Effective Range Corrections to Three-Body Recombination for Atoms with Large Scattering Length

Few-body systems with large scattering length a have universal properties that do not depend on the details of their interactions at short distances. The rate constant for three-body recombination of bosonic atoms of mass m into a shallow dimer scales as \hbar a^4/m times a log-periodic function of the scattering length. We calculate the leading and subleading corrections to the rate constant which are due to the effective range of the atoms and study the correlation between the rate constant and the atom-dimer scattering length. Our results are applied to 4He atoms as a test case.Comment: 6 pages, 2 figures, improved discussion, final versio

Energy spectra of small bosonic clusters having a large two-body scattering length

In this work we investigate small clusters of bosons using the hyperspherical harmonic basis. We consider systems with $A=2,3,4,5,6$ particles interacting through a soft inter-particle potential. In order to make contact with a real system, we use an attractive gaussian potential that reproduces the values of the dimer binding energy and the atom-atom scattering length obtained with one of the most widely used $^4$He-$^4$He interactions, the LM2M2 potential. The intensity of the potential is varied in order to explore the clusters' spectra in different regions with large positive and large negative values of the two-body scattering length. In addition, we include a repulsive three-body force to reproduce the trimer binding energy. With this model, consisting in the sum of a two- and three-body potential, we have calculated the spectrum of the four, five and six particle systems. In all the region explored, we have found that these systems present two bound states, one deep and one shallow close to the $A-1$ threshold. Some universal relations between the energy levels are extracted; in particular, we have estimated the universal ratios between thresholds of the three-, four-, and five-particle continuum using the two-body gaussia

Three-fermion problems in optical lattices

We present exact results for the spectra of three fermionic atoms in a single well of an optical lattice. For the three lowest hyperfine states of Li6 atoms, we find a Borromean state across the region of the distinct pairwise Feshbach resonances. For K40 atoms, nearby Feshbach resonances are known for two of the pairs, and a bound three-body state develops towards the positive scattering-length side. In addition, we study the sensitivity of our results to atomic details. The predicted few-body phenomena can be realized in optical lattices in the limit of low tunneling.Comment: 4 pages, 4 figures, minor changes, to appear in Phys. Rev. Let

The structure of the atomic helium trimers: Halos and Efimov states

The Faddeev equations for the atomic helium-trimer systems are solved numerically with high accuracy both for the most sophisticated realistic potentials available and for simple phenomenological potentials. An efficient numerical procedure is described. The large-distance asymptotic behavior, crucial for weakly bound three-body systems, is described almost analytically for arbitrary potentials. The Efimov effect is especially considered. The geometric structures of the bound states are quantitatively investigated. The accuracy of the schematic models and previous computations is comparable, i.e. within 20% for the spatially extended states and within 40% for the smaller ^4He-trimer ground state.Comment: 32 pages containing 7 figures and 6 table

The Four-Boson System with Short-Range Interactions

We consider the non-relativistic four-boson system with short-range forces and large scattering length in an effective quantum mechanics approach. We construct the effective interaction potential at leading order in the large scattering length and compute the four-body binding energies using the Yakubovsky equations. Cutoff independence of the four-body binding energies does not require the introduction of a four-body force. This suggests that two- and three-body interactions are sufficient to renormalize the four-body system. We apply the equations to 4He atoms and calculate the binding energy of the 4He tetramer. We observe a correlation between the trimer and tetramer binding energies similar to the Tjon line in nuclear physics. Over the range of binding energies relevant to 4He atoms, the correlation is approximately linear.Comment: 23 pages, revtex4, 5 PS figures, discussion expanded, results unchange

Anomalies in Quantum Mechanics: the 1/r^2 Potential

An anomaly is said to occur when a symmetry that is valid classically becomes broken as a result of quantization. Although most manifestations of this phenomenon are in the context of quantum field theory, there are at least two cases in quantum mechanics--the two dimensional delta function interaction and the 1/r^2 potential. The former has been treated in this journal; in this article we discuss the physics of the latter together with experimental consequences.Comment: 16 page latex file; to be published in Am. J. Phy

Strong and radiative decays of the Ds0*(2317) meson in the DK-molecule picture

We consider a possible interpretation of the new charm-strange meson Ds0*(2317) as a hadronic molecule - a bound state of D and K mesons. Using an effective Lagrangian approach we calculate the strong Ds0* to Ds pi0 and radiative Ds0* to Ds* gamma decays. A new impact related to the DK molecular structure of the Ds0*(2317) meson is that the presence of u(d) quarks in the D and K mesons gives rise to a direct strong isospin-violating transition Ds0* to Ds pi0 in addition to the decay mechanism induced by eta-pi0 mixing considered previously. We show that the direct transition dominates over the eta-pi0 mixing transition in the Ds0* to Ds pi0 decay. Our results for the partial decay widths are consistent with previous calculations.Comment: 22 pages, 4 figures, accepted for publication in Phys. Rev.

Limiting Case of Modified Electroweak Model for Contracted Gauge Group

The modification of the Electroweak Model with 3-dimensional spherical geometry in the matter fields space is suggested. The Lagrangian of this model is given by the sum of the {\it free} (without any potential term) matter fields Lagrangian and the standard gauge fields Lagrangian. The vector boson masses are generated by transformation of this Lagrangian from Cartesian coordinates to a coordinates on the sphere $S_3$. The limiting case of the bosonic part of the modified model, which corresponds to the contracted gauge group $SU(2;j)\times U(1)$ is discussed. Within framework of the limit model Z-boson and electromagnetic fields can be regarded as an external ones with respect to W-bosons fields in the sence that W-boson fields do not effect on these external fields. The masses of all particles of the Electroweak Model remain the same, but field interactions in contracted model are more simple as compared with the standard Electroweak Model.Comment: 12 pages, talk given at the XIII Int. Conf. on SYMMETRY METHODS IN PHYSICS, Dubna, Russia, July 6-9, 2009; added references for introduction, clarified motivatio

Non-commutative low dimension spaces and superspaces associated with contracted quantum groups and supergroups

Quantum planes which correspond to all one parameter solutions of QYBE for the two-dimensional case of GL-groups are summarized and their geometrical interpretations are given. It is shown that the quantum dual plane is associated with an exotic solution of QYBE and the well-known quantum $h$-plane may be regarded as the quantum analog of the flag (or fiber) plane. Contractions of the quantum supergroup $GL_q(1|2)$ and corresponding quantum superspace $C_q(1|2)$ are considered in Cartesian basis. The contracted quantum superspace $C_h(1|2;\iota)$ is interpreted as the non-commutative analog of the superspace with the fiber odd part.Comment: Talk given at the XIII Int. Coll. on Integrable Systems and Quantum Groups, June 17-19, 2004, Prague, Czech Republic. Submitted in Czech. J. of Physic