Five- and six-body resonances tied to an Efimov trimer

We explore the properties of weakly bound bosonic states in the strongly interacting regime. Combining a correlated-Gaussian basis set expansion with a complex-scaling method, we extract the energies and structural properties of bosonic cluster states with N ≤ 6 for different two-body potentials. The identification of five- and six-body resonances attached to the first-excited-Efimov trimer provides strong support to the premise of Efimov universality in bosonic systems. Our study also reveals a rich structure of bosonic cluster states. Besides the lowest cluster states that behave as bosonic droplets, we identify cluster states weakly bound to one or two atoms forming effective cluster-atom dimers and cluster-atom-atom "trimers." The experimental signatures of these cluster states are discussed.     

Use of supersymmetric isospectral formalism to realistic quantum many-body problems

We propose a novel mathematical approach for the calculation of resonances in weakly bound systems. For any potential, families of strictly isospectral potentials (with very different shape) having desirable and adjustable features can be generated. For systems having no bound ground state, an isospectral potential with a bound state in the continuum is possible. The quasi-bound state in the original shallow potential will be effectively trapped in the deep well of the isospectral family, facilitating more accurate calculation of resonance energy. Application to ⁶He, ⁶Li and ⁶Be yield excellent results. Another application is the calculation of Efimov states in weakly bound threebody system. We present the result of ⁴He trimer, where the first excited state is claimed to be an Efimov state.     

He-He-Ba三原子体系弱束缚态计算

本文利用含有绝热近似的超球坐标方法计算了碱土金属原子Ba和氦原子组成的弱束缚三原子分子体系He₂Ba的基态性质. 系统地研究了该系统的道函数和超球势曲线特征, 进而得到体系的束缚能. 研究结果显示, ¹³⁸Ba 与⁴He, ³He 的各种组合⁴He-⁴He-¹³⁸Ba, ⁴He-³He-¹³⁸Ba和³He-³He-¹³⁸Ba都分别只有一个束缚态.     

3D projection sideband cooling

We demonstrate 3D microwave projection sideband cooling of trapped, neutral atoms. The technique employs state-dependent potentials that enable microwave photons to drive vibration-number reducing transitions. The particular cooling sequence we employ uses minimal spontaneous emission, and works even for relatively weakly bound atoms. We cool 76% of atoms to their 3D vibrational ground states in a site-resolvable 3D optical lattice.     

Structure and Occurrence of Three-Body Halos in Two Dimensions

 The quantum-mechanical three-body problem is reformulated in two dimensions by use of hyperspherical coordinates and an adiabatic expansion of the Faddeev equations. The effective radial potentials are calculated and their large-distance asymptotic behavior is derived analytically for short-range two-body interactions. Energies and wave functions are computed numerically for various potentials. An infinite series of Efimov states does not exist in two dimensions. Borromean systems, i.e. bound three-body systems without bound binary subsystems, can only appear when a short-range repulsive barrier at finite distance is present in the two-body interaction. The corresponding Borromean state is never spatially extended. For a system of three weakly interacting identical bosons we find two bound states with both binding energies proportional to the two-body binding energy. In the limit of small binding these states are spatially located at the very large distances characterized by the scattering length. Their properties are universal and independent of the details of the potential. We compare throughout with the corresponding properties in three dimensions. Received September 25, 1998; accepted for publication January 30, 1999     

Reactions with Weakly Bound Nuclei,at near Barrier Energies,and the Breakup and Transfer Influences on the Fusion and Elastic Scattering

We present a brief review of the reaction mechanisms involved in collisions of weakly bound projectiles with tightly bound targets, at near-barrier energies. We discuss systematic behaviors of the data, with emphasis in fusion, breakup, nucleon transfer and elastic scattering. The dependence of the breakup cross section on the charge and mass of the target is discussed, and the influence of the breakup channel on complete fusion is investigated. For this purpose, we compare reduced fusion cross sections with a benchmark universal curve. The behaviors observed in the comparisons are explained in terms of polarization potentials and of nucleon transfer followed by breakup. The influence of the breakup process on elastic scattering is also discussed. Some apparent contradictions between results of different authors are explained and some perspectives of the field are presented.     

