Tjon Lines and Scaling Limit in Four-Body Systems

The fixed-slope correlation between tetramer and trimer binding energies, observed by Tjon in the context of nuclear physics, is mainly a manifestation of the dominance of the two-nucleon force in the nuclear potential, which makes the four-body scale on the order of the three-body one. In a more general four-boson case, the correlation between tetramer and trimer binding energies has a non-fixed slope, which expresses the dependence on the new scale. The associated scaling function generates a family of Tjon lines. This conclusion relies on a recent study with weakly-bound four identical bosons, within a renormalized zero-range Faddeev-Yakubovsky formalism. © 2012 Springer-Verlag.

Four-boson scale near a Feshbach resonance

We show that an independent four-body momentum scale mu((4)) drives the tetramer binding energy for fixed trimer energy (or three-body scale mu((3))) and large scattering length (a). The three- and four-body forces from the one-channel reduction of the atomic interaction near a Feshbach resonance disentangle mu((4)) and mu((3)). The four-body independent scale is also manifested through a family of Tjon lines, with slope given by mu((4))/mu((3)) for a(-1) = 0. There is the possibility of a new renormalization group limit cycle due to the new scale.

OBSTACLE STEPPING and BODY SCALE MODULATING PARAMETERS

The purpose of this study was to investigate gait spatial parameters at the point of departure, with obstacle heights adjusted to individual body scale. Undergraduate student volunteers (M age=22.4 yr., SD=2.1; 6 women, 1 man) were asked to step once, then cross over an obstacle and stop. This behavior was video recorded to extract kinematic data. The obstacle heights corresponded to high (knee-height) and low obstacles (half the knee-height). Points of departure corresponded to far (length of the lower limb) and close (half the length of the lower limb). The close point of departure influenced the trailing foot's placement ahead of the obstacle as well as step length. The high obstacle influenced the trailing foot's toe clearance. An interaction between factors was observed for leading foot toe clearance. Results indicate that body scale affected the participants' locomotor behavior during the obstacle-avoidance task.

Universality in Four-Boson Systems

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. © 2012 Springer-Verlag.

Four-Boson Systems Close to a Universal Regime

Universal properties of weakly-bound four-boson systems near the scaling limit are discussed by considering recent results obtained from the solution of Faddeev-Yakubovsky (FY) equations, which confirm a previous conjecture on a four-body scale dependence. In the present contribution, within a discussion on our numerical results obtained for the binding energies of two consecutive tetramer states, we are analyzing the relative relevance of the two possible configurations of the four-body system. © 2013 Springer-Verlag Wien.

Universality and Scaling Limit of Weakly-Bound Tetramers

The occurrence of a new limit cycle in few-body physics, expressing a universal scaling function relating the binding energies of two successive tetramer states, is revealed by considering a renormalized zero-range two-body interaction in bound state of four identical bosons. The tetramer energy spectrum is obtained by adding a boson to an Efimov bound state with energy B-3 in the unitary limit (for zero two-body binding energy or infinite two-body scattering length). Each excited N-th tetramer energy B-4((N)) is shown to slide along a scaling function as a short-range four-body scale is changed, emerging from the 3+1 threshold for a universal ratio B-4((N))/B-3 = 4.6, which does not depend on N. The new scale can also be revealed by a resonance in the atom-trimer recombination process.

Binding and structure of tetramers in the scaling limit

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

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.

Trimer-Tetramer Interwoven States in the Scaling Limit

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

Structure of exotic three-body systems

The classification of large halos formed by two identical particles and a core is systematically addressed according to interparticle distances. The root-mean-square distances between the constituents are described by universal scaling functions obtained from a renormalized zero-range model. Applications for halo nuclei, Li-11 and Be-14, and for atomicn He-4(3) are briefly discussed. The generalization to four-body systems is proposed.

Borromean three-body heteroatomic resonances

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

Virtual States, Halos and Resonances in Three-Body Atomic and Nuclear Systems

By considering nuclear and ultracold trapped atomic systems, we review the trajectory of Efimov excited states in the complex plane by changing the two-body scattering lengths and one three-body scale.

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 with effective range corrections. The effective range correction is extracted with a weighted average given by 3.9±0.8R vdW, where RvdW is the van der Waals length scale, which is consistent with the van der Waals potential tail for the Cs2 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. © 2013 American Physical Society.

Irregular satellites of Jupiter: capture configurations of binary-asteroids

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Stochastic variational approach applied to 2, 3 and 4 alpha particles

A stochastic variational method is applied to calculate the binding energies and root-mean-square radii of 2, 3 and 4 alpha particles using an S-wave Ali-Bodmer potential. The results agree with other calculations. We discuss the application of the present method to study the universality in weakly-bound three and four-body systems in the context of ultracold atomic traps.