Binding Energy in Two- and Three-Body Relativistic Dynamics

 Two-body and three-body systems of scalar bosons are considered in the framework of covariant constraint dynamics. The reduced equation obtained after eliminating redundant degrees of freedom can be viewed as an eigenvalue equation for an observable which is intimately related with the relative motion. We display the connection of this observable with binding energy. Received October 30, 2001; accepted for publication November 9, 2001     

Solution of a Relativistic Three-Body Problem

 Starting from a relativistic s -wave scattering-length model for the two-particle input we construct an unambiguous, unitary solution of the relativistic three-body problem given only the masses m _a , m _b , m _c ,and the masses of the two-body bound states μ _bc ,μ _ca ,μ _bc . Received August 5, 1997; revised June 21, 1999; accepted for publication July 10, 1999     

Rigid-Rotator and Fixed-Shape Solutions to the Coulomb Three-Body Problem

Solutions to the general classical Coulomb three-body problem in the form of rigid-rotator and fixed-shape configurations are studied. In the collinear case, some necessary and/or sufficient conditions for the existence of the so-called charge-symmetrical, (−)(+)(−), and charge-asymmetrical, (−)(−)(+), configurations are stated. These conditions involve relations between the geometrical and dynamical parameters of the system under study. The impossibility of the existence of a planar Coulombic rigid rotator is demonstrated. In the two-dimensional case, fixed-shape solutions are studied analytically, and it is shown that, in the three-dimensional case, only fixed-shape solutions involving a triple collision and a static case are possible. Finally, some numerical experimentation, mostly based upon theoretical predictions of the work, is performed, and new bound (although unstable) rotating-oscillating orbits for systems such as the positronium negative ion and helium are found. Received February 27, 1996; revised September 2, 1996; accepted for publication October 22, 1996     

Treatment of Coulomb Interaction in Momentum Space for p-3He Elastic Scattering

Applying the method proposed by C.M.Vincent and S.C.Phatak to p-³He elastic scattering,we studied the treatment of Coulomb interaction in momentum space.The differetial cross sections and spin observables at 500,400,300 and 200MeV are calculated.The present results are discussed and compared with previous results and experimental data.     

Treatment of Coulomb Interaction in Momentum Space for p-3He Elastic Scattering

Applying the method proposed by R.Crespo and J.A.Tostevin to p-³He elastic scattering,we study the treatment of Coulomb interaction of momentum space.The differential cross sections and spin observables at 500 and 300 MeV are calculated with R=7fm.The present results are compared with those given in V-P method.It shows that the applicable range of angular momentum and momentum transfer in R-J method are wider than those in V-P method.     

Path Integral Solution for the Coulomb Potential in a Curved Space of Constant Positive Curvature

A new path integral treatment of a hydrogen-like atom in a uniformly curved space with a constant positive curvature is presented. By converting the radial path integral into a path integral for the modified Pöschl-Teller potential with the help of the space-time transformation technique, the radial Green’s function is expressed in closed form, from which the energy spectrum and the corresponding normalized wave functions of the bound states are extracted. In the limit of vanishing curvature, the Green’s function, the energy spectra and the correctly normalized wave functions of bound and scattering states for a standard hydrogen-like atom are found.     

Dynamics of Analytical Matter-Wave Solutions in Three-Dimensional Bose–Einstein Condensates with Two- and Three-Body Interactions

Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time- dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain （loss）. Various shapes of analytical matter-wave solutions which have important applications of physical interest are s~udied in details.     

Bose--Einstein Condensates with Two- and Three-Body Interactions in an Anharmonic Trap at Finite Temperature

The transition temperature, the depletion of the condensate atoms and the collective excitations of a Bose-Einstein condensation （BEC） with two- and three-body interactions in an anharmonic trap at finite temperature are studied in detail. By using the Popov version of the Hartree-Fock-Bogoliubov （HFB） approximation, an extended self-consistent model describing BEC with both two- and three-body interactions in a distorted harmonic potential at finite temperature is obtained and solved numerically. The results show that the transition temperature, the condensed atom number and the collective excitations are modified dramatically by the atomic three-body interactions and the distortion of the harmonic trap.     

