Faddeev Equations In Coordinate Space Research Articles

Geometrical properties of ΩNN three-body states by realistic NN and first principles Lattice QCD ΩN potentials

The Faddeev equations in coordinate space are solved to study the ΩNN and ΩΩN three-body systems using the latest ΩNS25 and ΩΩ S01 interactions developed by the HAL QCD Collaboration. We recalculate the binding energy of the ΩNN system by examining three NN potentials, i.e., modern realistic AV18 potential, Yukawa-type Malfliet-Tjon (MT) interaction, and Gogny-Pires-Tourreil (GPT) soft and local potential. We take into account the contribution of the Coulomb potential. Our numerical calculations for Ωd(T=0) in maximum spin 5/2+ confirm ground state binding energy of 20.953, 19.368, and 20.439 MeV and a matter radius of 1.097, 1.373, and 1.309 fm using MT, GPT, and AV18 NN potentials, respectively. In the case of Ωd(0)5/2+ system, our numerical analysis shows that considering higher partial waves than s wave in NN interactions leads to an increase of about 0.2 MeV using GPT and about 0.1 MeV reduction with AV18 potentials. We study the convergence of three-body binding energies in a cluster model using the hyperspherical harmonics method and investigate the geometrical properties of Ωd(0)5/2+ ground states.

Dipole excited states in 11Li with complex scaling

The 1 − excitations of the three-body halo nucleus 11Li are investigated. We use adiabatic hyperspherical expansion and solve the Faddeev equations in coordinate space. The method of complex scaling is used to compute the resonance states. The Pauli forbidden states occupied by core neutrons are excluded by constructing corresponding complex scaled phase equivalent two-body potentials. We use a recently derived neutron–core interaction consistent with known structure and reaction properties of 10Li and 11Li. The computed dipole excited states with J π =1/2 +, J π =3/2 +, and J π =5/2 + have energies ranging from 0.6 to 1.0 MeV and widths between 0.15 and 0.65 MeV. We investigate the dependence of the complex energies of these states on the 10Li spectrum. The finite spin-3/2 of the core and the resulting core–neutron spin–spin interaction are important. The connection with Coulomb dissociation experiments is discussed and a need for better measurements is pointed out.

Electron scattering on two-neutron halo nuclei: The case of 6He

The formalism to describe electron scattering reactions on two-neutron halo nuclei is developed. The halo nucleus is described as a three-body system (core + n + n), and the wave function is obtained by solving the Faddeev equations in coordinate space. We discuss elastic and quasielastic scattering using the impulse approximation to describe the reaction mechanism. We apply the method to investigate the case of electron scattering on 6He. Spectral functions, response functions, and differential cross sections are calculated for both neutron knockout and α knockout by the electron.

Three-body halos. V. Computations of continuum spectra for Borromean nuclei

We solve the coordinate space Faddeev equations in the continuum. We employ hyperspherical coordinates and provide analytical expressions allowing easy computation of the effective potentials at distances much larger than the ranges of the interactions where only s-waves in the different Jacobi coordinates couple. Realistic computations are carried out for the Borromean halo nuclei 6He (n+n+\alpha) for J\pi = 0+-, 1+-, 2+- and 11Li (n+n+9Li) for (1/2)+-, (3/2)+-, (5/2)+-. Ground state properties, strength functions, Coulomb dissociation cross sections, phase shifts, complex S-matrix poles are computed and compared to available experimental data. We find enhancements of the strength functions at low energies and a number of low-lying S-matrix poles.

Computations of the three-body continuum spectrum of 6He

We formulate a method to solve the coordinate space Faddeev equations for positive energies. The method employs hyperspherical coordinates and analytical expressions for the effective potentials at large distances. Realistic computations are carried out for the Borromean halo nucleus 6He (n+n+ α) for J π = 0 ±, 1 ±, 2 ±.

Computations of Three-Body Continuum Spectra

We formulate a method to solve the coordinate space Faddeev equations for positive energies. The method employs hyperspherical coordinates and analytical expressions for the effective potentials at large distances. Realistic computations of the parameters of the resonances and the strength functions are carried out for the Borromean halo nucleus 6He (n+n+alpha) for J = 0+, 0-, 1+, 1-, 2+,2-. PACS numbers: 21.45.+v, 11.80.Jy, 31.15.Ja, 21.60.Gx

The Pauli principle in a three-body cluster model and the momentum distributions after fragmentation of 6He and 11Li

We investigate two simple prescriptions to account for the Pauli principle in a three-body cluster model employing a new method based on an adiabatic hyperspherical expansion to solve the Faddeev equations in coordinate space. The resulting wave functions are computed and compared. Furthermore, they are tested on halo nuclei by calculations of momentum distributions and invariant mass spectra arising after fragmentation of fast 6He and 11Li in collisions with light targets. The prescriptions are very accurate and the available measured quantities are remarkably well reproduced when final state interactions are included.

The simplest strange three-body halo

The recently developed method to solve the Faddeev equations in coordinate space is used to study the weakly bound halo nucleus . The long distances are treated carefully to achieve convergence and high accuracy. We use several sets of two-body interactions which reproduce the deuteron properties and provide the low-energy - nucleon scattering data close to that of two of Nijmegen potentials. We show that the details of the potentials are unimportant unless the accuracy of the hypertriton binding energy is required to be better than 50 keV. We find that the most significant parameter of the - nucleon interaction, the singlet s-wave scattering length, must be within 10% of 1.85 fm, when the -separation energy from the deuteron is about 130 keV. Other details of the - nucleon interaction are less important for the hypertriton structure. The scattering length and effective range are computed for scattering of a -particle on a deuteron. The folding model reducing the three-body problem to a two-body problem is investigated in this context and found to be inadequate.

The three-body continuum Coulomb problem and the 3α structure of 12C

We introduce an approach, based on the coordinate space Faddeev equations, to solve the quantum mechanical three-body Coulomb problem in the continuum. We apply the approach to compute measured properties of the first two 0 + levels in 12C, including the width of the excited level, in a 3α-particle model. We use the two-body interaction which reproduces the low energy α-α scattering data and add a three-body force to account for the compound state admixture.

The three-body continuum Coulomb problem and the 3α structure of 12C

We introduce an approach, based on the coordinate space Faddeev equations, to solve the quantum mechanical three-body Coulomb problem in the continuum. We apply the approach to compute measured properties of the first two $0^+$ levels in $^{12}$C, including the width of the excited level, in a 3$\alpha$-particle model. We use the two-body interaction which reproduces the low energy $\alpha$-$\alpha$ scattering data and add a three-body force to account for the compound state admixture.

Efimov effect in coordinate space Faddeev equations.

A novel mathematically simple and physically transparent derivation of the Efimov effect is presented by means of a new efficient method for solving coordinate space Faddeev equations. The method, which is directly applicable on small computers, is used to obtain energies and wave functions of the Efimov states.