Evolution of the vortex state in the BCS-BEC crossover of a quasi two-dimensional superfluid Fermi gas

We use the path-integral formalism to investigate the vortex properties of a quasi-two dimensional(2D) Fermi superfluid system trapped in an optical lattice potential.Within the framework of mean-field theory,the cooper pair density,the atom number density,and the vortex core size are calculated from weakly interacting BCS regime to strongly coupled while weakly interacting BEC regime.Numerical results show that the atoms gradually penetrate into the vortex core as the system evolves from BEC to BCS regime.Meanwhile,the presence of the optical lattice allows us to analyze the vortex properties in the crossover from three-dimensional(3D) to 2D case.Furthermore,using a simple re-normalization procedure,we find that the two-body bound state exists only when the interaction is stronger than a critical one denoted by G_c which is obtained as a function of the lattice potential's parameter.Finally,we investigate the vortex core size and find that it grows with increasing interaction strength.In particular,by analyzing the behavior of the vortex core size in both BCS and BEC regimes,we find that the vortex core size behaves quite differently for positive and negative chemical potentials.     

Resonances in A=6 Nuclei: Use of Supersymmetric Quantum Mechanics

We propose a novel theoretical technique for the calculation of resonances at low excitation energies in weakly bound systems. Starting from an effective potential, supersymmetric quantum mechanics can be successfully used to generate families of isospectral potentials having desirable and adjustable properties. For resonance states, for which there is no bound ground state of the same spin-parity, one can construct an isospectral potential with a bound state in the continuum (BIC). The potential looks quite different but is strictly isospectral with the original one. The quasi-bound state in the original shallow potential will be effectively trapped in the deep well of the isospectral family facilitating an easier and more accurate calculation of the resonance energy. Application to ⁶He, ⁶Be, and ⁶Li systems yields quite accurate results. The beauty of our technique: We get both the bound ground state and the resonances by a single technique and using the same potential.     

Discontinuous unbinding of lipid multibilayers

We have observed a discontinuous unbinding transition of lipid bilayer stacks composed of phosphatidylethanolamine and phosphatidylglycerol using x-ray diffraction. The unbinding is reversible and coincides with the main (L(beta)-->L(alpha)) transition of the lipid mixture. Interbilayer interaction potentials deduced from the diffraction data reveal that the bilayers in the L(beta) phase are only weakly bound. The unbinding transition appears to be driven by an abrupt increase in steric repulsion resulting from increased thermal undulations of the bilayers upon entering the fluid L(alpha) phase.     

The three-body problem with short-range interactions

The quantum mechanical three-body problem is studied for general short-range interactions. We work in coordinate space to facilitate accurate computations of weakly bound and spatially extended systems. Hyperspherical coordinates are used in both the interpretation and as an integral part of the numerical method. Universal properties and model independence are discussed throughout the report. We present an overview of the hyperspherical adiabatic Faddeev equations. The wave function is expanded on hyperspherical angular eigenfunctions which in turn are found numerically using the Faddeev equations. We generalize the formalism to any dimension of space d greater or equal to two. We present two numerical techniques for solving the Faddeev equations on the hypersphere. These techniques are effective for short and intermediate/large distances including use for hard core repulsive potentials. We study the asymptotic limit of large hyperradius and derive the analytic behaviour of the angular eigenvalues and eigenfunctions. We discuss four applications of the general method. We first analyze the Efimov and Thomas effects for arbitrary angular momenta and for arbitrary dimensions d. Second we apply the method to extract the general behaviour of weakly bound three-body systems in two dimensions. Third we illustrate the method in three dimensions by structure computations of Borromean halo nuclei, the hypertriton and helium molecules. Fourth we investigate in three dimensions three-body continuum properties of Borromean halo nuclei and recombination reactions of helium atoms as an example of direct relevance for the stability of Bose–Einstein condensates.     

Vibrational and rotational bound states in floppy triatomic systems: The distributed Gaussian functions approach

A variational method based on the use of bond coordinates and of a basis set expansion described by distributed Gaussian functions (DGF) is reviewed for its applications to the study of weakly bound triatomic clusters. This approach will be shown to be particularly well suited to treat very diffuse states as those presented by Noble gas (Ng) containing systems like the Ng₃, and Ng₂X, with X being also a very weakly bound atomic impurity. Several statistical properties such as radial distributions, sizes and dominance of triangular configurations for the corresponding bound states are shown to be directly obtained with this method over the whole spectrum of the floppy cluster bound states, in both the rotationless case and also when special care is taken to define rotational constants to yield rovibrational states and their energy levels.     

