The Modified CHHE-MRT Method in Few-Body System

Based on the continuum hyperspherical harmonics expansion momentum rep-resentation transformation(CHHE-MRT)method,a new approach is proposed to cal-culate the matrix elements of any forms of potential.By introducing the modifiedCHHE-MRT function,the 3N dimensional Bessel oscillatory integral appearing in po-tential calculation can be reduced to 3M dimension(N≥M).The method presentedhere can be used not only for bound stute but also for scattering state in few-body sys-tem.

Study of various few-body systems using Gaussian expansion method （GEM）

We review our calculation method, Gaussian expansion method （GEM）, to solve accurately the Schrodinger equations for bound, resonant and scattering states of few-body systems. Use is made of the Rayleigh-Ritz variational method for bound states, the complex-scaling method for resonant states and the Kohn-type variational principle to S-matrix for scattering states. GEM was proposed 30 years ago and has been applied to a variety of subjects in few-body （3- to 5-body） systems, such as 1） few-nucleon systems, 2） few-body structure of hypernuelei, 3） clustering structure of light nuclei and unstable nuclei, 4） exotic atoms/molecules, 5） cold atoms, 6） nuclear astrophysics and 7） structure of exotic hadrons. Showing examples in our published papers, we explain i） high accuracy of GEM calculations and its reason, ii） wide applicability of GEM to various few-body systems, iii） successful predictions by GEM calculations before measurements. The total bound-state wave function is expanded in terms of few-body Gaussian basis functions spanned over all the sets of rearrangement Jacobi coordinates. Gaussians with ranges in geometric progression work very well both for short- range and long-range behavior of the few-body wave functions. Use of Gaussians with complex ranges gives much more accurate solution than in the case of real-range Gaussians, especially, when the wave function has many nodes （oscillations）. These basis functions can well be applied to calculations using the complex-scaling method for resonances. For the few-body scattering states, the amplitude of the interaction region is expanded in terms of those few-body Gaussian basis functions.

Two—Electron Energy Spectrum in a Parabolic Quantum Dot Under a Magnetic Field

Two interacting electrons in a harmonic oscillator potential under the influence of a perpendicular homo-geneous magnetic field are considered. The energies of two-electron quantum dots with the electron-LO-phonon couplingas a function of magnetic field are calculated. Calculations are made by using the method of few-body physics withinthe effective-mass approximation. Our results show that the electron-LO-phonon coupling effect is very important insemiconductor quantum dots.

Effect of the Electron—Phonon Coupling on Barrier D^— Quantum Dots in Magnetic Fields

The influence of the electron-phonon coupling on the energy of low-lying states of the barrier D- center, which consists of a positive ion located on the z-axis at a distance from the two-dimensional quantum dot plane and two electrons in the dot plane bound by the ion, is investigated at arbitrary strength of magnetic field by making use of the method of few-body physics. Discontinuous ground-state energy transitions induced by the magnetic field are reported. The dependence of the binding energy of the D- ground state on the quantum dot radius is obtained. A considerable enhancement of the binding is found for the D- ground state, which results from the confinement of electrons and electron-phonon coupling.

Binding Energy of an Exciton Bound to Ionized Acceptor in Quantum Dots

Binding energiesfor an exciton (X ) trapped in the two-dimensional quantum dot by a negative ion located on the z axis at a distance from the dot plane are calculated by using the method of few-body physics.This configuration is called a barrier (A-,X) center.The dependence of the binding energy of the ground state of the barrier (A-,X)center on the electron-to-hole mass ratio for a few values of the distance d between the fixed negative ion on the z axis and the dot plane is obtained.We find that when d → 0,the barrier (A-,X) center has not any bound state.We also studied the stability and binding energy of the ground state of the barrier (A-,X) center in a parabolic quantum dot as a function of the distance d between the fixed negative ion on the z axis and the dot plane.

