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The analysis of the core recoil momentum distribution of neutron-rich isotopes of light exotic nuclei is performed within a model of the halo nuclei described by a core and two neutrons dominated by the $s-$wave channel. We adopt the renormalized three-body model with a zero-range force, that accounts for the universal Efimov physics. This model is applicable to nuclei with large two-neutron halos compared to the core size, and a neutron-core scattering length larger than the interaction range. The halo wave function in momentum space is obtained by using as inputs the two-neutron separation energy and the energies of the singlet neutron-neutron and neutron-core virtual states. Within our model, we obtain the momentum probability densities for the Borromean exotic nuclei Lithium-11 ($^{11}$Li), Berylium-14 ($^{14}$Be) and Carbon-22 ($^{22}$C). A fair reproduction of the experimental data was obtained in the case of the core recoil momentum distribution of $^{11}$Li and $^{14}$Be, without free parameters. By extending the model to $^{22}$C, the combined analysis of the core momentum distribution and matter radius suggest (i) a $^{21}$C virtual state well below 1 MeV; (ii) an overestimation of the extracted matter $^{22}$C radius; and (iii) a two-neutron separation energy between 100 and 400 keV.

We introduce an effectively one-dimensional (1D) model of a bosonic gas of particles carrying collinear dipole moments which are induced by an external polarizing field with the strength periodically modulated along the coordinate, which gives rise to an effective nonlocal nonlinear lattice in the condensate. The existence, shape and stability of bright solitons, appearing in this model, are investigated by means of the variational approximation and numerical methods. The mobility of solitons and interactions between them are studied too., Comment: Journal of Physics B, in press. 20 pages, 9 figures (21 frames)

We report recent advances on the study of universal weakly bound four-boson states from the solutions of the Faddeev-Yakubovsky equations with zero-range two-body interactions. In particular, we present the correlation between the energies of successive tetramers between two neighbor Efimov trimers and compare it to recent finite range potential model calculations. We provide further results on the large momentum structure of the tetramer wave function, where the four-body scale, introduced in the regularization procedure of the bound state equations in momentum space, is clearly manifested. The results we are presenting confirm a previous conjecture on a four-body scaling behavior, which is independent of the three-body one. We show that the correlation between the positions of two successive resonant four-boson recombination peaks are consistent with recent data, as well as with recent calculations close to the unitary limit. Systematic deviations suggest the relevance of range corrections., Comment: Accepted for publication in special issue of Few-Body Systems devoted to the Sixth Workshop on the Critical Stability of Quantum Few-Body Systems, October 2011, Erice, Sicily, Italy

The momentum-space structure of the Faddeev-Yakubovsky (FY)components of weakly-bound tetramers is investigated at the unitary limit using a renormalized zero-range two-body interaction. The results, obtained by considering a given trimer level with binding energy $B_3$, provide further support to a universal scaling function relating the binding energies of two successive tetramer states. The correlated scaling between the tetramer energies comes from the sensitivity of the four-boson system to a short-range four-body scale. Each excited $N-$th tetramer energy $B_4^{(N)}$ moves as the short-range four-body scale changes, while the trimer properties are kept fixed, with the next excited tetramer $B_4^{(N+1)}$ emerging from the atom-trimer threshold for a universal ratio $B_4^{(N)}/B_3 = B_4^ {(N)}/B_4^{(N+1)} \simeq 4.6$, which does not depend on $N$. We show that both channels of the FY decomposition [atom-trimer ($K-$type) and dimer-dimer ($H-$type)] present high momentum tails, which reflect the short-range four-body scale. We also found that the $H-$channel is favored over $K-$channel at low momentum when the four-body momentum scale largely overcomes the three-body one., Comment: To appear in PRA

The recently extracted matter radius of carbon isotope $^{22}$C allows us to estimate the mean-square distance of a halo neutron with respect to the center-of-mass of this nucleus. By considering this information, we suggest an energy region for an experimental investigation of the unbound $^{21}$C virtual state. Our analysis, in a renormalized zero-ranged three-body model, also indicates that the two-neutron separation energy in $^{22}$C is expected to be found below $\sim$0.4~MeV, where the $^{22}$C is approximated by a Borromean configuration with a pointlike $^{20}$C and two $s$-wave halo neutrons. A virtual-state energy of $^{21}$C close to zero, would make the $^{22}$C, within Borromean nuclei configurations, the most promising candidate to present an excited bound Efimov state or a continuum three-body resonance.

