Six-Bodies Calculations Using the Hyperspherical Harmonics Method

In this work we show results for light nuclear systems and small clusters of helium atoms using the hyperspherical harmonics basis. We use the basis without previous symmetrization or antisymmetrization of the state. After the diagonalization of the Hamiltonian matrix, the eigenvectors have well defined symmetry under particle permutation and the identification of the physical states is possible. We show results for systems composed up to six particles. As an example of a fermionic system, we consider a nucleon system interacting through the Volkov potential, used many times in the literature. For the case of bosons, we consider helium atoms interacting through a potential model which does not present a strong repulsion at short distances. We have used an attractive gaussian potential to reproduce the values of the dimer binding energy, the atom-atom scattering length, and the effective range obtained with one of the most widely used He–He interaction, the LM2M2 potential. In addition, we include a repulsive hypercentral three-body force to reproduce the trimer binding energy.     

Structure and dynamics of few-helium clusters using soft-core potentials

In this work we investigate the structure and dynamics of small clusters of Helium atoms. We consider bound states of clusters having A = 2, 3, 4, 5, 6 atoms and continuum states in the three-atom system. Motivated by the fact that the He-He system has a very large scattering length a compared to the range r ₀ of the He-He potential (r ₀/a < 1/10), we propose the use of a soft-core interparticle potential. We use an attractive gaussian potential that reproduces the values of the dimer binding energy and the atomatom scattering length obtained with one of the widely used He-He interactions, the LM2M2 potential. 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 a three-body potential, we show the spectrum of the four, five, and sixparticle systems and phase-shifts and inelasticities in the three-atom system. Comparisons to calculations using realistic He-He potentials are given. In addition some universal relations are explored.     

Efimov Physics in Small Bosonic Clusters

We study small clusters of bosons, A = 2, 3, 4, 5, 6, characterized by a resonant interaction. Firstly, we use a soft-gaussian interaction that reproduces the values of the dimer binding energy and the atom-atom scattering length obtained with LM2M2 potential, a widely used ⁴He-⁴He interaction. We change the intensity of the potential to explore the clusters’ spectra in different regions with large positive and large negative values of the two-body scattering length and we report the clusters’ energies on Efimov plot, which makes the scale invariance explicit. Secondly, we repeat our calculation adding a repulsive three-body force to reproduce the trimer binding energy. In all the region explored, we have found that these systems present two states, one deep and one shallow close to the A ? 1 threshold, and scale invariance has been investigated for these states. The calculations are performed by means of Hyperspherical Harmonics basis set.     

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     

THE STUDY OF HYPERTRITON WITH THREE-BODY INTEGRAL EQUATION

From a Faddeev-type integral equation for three-body bound state, the hypertriton binding energy is calculated by using the nonlocal two-body separable potential with the parameters taken from the scattering data of meson theoretical potential.The effects of n-p and N(n or p)-Λ interactions in three-body bound state are studied and the meson theoretical potentials of Refs.[1-3] are examined. The calculated results are reasonably close to the experimental values.The comparisons of our results with others are made.     

Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order

We use an effective field theory for short-range forces (SREFT) to analyze systems of three identical bosons interacting via a two-body potential that generates a scattering length, a, which is large compared to the range of the interaction, ?. The amplitude for the scattering of one boson off a bound state of the other two is computed to next-to-next-to-leading order (N²LO) in the ?/a expansion. At this order, two pieces of three-body data are required as input in order to renormalize the amplitude (for fixed a). We apply our results to a model system of three Helium-4 atoms, which are assumed to interact via the TTY potential. We generate N²LO predictions for atom-dimer scattering below the dimer breakup threshold using the bound-state energy of the shallow Helium-4 trimer and the atom-dimer scattering length as our two pieces of three-body input. Based on the convergence pattern of the SREFT expansion, as well as differences in the predictions of two renormalization schemes, we conclude that our N²LO phase- shift predictions will receive higher-order corrections of < 0.2 %. In contrast, the prediction of SREFT for the binding energy of the “deep” trimer of Helium-4 atoms displays poor convergence.     

Delta function model for the helium trimer: origin of three-body forces

The Dirac bubble potential, previously used to model the helium dimer, is applied to the trimer. It is shown that the quantum mechanical kinetic energy operator for a three-body system contains terms over and above the analogues of classical pairwise contributions. The additional terms, the ‘Borromean couplings’, are responsible for a dramatic increase in the binding energy of the trimer. For example, ⁴He₃ is bounded by two orders of magnitude more strongly than ⁴He₂, 279 mK versus 1.31 mK, respectively, according to our calculations. Moreover, the trimer is considerably more compact than the dimer, with (r₁₂) decreasing to 9.01 Å from 51.9 Å.     