Off—Center D—Centers in a Quantum Dot in the Presence of a Perpendicular Magnetic Fields

We investigate the effect of the position of the donor in quantum dots on the energy spectrum in the presence of a perpendicular magnetic field by using the method of few-body physics. As a function of the magnetic field, we find, when D- centers are placed sufficiently off-center, discontinuous ground-state transitions which are similar to those found in many-electron parabolic quantum dots. Series of magic numbers of angular momentum which minimize the ground-state electron-electron interaction energy have been discovered. The dependence of the binding energy of the ground-state of the D- center on the dot radius for a few values of the magnetic field strength is obtained and compared with other results.

Quantum Size Effects on Two Electrons and Two Holes in Double-Layer Quantum Dots

We propose a procedure to solve exactly the Schrodinger equation for a system of two electrons and two holes in a double-layer quantum dot by using the method of few-body physics. The features of the low-lying spectra have been deduced based on symmetry. The binding energies of the ground state are obtained as a function of the electron-to-hole mass ratio σ for a few values of the quantum dot size.

Charged-Exciton Complexes in Quantum Dots

It is known experimentally that stable charged-exciton complexes can exist in low-dimensional semiconductor nanostructures. Much less is known about the properties of such charged-exciton complexes since three-body problems are very difficult to be solved, even numerically. Here we introduce the correlated hyperspherical harmonics as basis functions to solve the hyperangular equation for negatively and positively charged excitons (trions) in a harmonic quantum dot. By using this method, we have calculated the energy spectra of the low-lying states of a charged exciton as a function of the radius of quantum dot. Based on symmetry analysis, the level crossover as the dot radius increases can be fully explained as the results of symmetry constraint.

Effects of Magnetic Field on Fracture of Al-Li Alloy Containing Ce rium

The effects of magnetic field on fracture feature and microstructure of Al-Li a lloys containing Ce were investigated. Experiment results show that the fracture features and the microstructures are changed with the magnetic field. The fract ure surface of the alloys is mainly quasi-cleavage without applying magnetic fi eld. With a magnetic field, the fracture of quasi-cleavage changes to more second ary cracks and less quasi-cleavage plates on fracture surface. Grains become thinner and uniform with applying magnetic field. The influence of magnetic f ield on atom diffusion was discussed.

Peculiar features of the interaction potential between hydrogen and antihydrogen at intermediate separations

This paper evaluates the interaction potential between a hydrogen and an antihydrogen using the second-order perturbation theory within the framework of the four-body system in a separable two-body basis. It finds that the H-H interaction potential possesses the peculiar features of a shallow local minimum located around interatomic separations of r ～ 6a.u. and a barrier rising at τ ≤5a.u.

Aharonov-Anandan Phases in Lipkin-Meskov-Glick Model

In the system of several interacting spins,geometric phases have been researched intensively.However,the studies are mainly focused on the adiabatic case (Berry phase),so it is necessary for us to study the non-adiabaticcounterpart (Aharonov and Anandan phase).In this paper,we analyze both the non-degenerate and degenerate geometricphase of Lipkin-Meskov-Glick type model,which has many application in Bose-Einstein condensates and entanglementtheory.Furthermore,in order to calculate degenerate geometric phases,the Floquet theorem and decomposition ofoperator are generalized.And the general formula is achieved.

Low—Lying States of the A^＋B^—A^＋B^— Coulomb systems in Two—Dimensional Quantum Dots

The features of the low-lying spectra of four-body A+B-A+B- systems have been deduced based on symmetry. Using the method of few-body physics, we calculate the energy spectra of A+B-A+B- systems in a harmonic quantum dot. We find that the biexciton in a two-dimensional quantum dot may have other bound excited states and the quantum mechanical symmetry plays a crucial role in determining the energy levels and structures of the low-lying states.

Two Interacting Electrons in a Vertically Coupled Quantum Dot

We study a two-electron system in a double-layer quantum dot under a magnetic field by means of the exact diagonalization of the Hamiltonian matrix.We find that discontinuous ground-state energy transitions are induced by an external magnetic field in the case of strong coupling.However,in the case of weak coupling,the angular momentum L of the true ground state does not change in accordance with the change of the magnetic field B and remains L=0.