Density-dependent potential for multi-neutron halo nuclei

We apply a simple density-dependent potential model to the three-body calculation of the ground-state structure of drip-line nuclei with a weakly bound core. The hyperspherical harmonics method is used to solve the Faddeev equations. There are no undetermined potential parameters in this calculation. We find that for the halo nuclei with a weakly-bound core, the calculated properties of the ground-state structure are in better agreement with experimental data than the results calculated from the standard Woods-Saxon and Gauss type potentials. We also successfully reproduce the experimental cross sections by using the density calculated from this method. This may be explained by the fact that the simple Fermi or Gaussian function can not exactly describe the density distribution of the drip-line nuclei.     

Suppression of molecular decay in ultracold gases without Fermi statistics

We study inelastic processes for ultracold three-body systems in which only one interaction is resonant. We show that at ultracold temperatures three-body recombination in such systems leads mainly to the formation of weakly bound molecules. In addition, and perhaps more importantly, we have found that the decay rates for weakly bound molecules due to collisions with other atoms can be suppressed not only without fermionic statistics but also when bosonic statistics applies. These results indicate that recombination in three-component atomic gases can be used as an efficient mechanism for molecular formation, allowing the achievement of high molecular densities.     

Violation of the Bloch-Nordsieck mechanism in general non-abelian theories and SUSY QCD

We discuss the ordering of energy levels of bound states of various relativistic wave equations with local potentials. We concentrate on wave equations for two spinless particles. We point out differences and similarities to the case of the nonrelativistic Schrödinger equation.     

Asymptotic Properties of Solvable $\mathcal{PT}$-Symmetric Potentials

The asymptotic region of potentials has strong impact on their general properties. This problem is especially interesting for PT\mathcal{PT}-symmetric potentials, the real and imaginary components of which allow for a wider variety of asymptotic properties than in the case of purely real potentials. We consider exactly solvable potentials defined on an infinite domain and investigate their scattering and bound states with special attention to the boundary conditions determined by the asymptotic regions. The examples include potentials with asymptotically vanishing and non-vanishing real and imaginary potential components (Scarf II, Rosen-Morse II, Coulomb). We also compare the results with the asymptotic properties of some exactly non-solvable PT\mathcal{PT}-symmetric potentials. These studies might be relevant to the experimental realization of PT\mathcal{PT}-symmetric systems.     

Assessing the adequacy of the bare optical potential in near-barrier fusion calculation

We critically examine the differences among the different bare nuclear interactions used in near-barrier heavy-ion fusion analysis and coupled-channels calculations, and discuss the possibility of extracting the barrier parameters of the bare potential from above-barrier data. We show that the choice of the bare potential may be critical for the analysis of the fusion cross sections. Although this may seem trivial, several recent papers use different bare potentials and reach different conclusions, especially when weakly bound systems are considered and possible relatively small fusion cross section enhancements or suppressions are found. We show also that the barrier parameters taken from above-barrier data may be very wrong.     

Reaction functions for weakly bound systems

We propose a new technique to analyze total reaction cross sections. In this technique, which has been previously applied to fusion reactions, the experimental data are used to build a dimensionless reaction function, which does not depend on the system size or details of the optical potential. In this way, total reaction cross sections for different systems can be directly compared. We employ this technique to perform a systematic study of reaction cross sections of weakly bound systems in different mass ranges, and compare their reaction functions with the ones of tightly bound systems with similar masses. We show that breakup reactions and neutron transfers in halo systems lead to large reaction functions, well above the ones of typical tightly or weakly bound stable systems.     

Bound States of Energy Dependent Singular Potentials

We consider attractive power-law potentials depending on energy through their coupling constant. These potentials are proportional to 1/|x| ^m with m ≥ 1 in the D = 1 dimensional space, to 1/r ^m with m ≥ 2 in the D = 3 dimensional space. We study the ground state of such potentials. First, we show that all singular attractive potentials with an energy dependent coupling constant are bounded from below, contrarily to the usual case. In D = 1, a bound state of finite energy is found with a kind of universality for the eigenvalue and the eigenfunction, which become independent on m for m > 1. We prove the solution to be unique. A similar situation arises for D = 3 for m > 2, except that, in this case, the solution is not directly comparable to a bound state: the wave function, though square integrable, diverges at the origin.     

Exact Solutions of Klein-Gordon Equation with Exponential Scalar and Vector Potentials

We obtain the exact analytical solution of the Klein-Gordon equation for the exponential vector and scalar potentials by using the asymptotic iteration method. For the scalar potential greater than the vector potential case, the exact bound state energy eigenvalues and corresponding eigenfunctions are presented. The bound state eigenfunction solutions are obtained in terms of the confluent hypergeometric functions.