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In this study, the πD*... three meson system is calculated in unitary chiral perturbation theory using the fixed center approximation to the Faddeev equation. In this method, two particles are taken as a cluster and the third particle is scattered from this cluster to search for the three particle system. In this calculation, the D*... state was taken as a cluster and the scattering of the pion from this cluster was analyzed. The scattering of the pion from the first particle of the cluster (πD*) and the scattering of the pion from the second particle of the cluster (π...) were calculated by solving the Bethe-Salpeter equation in the isospin basis in the unitary chiral perturbation theory in coupled channels. As a result of our calculations, we obtained a quasi-bound state with isospin 1=1, mass 4156 MeV and width about 130 MeV. The peak was associated with the X(4160) meson with a mass of 4153-35+23 MeV and a width of 136-35+60 MeV. [ABSTRACT FROM AUTHOR]

In this paper we consider a operator matrix . We construct an analog of the well-known Faddeev equation for the eigenvectors of and study some important properties of this equation, related with the number of eigenvalues. In particular, the Birman–Schwinger principle for is proven. [ABSTRACT FROM AUTHOR]

Neutron induced nuclear reaction on light nuclei is an important subject in nuclear data research. The reaction of the n+d three nucleons system is also an important platform for examining the nucleonnucleon interaction theories. The progress on calculations of neutron induced nuclear reactions on deuterons with the FaddeevAGS equations was introduced in this paper. The equations were solved with the wave packet continuum discretization method in momentum space. The calculated results include the angular distributions of elastic scattering, doubledifferential cross sections of the emitting neutrons and protons from breakup reactions, excitation functions of the total elastic scattering cross sections, and the excitation function of the total breakup reaction cross sections. The elastic scattering cross sections were calculated with the separable Paris nucleonnucleon interaction for incident energy below 20 MeV and with the Nijmegen potential for incident energy above 20 MeV. A comparison between results with the Paris potential, which consists of both s and pwave nucleonnucleon (NN) interactions, and those with the swave Yamaguchi potential for the n+d elastic scattering suggest that NN interactions that are beyond the swave are necessary to describe the experimental data, especially at higher incident energy. Due to practical reasons, calculations of the breakup cross sections, namely, the double differential cross sections of the emitting neutrons and protons are limited with a separable swave Yamaguchitype nucleonnucleon interaction, which limited the calculation of the double differential cross sections to below 20 MeV. Fair agreements are found between the results in this paper and the experimental data and with the evaluated data in CENDL32, ENDF/BⅧ.0, JENDL5, and JEFF33.

Based on the effective-mass concept, we perform the Faddeev calculations for a low-lying spectrum of 3 α states in 1 2 C nucleus. A three-body potential is used to describe the known breaking of the 3 α -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 α -particle free mass. The effective-mass values are adjusted to reproduce the experimental data for the 1 2 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. [ABSTRACT FROM AUTHOR]

A symmetry-preserving Poincaré-covariant quark+diquark Faddeev equation treatment of the nucleon is used to deliver parameter-free predictions for the nucleon's axial and induced pseudoscalar form factors, GA and GP, respectively. The result for GA can reliably be represented by a dipole form factor characterised by an axial charge gA=GA(0)=1.25(3) and a mass-scale MA=1.23(3)mN, where mN is the nucleon mass; and regarding GP, the induced pseudoscalar charge gp⁎=8.80(23), the ratio gp⁎/gA=7.04(22), and the pion pole dominance Ansatz is found to provide a reliable estimate of the directly computed result. The ratio of flavour-separated quark axial charges is also calculated: gAd/gAu=−0.16(2). This value expresses a marked suppression of the size of the d-quark component relative to that found in nonrelativistic quark models and owes to the presence of strong diquark correlations in the nucleon Faddeev wave function – both scalar and axial-vector, with the scalar diquark being dominant. The predicted form for GA should provide a sound foundation for analyses of the neutrino-nucleus and antineutrino-nucleus cross-sections that are relevant to modern accelerator neutrino experiments.

The properties of the two-neutron halo nucleus 11Li are investigated. The calculations are performed using the Faddeev equation with core excitation and Woods-Saxon potential. The core has been deformed and allowed to be excited to first 2+ state. This model enables to include the excitation of core of the three bodies, while the other two particles remain inert. Also, it is particularly suitable for obtaining the bound states structure compositions and binding energies of light exotic nuclei considered as three-body systems, which given the three effective of two body interactions. Results were compared with experimental data and three-body model. The handling of 11Li with an excited core in a microscopic cluster model was more accurate than that with an inert core in the three-body model. The dependence of three-body system energy on the quadruple of the core was investigated, and the core has an oblate shape.

In this work we numerically calculate cross sections of the reactions 6Li (n , n ′ γ) 6Li and 7Li (n , n ′ γ) 7Li reactions in the region of neutron kinetic energy E n = 0.5 − 20 MeV. Neutron-nucleus interaction is defined in terms of the three-body problem wherein the target-nucleus is a bound two-body system. Dynamics in all two-body segments is described by the coupled Lippman-Schwinger equations with separable potentials. Free parameters of these potentials are chosen based on a fairly good description of elastic scattering phase shifts and radiation cross sections: t α → γ 7 Li, d α → γ 6 Li, n d → γ t. The system of three-body strongly interacting particles is described by the Faddeev equations. Radiative relaxation of the excited nucleus is effectively taken into account by the electromagnetic vertex inserted in the three-body scattering amplitude. Total cross sections and also poorly measured double differential cross sections of 6Li (n , n ′ γ) 6Li and 7Li (n , n ′ γ) 7Li are obtained and briefly analyzed. [ABSTRACT FROM AUTHOR]