Electric Multipole Polarizabilities of Quantum Bound Systems in the Transition Matrix Formalism

A new general formalism for determining the electric multipole polarizabilities of quantum (atomic and nuclear) bound systems based on the use of the transition matrix in momentum space has been developed. As distinct from the conventional approach with the application of the spectral expansion of the total Green’s function, our approach does not require preliminary determination of the entire unperturbated spectrum;instead, it makes possible to calculate the polarizability of a few-body bound complex directly based on solving integral equations for the wave function of the ground bound state and the transition matrix at negative energy, both of them being real functions of momenta. A formula for the multipole polarizabilities of a two-body bound complex formed by a central interaction potential has been derived and studied. To test, the developed t-matrix formalism has been applied to the calculation of the dipole, quadrupole and octupole polarizabilities of the hydrogen atom.

Structures and Internal Motion of a Ar_3 Cluster

The eigenvalues of a Ar3 cluster subject to a Lennerd-Jones pairwise interaction arecalculated by using harmonic oscillator product states,The geometric structures and theinternal motion of a Ar3 cluster are investigated from an anaysis of the wavefunctions.Thisinvestigation reveals the general shape and motional features of a Ar3 cluster.

Dynamically generated N* resonances from the interaction of two mesons and a baryon

We have studied the ππN system and coupled channels by using of the Faddeev equations and two N＊ and one A states, all of them with jR =1/2＋, have been found in the formalism as dynamically generated states. In addition, signatures for a new N＊ resonance with JR = 1/2＋ are found around an energy of 1920 MeV in the three-body center of mass system.

Structural characteristics of a four-boson system and effect of symmetries

With four-body model theory the energy spectra of a four-boson system and the distribution of the wave-functions of low-lying states in coordinate space are investigated. On the basis of the analysis for low-lying states, the effect of the symmetries is studied. Various structural characteristics are determined by symmetries.

Relativistic Borromean states

In this work,the existence of Borromean states is discussed for bosonic and fermionic cases in both therelativistic and non-relativistic limits from the 3-momentum shell renormalization.With the linear bosonic model,we check the existence of Efimov-like states in the bosonic system.In both limits a geometric series of singularities is found in the 3-boson interaction vertex,while the energy ratio is reduced by around 70%in the relativistic limit because of the anti-particle contribution.Motivated by the quark-diquark model in heavy baryon studies,we have carefully examined the p-wave quark-diquark interaction and found an isolated Borromean pole at finite energy scale.This may indicate a special baryonic state of light quarks in high energy quark matter.In other cases,trivialresults are obtained as expected.In the relativistic limit,for both bosonic and fermionic cases,potential Borromean states are independent of the mass,which means the results would also be valid even in the zero-mass limit.

Ξ^-t quasibound state instead of ΛΛnn bound state

The coupledΛΛnn-Ξ-pnn system was studied to investigate whether the inclusion of channel coupling is able to bind theΛΛnn system.We use a separable potential three-body model of the coupledΛΛnn-Ξ-pnn system and a variational four-body calculation with realistic interactions.Our results exclude the possibility of aΛΛnn bound state by a large margin.Instead,we found aΞ-t quasibound state above theΛΛnn threshold.

Three-body hadronic molecules

In this talk,I discuss our recent studies of three-hadron systems and the resonances found therein.The studies consist of solving Faddeev equations with the input two body interactions obtained from the chiral Lagrangians.The systems which we study are either made of two mesons and a baryon or of three mesons.The motivation for these studies comes from the data on many baryon resonances,especially the ones with J ^π = 1/2 ^＋,which show a large branching ratio to the two meson-one baryon decay channels.In addition to this,several new studies at BES,BELLE,BABAR etc.,claim the existence of new meson resonances which seem to couple strongly to three-meson systems,where mostly two out of the three mesons appear as a known resonance.Hitherto,we have studied two meson-one baryon systems with strangeness =-1,0 and 1 and three-meson systems made of two-pseudoscalars and a vector meson.As we will show in this manuscript,we find many resonances which couple to three-hadrons.