We investigate the occurrence of Borromean three-body continuum s-wave resonances, in an $\alpha\alpha\beta$ system for large negative two-body scattering lengths. The energy and width are determined by a scaling function with arguments given by energy ratios of the two-body virtual state subsystem energies with the shallowest three-body bound state. The Borromean continuum resonances emerging from Efimov states present a peculiar behavior for trapped ultracold atoms near a Feshbach resonance: two resonances with equal energies at different values of the scattering length. The corresponding three-body recombination peaks should merge as the temperature is raised, with one moving towards lower values of the scattering length as the other moves to larger values.

As an application of the new realistic three-dimensional (3D) formalism reported recently for three-nucleon (3N) bound states, an attempt is made to study the effect of three-nucleon forces (3NFs) in triton binding energy in a non partial wave (PW) approach. The spin-isospin dependent 3N Faddeev integral equations with the inclusion of 3NFs, which are formulated as function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angle between them, are solved with Bonn-B and Tucson-Melbourne NN and 3N forces in operator forms which can be incorporated in our 3D formalism. The comparison with numerical results in both, novel 3D and standard PW schemes, shows that non PW calculations avoid the very involved angular momentum algebra occurring for the permutations and transformations and it is more efficient and less cumbersome for considering the 3NF., Comment: 4 pages, 1 figure, 1 table.

The first step toward the application of an effective non partial wave (PW) numerical approach to few-body atomic bound states has been taken. The two-body transition amplitude which appears in the kernel of three-dimensional Faddeev-Yakubovsky integral equations is calculated as function of two-body Jacobi momentum vectors, i.e. as a function of the magnitude of initial and final momentum vectors and the angle between them. For numerical calculation the realistic interatomic interactions HFDHE2, HFD-B, LM2M2 and TTY are used. The angular and momentum dependence of the fully off-shell transition amplitude is studied at negative energies. It has been numerically shown that, similar to the nuclear case, the transition amplitude exhibits a characteristic angular behavior in the vicinity of 4He dimer pole., Comment: 8 pages, 6 figures, 4 tables. Oral contribution to the 19th International IUPAP Conference on Few-Body Problems In Physics, 31 Aug-5 Sep 2009, Bonn, Germany

The pole trajectory of Efimov states for a three-body $\alpha\alpha\beta$ system with $\alpha\alpha$ unbound and $\alpha\beta$ bound is calculated using a zero-range Dirac-$\delta$ potential. It is showed that a three-body bound state turns into a virtual one by increasing the $\alpha\beta$ binding energy. This result is consistent with previous results for three equal mass particles. The present approach considers the $n-n-^{18}C$ halo nucleus. However, the results have good perspective to be tested and applied in ultracold atomic systems, where one can realize such three-body configuration with tunable two-body interaction., Comment: Proceedings of the 20th European Conference on Few-Body Problems in Physics. To be published in Few-Body Systems

By introducing a mass asymmetry in a non-Borromean three-body system, without changing the energy relations, the virtual state pole cannot move from the negative real axis of the complex energy plane (with nonzero width) and become a resonance, because the analytical structure of the unitarity cuts remains the same., Comment: To be published in PRL

The results of a recent experiment with $^{85}$Rb Bose-Einstein condensates are analyzed within the mean-field approximation including dissipation due to three-body recombination. The intensity of the dissipative term is chosen from the three-body theory for large positive scattering lengths. The remaining number of condensed atoms in the experiment, obtained with applied magnetic field pulses, were used to adjust the intensity of the dissipative term. We found that the three-body recombination parameter depends on the pulse rise time; i.e., for longer rise times the values found become consistent with the three-body theory, while for shorter pulses this coefficient is found to be much larger. We interpret this finding as an indication of a coherent formation of dimers., Comment: Total of 4 pages, 5 figures and 1 table. Submitted to Phys. Rev

