. Three different methods-Alt, Grassberger and Sandhas, Hyperspherical Harmonics, and Faddeev-Yakubovsky-have been used and their results are compared. For both n − H and p − He we observe a rather good agreement between the three different theoretical methods. In the second part of the contribution, we study the longitudinal asymmetry $${A_z^{n^3{\rm He}}}$$ in the He( n, p)H reaction in order to obtain information about the parity-violating components of the nucleon-nucleon interaction. [ABSTRACT FROM AUTHOR]

The three-body Faddeev-type AGS equations were used for investigation of scattering states in the $${\bar{K} NN - \pi \Sigma N}$$ system. Newly constructed 'chirally motivated' potentials describing $${\bar{K} N - \pi \Sigma}$$ interaction were used as an input. The results of the three-body calculations were then used for calculations of the corresponding 1 s level shift and width of kaonic deuterium. [ABSTRACT FROM AUTHOR]

Inelastic neutron-deuteron scattering is studied on the basis of configuration-space Faddeev equations. Calculated are neutron-deuteron breakup amplitudes using AV14 nucleon-nucleon potential at incident neutron energy of 14.1 MeV. The results of calculations are presented for the differential cross sections under quasi free scattering and space-star configurations, and compared with those of the previous calculations and experimental data. The choice of the cutoff radius R for asymptotic conditions is discussed. [ABSTRACT FROM AUTHOR]