A Three-Body Model of 11Li,14Be and 17B

The nuclei ¹¹Li,¹⁴Be and ¹⁷B are considered as three-body systems composed of the N=2Z core and two outside neutrons.The core-neutron and neutronneutron interactions are assumed to be the attractive exponential potentials.It has been shown that the three-body system can have a bound state although any two constituents of the system cannot have a bound state. The experimental data of the binding energy and extraordinarily large matter root-mean-square radius can be explained in the frame of the three-body model.     

Dependence of the Three-Nucleon Binding Energy on Some Different Effects

The bound state of three-nucleon system is studied as a three-body problem which is solved following the different approaches of the Faddeev formalism as well as the unitary pole approximation. The three-body problem is reduced to a set of coupled integral equations by using separable approximations. Numerical calculations are carried out for the resulting integral equations and the separable expansion. In the present work, we calculate the ground-state binding energy of the bound three-nucleon system ³H. The main interest of the present work is to investigate the sensitivity of the three-nucleon binding energy to different effects. For this reason, we study the dependence of this energy on different forms of local and separable nucleon-nucleon potentials, the effective range of the nucleon-nucleon interaction, and on the percent of the D state in the deuteron wave function. Also we test the sensitivity of the three-nucleon binding energy to the considered number of terms from the separable expansion.     

Condensate fraction and critical temperature of interacting Bose gas in anharmonic trap

The spectral flow of three-body (trimer) states consisting of two heavy (impurity) particles sitting in a condensate of light bosons is considered. Assuming that the condensate is weakly interacting and that an impurity and a boson have a resonant zero-range two-body interaction, we use the Born-Oppenheimer approximation to determine the effective three-body potential. We solve the resulting Schrödinger equation numerically and determine the trimer binding energies as a function of the coherence length of the light bosonic condensate particles. The binding energy is found to be suppressed by the presence of the condensate when the energy scale corresponding to the coherence length becomes of order the trimer binding energy in the absence of the condensate. We find that the Efimov scaling property is reflected in the critical values of the condensate coherence length at which the trimers are pushed into the continuum.     

Three-Body Recombination in Ultracold Systems: Prediction of Weakly-Bound Atomic Trimer Energies

The three-body recombination coefficient of an ultracold atomic system, together with the corresponding two-body scattering length a, allow us to predict the energy E₃ of the shallow trimer bound state, using a universal scaling function. The production of dimers in trapped Bose-Einstein condensates, from three-body recombination processes, in the regime of short magnetic pulses near a Feshbach resonance, is also studied in line with the experimental observation.     

Sensitivity of the three-body calculations to different effects

The bound state of few-body systems in light nuclei is studied as a three-body problem. The three-body problem is solved following the different approaches of the Faddeev formalism as well as the unitary pole approximation. Separable approximations are introduced to reduce the three-body problem to a set of coupled integral equations. Numerical calculations are carried out for the resulting integral equations and the separable expansion. In the present work, we calculate the ground-state binding energy of the bound three-nucleon system³H. The main interest of the present work is to investigate the sensitivity of the three-body binding energy to different effects in the problem. For this reason, we study the dependence of the three-body binding energy of different forms of local and separable two-body potentials, on the effective range of the two-body potentials, and on the percent of theD state in the deuteron wave function. Also, we test the sensitivity of the three-body binding energy to the considered number of terms from the separable expansion.     

How to study the elusive efimov state of the 4He3 molecule through a new atom-optical state-selection technique

Excited states and excitation energies of weakly bound systems, e.g., atomic few-body systems and clusters, are difficult to study experimentally. For this purpose we propose a new and very general atom-optical method which is based on inelastic diffraction from transmission gratings. The technique is applicable to the recently found helium trimer molecule 4He3, allowing for the first time an investigation of the possible existence of an excited trimer state and determination of its excitation energy. This would be of fundamental importance for the famous Efimov effect.     

Universal fermi gas with two- and three-body resonances

We consider a Fermi gas with two components of different masses, with the s-wave two-body interaction tuned to unitarity. In the range of mass ratio 8.62相似文献   

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.     

Trajectory of virtual, bound and resonant Efimov states

The pole trajectory of Efimov states for a three-body ααβ system with αα unbound and αβ bound is calculated using a zero-range Dirac-δ potential. It is shown that a three-body bound state turns into a virtual one by increasing the αβ binding energy. This result is consistent with previous results for three equal mass particles. The present approach considers the n-n-¹⁸C 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.     

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.     

Binding energies and scattering observables in the 4He3 atomic system

The ⁴He₃ system is investigated using a hard-core version of the Faddeev differential equations. Realistic ⁴He-⁴He interactions are employed, among them the LM2M2 potential by Aziz and Slaman and the recent TTY potential by Tang, Toennies and Yiu. We calculate the binding energies of the ⁴He trimer, but concentrate in particular on scattering observables. The scattering lengths and the atom-diatom phase shifts are calculated for center of mass energies up to 2.45 mK. It is found that the LM2M2 and TTY potentials, although of quite different structure, give practically the same bound-state and scattering results. Received 19 June 2000