The systematic approach to calculating cross section of inelastic neutron scattering on 6Li and 7Li nuclei in the range of kinetic energies E n = 0.1 − 20 MeV is presented. The reaction mechanism is described using the Faddeev equations within the problem of neutron interaction with two clusters which form the target nucleus bound state. The length a n Li of elastic n −Li scattering are calculated. The coherence effect on n 5 Li and αd contributions to 6Li nucleus ground state is demonstrated by the example of elastic neutron scattering reaction. Total and differential cross sections of inelastic neutron scattering on 6Li and 7Li nuclei with formation of three and four particles in the final state are calculated. Three-body interaction of clusters which form the target nucleus ground state in 6Li (n , n ′) d α and 7Li (n , n ′ α) t reactions is shown to be of great importance. [ABSTRACT FROM AUTHOR]

The low-energy properties of the elastic s-wave scattering for the n-19C are studied near the critical condition for the occurrence of an excited Efimov state in n–n-18C. It is established to which extent the universal scaling laws, strictly valid in the zero-range limit, survive when finite range potentials are considered. By fixing the two-neutrons separation energy in 20C with available experimental data, it is studied the scaling of the real (δ0R) and imaginary parts of the s-wave phase-shift with the variation of the n-18C binding energy. We obtain some universal characteristics given by the pole-position of kcot⁡(δ0R) and effective-range parameters. By increasing the n-18C binding energy, it was verified that the excited state of 20C goes to a virtual state, resembling the neutron–deuteron behavior in the triton. It is confirmed that the analytical structure of the unitary cut is not affected by the range of the potential or mass asymmetry of the three-body system.

In this paper, we reformulate three-nucleon breakup scattering in leading order approximation by considering spin-isospin degrees of freedom. At first, considering the inhomogeneous part of Faddeev equation, which is a valid approximation in high and intermediate energles, we present the Faddeev equation as a function of vector Jacobi momenta and spin and isospin quantum numbers. In this new formulation, a three-dimensional representation of deuteron wave function instead of its partial wave representation. Then, this equation is rewritten in suitable coordinate system as a function of vector magnitudes and angles between them for numerical calculation. Finally, by applying the Bonn-B potential the proton-deuteron breakup scattering cross section is calculated and the results are compared with the experimental data.

A model operator H associated with the system of three-identical particles on a lattice ℤ3 is considered. The location of the essential spectrum of H is described by the spectrum of the corresponding Friedrichs model, that is, the two-particle and three-particle branches of the essential spectrum of H are singled out. It is proved that the essential spectrum of H consists of no more than three bounded closed intervals. An appearance of two-particle branches on the both sides of the three-particle branch is shown. Moreover, we obtain an analogue of the Faddeev equation and its symmetric version, for the eigenfunctions of H.

In this paper a model operator H associated to a system of three-particles on a lattice is considered. The location of the essential spectrum of H is described by the spectrum of channel operators. The Faddeev type equation for the eigenvectors of H is obtained.

The NJL model for the octet baryons, using proper time regularisation to simulate some of the features of confinement, is solved self-consistently in nuclear matter. This provides an alternative framework to the MIT bag model which has been used in the quark–meson coupling model. After fitting the parameters of the model to the saturation properties of symmetric nuclear matter the model is used to explore the equation of state of pure neutron matter as well as nuclear matter at densities relevant to heavy ion collisions. With a view to future studies of high mass neutron stars, the binding of hyperons is also explored. [ABSTRACT FROM AUTHOR]

The core momentum distribution of a weakly-bound neutron–neutron–core exotic nucleus is computed within a renormalized zero-range three-body model, with interactions in the s-wave channel. The halo wave-function in momentum space is obtained by using as inputs the two-body scattering lengths and the two-neutron separation energy. The core momentum densities are computed for 11 Li, 14 Be 20 C and 22 C. The model describes the experimental data for 11 Li, 14 Be and to some extent 20 C. The recoil momentum distribution of the 20 C from the breakup of 22 C nucleus is computed for different two-neutron separation energies, and from the comparison with recent experimental data the two-neutron separation energy is estimated in the range 100 ≲ S 2 n ≲ 400 keV . The recoil momentum distribution depends weakly on the neutron- 20 C scattering length, while the matter radius is strongly sensitive to it. The expected universality of the momentum distribution width is verified by also considering excited states for the system. [ABSTRACT FROM AUTHOR]

Investigations of three-body nuclear systems using pionless effective field theory () are reviewed. The history of in and scattering is briefly discussed and emphasis put on the use of strict perturbative techniques. In addition renormalization issues appearing in scattering are also presented. Bound state calculations are addressed and new perturbative techniques for describing them are highlighted. Three-body breakup observables in scattering are also considered and the utility of for addressing them. [ABSTRACT FROM AUTHOR]

In this work we have applied a three-dimensional approach to solve the three-nucleon Faddeev equation in the Jacobi momenta space. To this end, we have considered the inhomogeneous part of the Faddeev equation as an appropriate approximation for projectile intermediate energies. As an application the Bonn-B and the Tucson–Melbourne two- and three-nucleon forces have been used for calculating the differential cross section for proton–deuteron break-up process. Finally, comparing our results with the experimental data has been performed for 197 MeV and 346 MeV projectile energies. [ABSTRACT FROM AUTHOR]