Solution of Two-Body Bound State Problems with Confining Potentials

The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to remove the singularity of the kernel of the integral equation, a regularized form of the potentials is used. As an application of the method, the mass spectra of heavy quarkonia, mesons consisting from heavy quark and antiquark $(\Upsilon(b\bar{b}), \psi(c\bar{c}))$, are calculated for linear and quadratic confining potentials. The results are in good agreement with configuration space and experimental results.Comment: 6 pages, 5 table

Radii in weakly-bound light halo nuclei

A systematic study of the root-mean-square distance between the constituents of weakly-bound nuclei consisting of two halo neutrons and a core is performed using a renormalized zero-range model. The radii are obtained from a universal scaling function that depends on the mass ratio of the neutron and the core, as well as on the nature of the subsystems, bound or virtual. Our calculations are qualitatively consistent with recent data for the neutron-neutron root-mean-square distance in the halo of $^{11}$Li and $^{14}$Be nuclei

Scaling functions of two-neutron separation energies of 20C^{20}C with finite range potentials

The behaviour of an Efimov excited state is studied within a three-body Faddeev formalism for a general neutron-neutron-core system, where neutron-core is bound and neutron-neutron is unbound, by considering zero-ranged as well as finite-ranged two-body interactions. For the finite-ranged interactions we have considered a one-term separable Yamaguchi potential. The main objective is to study range corrections in a scaling approach, with focus in the exotic carbon halo nucleus $^{20}C$

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two component Bose-Einstein condensate confined in a nonlinear periodic potential [nonlinear optical lattice] are investigated. We reveal the existence of new types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to the NOL are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components, bright localized modes of mixed symmetry type, as well as, dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi 1D nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.Comment: 13 pages, 14 figure

Effective range from tetramer dissociation data for cesium atoms

The shifts in the four-body recombination peaks, due to an effective range correction to the zero-range model close to the unitary limit, are obtained and used to extract the corresponding effective range of a given atomic system. The approach is applied to an ultracold gas of cesium atoms close to broad Feshbach resonances, where deviations of experimental values from universal model predictions are associated to effective range corrections. The effective range correction is extracted, with a weighted average given by 3.9$\pm 0.8 R_{vdW}$, where $R_{vdW}$ is the van der Waals length scale; which is consistent with the van der Waals potential tail for the $Cs_2$ system. The method can be generally applied to other cold atom experimental setups to determine the contribution of the effective range to the tetramer dissociation position.Comment: A section for two-, three- and four-boson bound state formalism is added, accepted for publication in Phys. Rev.

Probing the Efimov discrete scaling in atom-molecule collision

The discrete Efimov scaling behavior, well-known in the low-energy spectrum of three-body bound systems for large scattering lengths (unitary limit), is identified in the energy dependence of atom-molecule elastic cross-section in mass imbalanced systems. That happens in the collision of a heavy atom with mass $m_H$ with a weakly-bound dimer formed by the heavy atom and a lighter one with mass $m_L \ll m_H$. Approaching the heavy-light unitary limit the $s-$wave elastic cross-section $\sigma$ will present a sequence of zeros/minima at collision energies following closely the Efimov geometrical law. Our results open a new perspective to detect the discrete scaling behavior from low-energy scattering data, which is timely in view of the ongoing experiments with ultra-cold binary mixtures having strong mass asymmetries, such as Lithium and Caesium or Lithium and Ytterbium