We discuss the possible observation of a new type of standing nonlinear atomic matter wave in the condensate: the nonlinear impurity mode. It is investigated dynamical effects of a bright soliton in Bose-Einstein-condensed (BEC) systems with local space variations of the two-body atomic scattering length. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. Processes as trapping, reflection and transmission of the bright matter soliton due to the impurity are studied considering an analytical time-dependent variational approach and also by full numerical simulation. A condition is obtained for the collapse of the bright solitary wave in the quasi-one-dimensional BEC with attractive local inhomogeneity., Comment: 8 pages, 5 figures

The recent Bose-Einstein condensation of ultracold atoms with attractive interactions led us to consider the novel possibility to probe the stability of its ground state in arbitrary three-dimensional harmonic traps. We performed a quantitative analysis of the critical number of atoms through a full numerical solution of the mean field Gross-Pitaevskii equation. Characteristic limits are obtained for reductions from three to two and one dimensions, in perfect cylindrical symmetries as well as in deformed ones., Comment: 5 pages, 3 figures. To appear in Phys. Rev. A

We develop a relativistic quark model for pion structure, which incorporates the non-trivial structure of the vacuum of Quantum Chromodynamics as modelled by instantons. Pions are boundstates of quarks and the strong quark-pion vertex is determined from an instanton induced effective lagrangian. The interaction of the constituents of the pion with the external electromagnetic field is introduced in gauge invariant form. The parameters of the model, i.e., effective instanton radius and constituent quark masses, are obtained from the vacuum expectation values of the lowest dimensional quark and gluon operators and the low-energy observables of the pion. We apply the formalism to the calculation of the pion form factor by means of the isovector nonforward parton distributions and find agreement with the experimental data., Comment: LaTeX; altered version; references and figures added. Published: paper has been accepted for publication in Nucl. Phys. A

In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schroedinger equation. A particular scaling is used in the equation, which permits to evaluate the wave-function normalization after the numerical solution. We have a two point boundary value problem, where the second point is taken at infinity. The differential equation is solved using the shooting method and Runge-Kutta integration method, requiring that the asymptotic constants, for the function and its derivative, are equal for large distances. In order to obtain fast convergence, the secant method is used., Comment: 2 figures

We study the effects of a repulsive three-body interaction on a system of trapped ultra-cold atoms in a Bose-Einstein condensed state. The corresponding $s-$wave non-linear Schr\"{o}dinger equation is solved numerically and also by a variational approach. A first-order liquid-gas phase transition is observed for the condensed state up to a critical strength of the effective three-body force., Comment: 4 pages, 3 figures

The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms is investigated under the assumption of an attractive two-body and a repulsive three-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear Schr\"odinger equation is extended to include an effective potential dependent on the square of the density and solved numerically for the $s-$wave. The lowest frequency of the collective mode is determined through the Fourier transform of the time dependent solution and its dependences on the number of atoms and the strength of the three-body force are studied. We show that the addition of three-body dynamics can allow the number of condensed atoms to increase considerably, even when the strength of the three-body force is very small compared with the strength of the two-body force., Comment: Contribution to the "Internationl Workshop on Collective Excitations in Fermi and Bose Systems", Serra Negra, Brazil, September 14-17, 1998. To be published by World Scientific, Singapore

A recently proposed renormalization scheme can be used to deal with nonrelativistic potential scattering exhibiting ultraviolet divergence in momentum space. A numerical application of this scheme is made in the case of potential scattering with $r^{-2}$ divergence for small r, common in molecular and nuclear physics, by the use of cut-offs in momentum and configuration spaces. The cut-off is finally removed in terms of a physical observable and model-independent result is obtained at low energies. The expected variation of the off-shell behavior of the t matrix arising from the renormalization scheme is also discussed., Comment: 15 pages plus 5 figures