Narrow Results

The phase equivalent relativistic NN potential, which is related by a nonlinear equation to the original nonrelativistic potential, is used to construct the mass operator (rest Hamiltonian) of the 3-nucleon system. Employing the CD Bonn NN potential, the solution of the relativistic 3N Faddeev equation for ³H shows slightly less binding energy than the corresponding nonrelativistic result. The effect of the Wigner spin rotation on the binding is very small.

Dyson–Schwinger equations furnish a Poincaré covariant framework within which to study hadrons. A particular feature is the existence of a nonperturbative, symmetry preserving truncation that enables the proof of exact results. The gap equation reveals that dynamical chiral symmetry breaking is tied to the long-range behavior of the strong interaction, which is thereby constrained by observables, and the pion is precisely understood, and seen to exist simultaneously as a Goldstone mode and a bound state of strongly dressed quarks. The systematic error associated with the simplest truncation has been quantified, and it underpins a one-parameter model efficacious in describing an extensive body of mesonic phenomena. Incipient applications to baryons have brought successes and encountered challenges familiar from early studies of mesons, and promise a covariant field theory upon which to base an understanding of contemporary large momentum transfer data.

The general properties of exotic carbon systems, considered as a core with a two-neutron (n - n) halo, are described within a renormalized zero-range three-body model. In particular, it is addressed the cases with a core of ¹⁸C and ²⁰C. In such a three-body framework, ²⁰C has a bound subsystem (¹⁹C), whereas ²²C has a Borromean structure with all subsystems unbound. ²²C is also known as the heaviest carbon halo nucleus discovered. The spatial distributions of such weakly-bound three-body systems are studied in terms of a universal scaling function, which depends on the mass ratio of the particles, as well as on the nature of the subsystems.

The quark exchange model and the full three-nucleon wave function in the configuration space are used to evaluate the role of Fermi motion on the structure functions (SFs) of helium-3 and tritium nuclei. The three-nucleon wave function is obtained from the solution of the Faddeev equations with the Malfliet–Tjon-type potential, by using the three-dimensional approach as a function of the magnitudes of the Jacobi momenta vectors and the angle between them. In this calculation, the initial valence quarks inputs are taken from the GRV's (Glück, Reya and Vogt) fitting procedure and the next-to-leading order (NLO) QCD calculation on , which give a very good fit to the available experimental data in the (x, Q²)-plane. The role of Fermi motion on the EMC ratio of the SFs of ³He and ³H nuclei are analyzed through the NLO expansion of the nuclear wave function in the coordinate space. A good agreement between the calculated EMC ratios, the corresponding experimental data and the theoretical results is found. Finally, the ratios of the SFs of the neutron to the proton (with the isospin symmetry assumption) with and without the Fermi motion effect, are also calculated, and they are compared with the available experimental data. Our results show that the roles of the Fermi motion in the framework of the quark exchange model for the calculations of the nuclear SFs are important.

Investigations of three-body nuclear systems using pionless effective field theory (${\mathrm{\text{EFT}}}_{\mathrm{\pi ̸}}$) are reviewed. The history of ${\mathrm{\text{EFT}}}_{\mathrm{\pi ̸}}$ in $nd$ and $pd$ scattering is briefly discussed and emphasis put on the use of strict perturbative techniques. In addition renormalization issues appearing in $pd$ scattering are also presented. Bound state calculations are addressed and new perturbative techniques for describing them are highlighted. Three-body breakup observables in $nd$ scattering are also considered and the utility of ${\mathrm{\text{EFT}}}_{\mathrm{\pi ̸}}$ for addressing them.

Based on the effective-mass concept, we perform the Faddeev calculations for a low-lying spectrum of 3$\alpha$ states in ${}^{12}$C nucleus. A three-body potential is used to describe the known breaking of the 3$\alpha$-cluster structure in the nucleus. We show that the contribution of the three-body potential to the Hamiltonian can be compensated by increasing/decreasing the $\alpha$-particle free mass. The effective-mass values are adjusted to reproduce the experimental data for the ${}^{12}$C nucleus. The energy dependence of the effective mass and the correlation to a three-body potential are discussed. We show that the coupling between the $0^{+}$ ($2^{+}$) levels forms a specific picture of anti-crossing on the energy/effective-mass plane.

We discuss the importance of the three-nucleon isospin $T=3/2$ component in elastic neutron-deuteron scattering and in the deuteron breakup reaction. The contribution of this amplitude originates from charge-independence breaking of the nucleon-nucleon potential. We study the magnitude of that contribution to the elastic scattering and breakup observables, taking the Av18 nucleon-nucleon potential alone or combined with the Urbana IX three-nucleon force as well as the locally regularized chiral N⁴LO nucleon-nucleon potential alone or supplemented by the chiral N²LO three-nucleon force. We find that the isospin $T=3/2$ component is important for the breakup reaction and the proper treatment of charge-independence breaking in this case requires the inclusion of the ${}^1{S}_0$ state with isospin $T=3/2$. For neutron-deuteron elastic scattering the $T=3/2$ contributions are insignificant and charge-independence breaking can be accounted for by neglecting $T=3/2$ component and using the effective t-matrix generated with the so-called $“2/3-1/3^{″}$ rule.

We investigate the three-body systems of and , by taking the fixed center approximation to Faddeev equations. We find a clear and stable resonance structure around 1490 MeV in the scattering amplitude for the system, which is not sensitive to the renormalization parameters. This resonance is associated to the η(1475). We get only an enhancement effect of the threshold in the amplitude.