Exotic neutron-rich nuclei in a three-body model

We present results for spatial distributions of weakly-bound three-body systems, derived from a universal scaling function that depends on the mass ratio of the particles, as well as on the nature of the subsystems. © 2007 American Institute of Physics.

Relativistic three-body model for final state interaction in D+ → K-π+π+ decay

A challenge in mesonic three-body decays of heavy mesons is to quantify the contribution of re-scattering between the final mesons. D decays have the unique feature that make them a key to light meson spectroscopy, in particular to access the Kn S-wave phase-shifts. We built a relativis-tic three-body model for the final state interaction in D+ → K -π+π+ decay based on the ladder approximation of the Bethe-Salpeter equation projected on the light-front. The decay amplitude is separated in a smooth term, given by the direct partonic decay amplitude, and a three-body fully interacting contribution, that is factorized in the standard two-meson resonant amplitude times a reduced complex amplitude that carries the effect of the three-body rescattering mechanism. The off-shell reduced amplitude is a solution of an inhomogeneous Faddeev type three-dimensional integral equation, that includes only isospin 1/2 K -π+ interaction in the S-wave channel. The elastic K-π+ scattering amplitude is parameterized according to the LASS data[1]. The integral equation is solved numerically and preliminary results are presented and compared to the experimental data from the E791 Collaboration[2, 3] and FOCUS Collaboration[4, 5].

Halo nuclei in a three-body model and universal characteristics of low-energy few-body systems

Within general characteristics of low-energy few-body systems, we revise some well-known correlations found in nuclear physics, and the properties of low-mass halo nuclei in a three-body neutron-neutron-core model. In this context, near the critical conditions for the occurrence of an Efimov state, we report some results obtained for the neutron- 19C elastic scattering. © 2010 American Institute of Physics.

Scales, Universality and Finite-Range Correction in Three-body Systems

The scale invariance manifested by the weakly-bound Efimov states implies that all the Efimov spectrum can be merged in a single scaling function. By considering this scaling function, the ratio between two consecutive energy levels, E3 (N+1) and E3 (N), can be obtained from a two-body low-energy observable (usually the scattering length a), given in units of the three-body energy level N. The zero-ranged scaling function is improved by incorporating finite range corrections in first order of r0/a (r0 is the potential effective range). The critical condition for three-identical bosons in s-wave, when the excited E3 (N+1) state disappears in the 2 + 1 threshold, is given by √E2/E3 (N) ≈ 0.38+0.12(r0/a). © 2012 Springer-Verlag.

Contact parameters in two dimensions for general three-body systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Mass-Imbalanced Three-Body Systems in 2D: Bound States and the Analytical Approach to the Adiabatic Potential

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Universality of Three-Body Systems in 2D: Parametrization of the Bound States Energies

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A study of the errors of the averaged models in the restricted three-body problem in a short time scale

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Three-body Faddeev calculation for 11Li with separable potentials

The halo nucleus 11Li is treated as a three-body system consisting of an inert core of 9Li plus two valence neutrons. The Faddeev equations are solved using separable potentials to describe the two-body interactions, corresponding in the n-9Li subsystem to a p1/2 resonance plus a virtual s-wave state. The experimental 11Li energy is taken as input and the 9Li transverse momentum distribution in 11Li is studied. [S0556-2813(99)01703-3].

New Isomers in the Full Seniority Scheme of Neutron-Rich Lead Isotopes: The Role of Effective Three-Body Forces

The neutron-rich lead isotopes, up to Pb-216, have been studied for the first time, exploiting the fragmentation of a primary uranium beam at the FRS-RISING setup at GSI. The observed isomeric states exhibit electromagnetic transition strengths which deviate from state-of-the-art shell-model calculations. It is shown that their complete description demands the introduction of effective three-body interactions and two-body transition operators in the conventional neutron valence space beyond Pb-208.

Variational Calculation of the Hydrogen Molecular Cation Using Maple

The variational calculation of the energy of the Hydrogen Molecular (H2+) Cation's LCAO-MO for the sigma and sigma* states as functions of the AO's screening constant and the internuclear distance is carried out explicitly in great detail.

Momentum distributions from three-body decaying 9Be and 9B resonances

The complex-rotated hyperspherical adiabatic method is used to study the decay of lowlying 9Be and 9B resonances into α, α and n or p. We consider six low-lying resonances of 9Be (1/2±, 3/2± and 5/2±) and one resonance of 9B (5/2−) to compare with. The properties of the resonances at large distances are decisive for the momentum distributions of the three decaying fragments. Systematic detailed energy correlations of Dalitz plots are presented.

Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Symbolic Dynamics in the Free-Fall Equal-Mass Three-Body Problem

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006