Universality and Halo Nuclei

Universal aspects of few-body systems will be reviewed motivated by recent interest in atomic and nuclear physics. The critical conditions for the existence of excited states in three-body systems with two-identical particles will be explored. In particular, we consider halo nuclei that can be modeled as three-body nuclear systems, with two halo neutrons and a core. In this context, we also discuss the low-energy neutron-C-19 elastic scattering, near the conditions for the appearance of an Efimov state.

Bright vortex solitons in bose condensates

We suggest the possibility of observing and studying bright vortex solitons in attractive Bose-Einstein condensates in three dimensions with a radial trap. Such systems lie on the verge of critical stability and we discuss the conditions of their stability. We study the interaction between two such solitons. Unlike the text-book solitons in one dimension, the interaction between two radially trapped and axially free three-dimensional solitons is inelastic in nature and involves exchange of particles and deformation in shape. The interaction remains repulsive for all phase δ between them except for δ ≈ 0.

Universalities in halo nuclei

In this contribution I provide an overview of our group papers involving universalities in light exotic nuclei. It is also made a connection of these systems with some weakly bound ultracold molecules. © 2010 American Institute of Physics.

Range Corrections to Universal Tetramer Properties

The universal properties of weakly-bound tetramers close to the scaling limit are investigated by solving a subtracted set of Faddeev-Yakubovsky (FY) equations for identical bosons with a zero-range interaction. The solution demands a four-body scale independent of the trimer properties. Furthermore, the effect of a finite effective range is introduced in the FY equations, which we show produces results that are distinct from the scale variation. In particular range effects to two universal scaling functions for the tetramers are investigated. The correlation between successive tetramer energies corresponding to states within two Efimov trimer energies, proposed before and studied close to the unitary limit; and the correlation between the position of the four-atom recombination peaks. In this case, we found a shift in the scaling function due to the range, which can be associated to the shift of the data found for caesium atoms, with respect to zero-range calculations, due to a nonvanishing range in the actual experimental setups. © 2013 Springer-Verlag Wien.

A Combined Study of the Pion's Static Properties and form Factors

We study consistently the pion's static observables and the elastic and γ* γ → π0 transition form factors within a light-front model. Consistency requires that all calculations are performed within a given model with the same and single adjusted length or mass-scale parameter of the associated pion bound-state wave function. Our results agree well with all extent data including recent Belle data on the γ* γ → π0 form factor at large q2, yet the BaBar data on this transition form factor resists a sensible comparison. We relax the initial constraint on the bound-state wave function and show the BaBar data can partially be accommodated. This, however, comes at the cost of a hard elastic form factor not in agreement with experiment. Moreover, the pion charge radius is about 40 % smaller than its experimentally determined value. It is argued that a decreasing charge radius produces an ever harder form factor with a bound-state amplitude difficultly reconcilable with soft QCD. We also discuss why vector dominance type models for the photon-quark vertex, based on analyticity and crossing symmetry, are unlikely to reproduce the litigious transition form factor data. © 2013 Springer-Verlag Wien.

Nonmesonic Weak Decay Spectra of Light Hypernuclei

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

Scattering Amplitudes Interpolating Between Instant Form and Front Form of Relativistic Dynamics

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the front form has the largest number of kinematic generators. This distinction provides useful consequences in the analysis of physical observables in hadron physics. Using the method of interpolation between the instant form and the front form, we introduce the interpolating scattering amplitude that links the corresponding time-ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time-ordered amplitude for an arbitrary interpolation angle. We discuss the rationale for using front form dynamics, nowadays known as light-front dynamics (LFD), and present a few explicit examples of hadron phenomenology that LFD uniquely can offer from first-principles quantum chromodynamics. In particular, model-independent constraints are provided for the analyses of deuteron form factors and the N Delta transition form factors at large momentum transfer squared Q(2). The swap of helicity amplitudes between the collinear and non-collinear kinematics is also discussed in deeply virtual Compton scattering.

Trimer-Tetramer Interwoven States in the Scaling Limit

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Single-Particle Momentum Distributions for Bosonic Trimer States in Two and Three Dimensions

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Many-body theory for systems of composite hadrons

Many-body systems of composite hadrons are characterized by processes that involve the simultaneous presence of hadrons and their constituents. We briefly review several methods that have been devised to study such systems and present a novel method that is based on the ideas of mapping between physical and ideal Fock spaces. The method, known as the Fock-Tani representation, was invented years ago in the context of atomic physics problems and was recently extended to hadronic physics. Starting with the Fock-space representation of single-hadron states, a change of representation is implemented by a unitary transformation such that composites are redescribed by elementary Bose and Fermi field operators in an extended Fock space. When the unitary transformation is applied to the microscopic quark Hamiltonian, effective, Hermitian Hamiltonians with a clear physical interpretation are obtained. The use of the method in connection with the linked-cluster formalism to describe short-range correlations and quark deconfinement effects in nuclear matter is discussed. As an application of the method, an effective nucleon-nucleon interaction is derived from a constituent quark model and used to obtain the equation of state of nuclear matter in the Hartree-Fock approximation.

EXOTIC CARBON SYSTEMS IN TWO-NEUTRON HALO THREE-BODY MODELS

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

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.

Trajectory of neutron-neutron-C-18 excited three-body state

The trajectory of the first excited Efimov state is investigated by using a renormalized zero-range three-body model for a system with two bound and one virtual two-body subsystems. The approach is applied to n-n-C-18, where the n-n virtual energy and the three-body ground state are kept fixed. It is shown that such three-body excited state goes from a bound to a virtual state when the n-C-18 binding energy is increased. Results obtained for the n-C-19 elastic cross-section at low energies also show dominance of an S-matrix pole corresponding to a bound or virtual Efimov state. It is also presented a brief discussion of these findings in the context of ultracold atom physics with tunable scattering lengths. (C) 2008 Elsevier B.V. All rights reserved.

Borromean three-body heteroatomic resonances

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Charged three-body system with arbitrary masses near conformal invariance

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