Coulombic Transformation in Momentum Space

We studied the Coulombic transformation of potential in momentum space. The Coulombic transformation is defined as a unitary transformation in momentum space, which is equivalent of the Coulomb–Fourier transformation in coordinate space. The analytic continuation scheme avoids the difficulty which is occurred from the singularity of the Coulomb wave function in momentum space. We adopted the point method to perform the analytic continuation. The validity of the new scheme is checked by comparing with the analytic solution for the Malfliet-Tjon potential. Numerical calculation of the integration was done by separating into four intervals. We demonstrate the high accuracy of our calculation.     

Stability and Collective Excitation of Two-Dimensional BECs with Two- and Three-Body Interactions in an Anharmonic Trap

The stability and collective excitation of Bose-Einstein condensates with both two- and three-body interactions in a two-dimensional anhaxmonic trap （i.e., harmonic plus quartic trap） are investigated. By using the variational method, the influence of the three-body interaction and the anharmonicity on the stability axe discussed in detail. It is found that the anhaxmonicity of the trap and the three-body interaction have significant effect on the stability and collective excitations of the system.     

Excitation Spectrum and Momentum Distribution of Bose-Hubbard Model with On-site Two-and Three-Body Interaction

An effective action for Bose-Hubbard model with two-and three-body on-site interaction in a square optical lattice is derived in the frame of a strong-coupling approach developed by Sengupta and Dupuis.From this effective action,superfluid-Mott insulator(MI) phase transition,excitation spectrum and momentum distribution for two phases are calculated by taking into account Gaussian fluctuation about the saddle-point approximation.In addition the effects of three-body interaction are also discussed.     

Stability of Three-Body Coulomb Systems with J = 1 in the Oscillator Representation

The oscillator representation is applied to calculate the energy spectrum of three-body Coulomb systems with total angular momentum ^J. For three-body Coulomb systems with J = 1 and arbitrary masses the region of stability is determined. For the systems (A ⁺ A ⁻ e ⁻), (pe ⁻ C ⁺), (pB ⁻ e ⁻), and (D ⁺ e ⁻ e ⁺), the values of the critical masses of the particles A, B, C, and D are obtained as m _A = 2.22m _e , m _B = 1.49m _e , m _C = 2.11m _e and m _D = 4.15m _e . Received November 6, 1995; received December 4, 1995; accepted for publication January 22, 1996     

Exact Solution of a Charge-Asymmetric Two-Dimensional Coulomb Gas

The model under consideration is an asymmetric two-dimensional Coulomb gas of positively (q ₁=+1) and negatively (q ₂=–1/2) charged pointlike particles, interacting via a logarithmic potential. This continuous system is stable against collapse of positive-negative pairs of charges for the dimensionless coupling constant (inverse temperature) <4. The mapping of the Coulomb gas is made onto the complex Bullough–Dodd model, and recent results about that integrable 2D field theory are used. The mapping provides the full thermodynamics (the free energy, the internal energy, the specific heat) and the large-distance asymptotics of the particle correlation functions, in the whole stability regime of the plasma. The results are checked by a small- expansion and close to the collapse =4 point. The comparison is made with the exactly solvable symmetric version of the model (q ₁=+1,q ₂=–1), and some fundamental changes in statistics caused by the charge asymmetry are pointed out.     

CHHE-MRT Method and Its Application in Three-Body Problem

Based on "Hybrid Method" by Dzhibuti,a CHHE-MRT method is suggested for threebody problem,which overcomes the difficulty of infinite integral of oscillatory Bassel functions in hybrid method,and enables us to study the bound states and scattering states of three-body problem by using Gauss,Exponential and Yukawa potential.     

非对易相空间中角动量的分裂

非对易空间效应是一种在弦尺度下出现的物理效应. 本文首先介绍了在Schwinger表象中角动量的3个分量用产生--消灭算符的表示形式, 接着讨论了非对易相空间的量子力学代数; 然后用对易空间谐振子的产生-消灭算符表示出了在非对易情况下的角动量; 最后讨论了非对易相空间中角动量的分裂.     

Quantum Monte Carlo Simulations in Momentum Space

Quantum Monte Carlo(QMC)methods are power-ful numerical tools that can simulate quantum many-body problems with strong interactions among par-ticles.Among them,...