Universality of Three-Body Systems in 2D: Parametrization of the Bound States Energies

Universal properties of mass-imbalanced three-body systems in 2D are studied using zero-range interactions in momentum space. The dependence of the three-particle binding energy on the parameters (masses and two-body energies) is highly non-trivial even in the simplest case of two identical particles and a distinct one. This dependence is parametrized for ground and excited states in terms of supercircles functions in the most general case of three distinguishable particles.     

Reaction Dynamics of Weakly-Bound Few-Body Nuclei at Energies Around the Coulomb Barrier

We present a quantum reaction approach that unambiguously quantifies the complete and incomplete fusion of weakly-bound few-body nuclei. Calculations carried out within a simple model for \({\text{}^{6}}\)Li + \({\text{}^{209}}\)Bi at energies near the Coulomb barrier show that converged probabilities for the total, complete and incomplete fusion as well as for the scattering process can be obtained with the time-dependent wave-packet dynamics.     

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, ¹¹Li and ¹⁴Be, and for atomic ⁴He₃ are briefly discussed. The generalization to four-body systems is proposed.     

Structures of Two-Dimensional Three-Body Systems

Features of the structure of L = 0 states of a two-dimensional three-body model system have been investigated. Three types of permutation symmetry of the spartial part, namely symmetric, antisymmetric, and mixed, have been considered. A comparison has been made between the two-dimensional system and the corresponding three-dimensional one. The effect of symmetry on microscopic structures is emphasized. Received December 30, 1994; revised March 13, 1995; accepted for publication April 25, 1995     

Systematic Calculations of Total Atomic Binding Energies

Hyperfine Interactions - We have calculated total atomic binding energies of 3- to 91-electron ions of all atoms with Z=3 to 118, in the Dirac–Fock model, for applications to atomic mass...     

Decisive Role of Symmetry in Structures of Three-Body Systems

A three-body system of identical particles is considered in order to demonstrate that the quantum-mechanical symmetry plays a decisive role in determining microscopic structures. Received March 14, 1994; revised July 29, 1994; accepted for publication October 19, 1994     

Optically Engineered Quantum States in Ultrafast and Ultracold Systems

This short account summarizes our recent achievements in ultrafast coherent control of isolated molecules in the gas phase, and its ongoing applications to an ensemble of ultracold Rydberg atoms to explore quantum many-body dynamics.     

The Q-Effect of the Structures of Three-Body Systems

By making use of two different modes, we made further investigation of how the competition between internal vibration energy and collective rotation energy affects the geometric structures and internal motions of three-body systems.     

Discussion on Weakly Bound States of Three-Body Systems

The equivalent two-body method for a three-body system has been generalized to an arbitrary three-body system with short-range two-body interactions. An analytical expression for the long-range effective potential is obtained for the Gaussian potential, the Yukawa potential and the exponential potential. The asymptotic behavior of the effective potential at very large distance is found to be universal and an explanation on the significance of universality is given. The weakly bound excited state for the system is first obtained although there is no bound state for two-body subsystems.     

Three-Body Systems with Square-Well Potentials in L = 0 States

The angular part of the Faddeev equations is solved analytically for s-states in case of two-body square-well potentials. The results are, still analytically, generalized to arbitrary short-range potentials for both small and large distances. We consider systems with three identical bosons, three non-identical particles, and two identical spin- fermions plus a third particle with arbitrary spin. The angular wave functions are in general linear combinations of trigonometric and exponential functions. The Efimov conditions are obtained at large distances. General properties and applications to short-range potentials are discussed. Gaussian potentials are used for illustrations. The results are useful for numerical calculations, where, for example, large distances can be treated analytically and matched to the numerical solutions at smaller distances. The saving in computational efforts could be substantial. Received May 20, 1996; revised January 24, 1997; accepted for publication January 27, 1997     

对称性对三体系统结构的影响

文中研究三全同费米子体系在具有排斥芯和吸引尾的短程两体力作用下的几何结构和内部运动模式，并与玻色体系作比较.     

A General T-Matrix Approach Applied to Two-Body and Three-Body Problems in Cold Atomic Gases

We propose a systematic T-matrix approach to solve few-body problems with s-wave contact interactions in ultracold atomic gases. The problem is generally reduced to a matrix equation expanded by a set of orthogonal molecular states, describing external center-of-mass motions of pairs of interacting particles; while each matrix element is guaranteed to be finite by a proper renormalization for internal relative motions. This approach is able to incorporate various scattering problems and the calculations of related physical quantities in a single framework, and also provides a physically transparent way to understand the mechanism of resonance scattering. For applications, we study two-body effective scattering in 2D–3D mixed dimensions, where the resonance position and width are determined with high precision from only a few number of matrix elements. We also study three fermions in a (rotating) harmonic trap, where exotic scattering properties in terms of mass ratios and angular momenta are uniquely identified in the framework of T-matrix.     

Interplay of the Staggered and Three-Body Interaction Potentials on the Quantum Phases of a Spin-1 Ultracold Atom in an Optical Lattice

The interplay of the staggered and the three-body interaction potentials on the quantum phases of a spin-1 Bose Hubbard model using a mean field approximation (MFA) is studied. In the antiferromagnetic (AF) case, a smaller value of the staggered potential (SP) results in the charge and the spin density wave ordering along with the Mott insulator (MI) and the staggered superfluid (SSF) phases. While the competition between two types of the potential leads to the stabilization of the higher order MI and charge density wave (CDW) phases with increasing three-body interaction strength. Further, the spin eigenvalue and nematic order parameters are calculated to scrutinize the spin singlet-nematic formation in the MI and the CDW phases and spin population fractions to analyze the nature of the SSF phase. A signature of the spin density wave (SDW) pattern is also observed in the gapped phase lobes. In case of a purely three-body interaction, the third and higher order insulating lobes become dominant with increasing staggered potential strength. Subsequently, all MFA phase diagrams are then nicely corroborated with the analytical results obtained using a perturbative expansion corresponding to the AF and ferromagnetic cases.     

Scattering States of Three-Body Systems with the Hyperspherical Adiabatic Method

In this paper, we investigate the feasibility of employing the Hyperspherical Adiabatic (HA) basis set to describe continuum states of the Helium trimer molecule.     

Photoionization of the Bound Systems at High Energies

We consider photoionization of a system bound by the central potential V(r). We demonstrate that the high energy nonrelativistic asymptotics of the photoionization cross section can be obtained without solving the wave equation. The asymptotics can be expressed in terms of the Fourier transform of the potential by employing the Lippmann–Schwinger equation. We find the asymptotics for the screened Coulomb field. We demonstrate that the leading corrections to this asymptotics are described by the universal factor. The high energy nonrelativistic asymptotics is found to be determined by the analytic properties of the potential V(r). We show that the energy dependence of the asymptotics of photoionization cross sections of fullerenes is to large extent model-dependent. We demonstrate that if the fullerene field V(r) is approximated by the function with singularities in the complex plane, the power drop of the asymptotics is reached at the energies which are so high that the cross section becomes unobservably small. The preasymptotic behavior with a faster decrease of the cross sections becomes important in these cases.     

Modes of Internal Motion of Three-Body Systems Containing a Lighter Particle

Since the internal motion of few-body systems appears as a variation of the shape, the shape-densities are extracted from the eigensolutions of the 0⁺ states of a 3-body system containing a lighter particle. Detailed analysis on the shape-densities is made and a certain modes of internal motion are discovered.