Faddeev approach to the three-body problem in total-angular-momentum representation

For a system of three charged particles the Faddeev equations are derived in the total-angular-momentum representation. They have the form of coupled sets of partial differential equations in three-dimensional space and can be used to develop new efficient numerical procedures to tackle the three-body Coulomb problem. The asymptotic conditions at large distances corresponding both to binary scattering and bound-state problems are presented. The behaviour of the Faddeev components near the triple and double collision points is studied.     

One family of 13315 stable periodic orbits of non-hierarchical unequal-mass triple systems

The three-body problem can be traced back to Newton in 1687,but it is still an open question today.Note that only a few periodic orbits of three-body systems were found in 300 years after Newton mentioned this famous problem.Although triple systems are common in astronomy,practically all observed periodic triple systems are hierarchical(similar to the Sun,Earth and Moon).It has traditionally been believed that non-hierarchical triple systems would be unstable and thus should disintegrate into a stable binary system and a single star,and consequently stable periodic orbits of non-hierarchical triple systems have been expected to be rather scarce.However,we report here one family of 135445 periodic orbits of non-hierarchical triple systems with unequal masses;13315 among them are stable.Compared with the narrow mass range(only 10-5)in which stable"Figure-eight"periodic orbits of three-body systems exist,our newly found stable periodic orbits have fairly large mass region.We find that many of these numerically found stable non-hierarchical periodic orbits have mass ratios close to those of hierarchical triple systems that have been measured with astronomical observations.This implies that these stable periodic orbits of non-hierarchical triple systems with distinctly unequal masses quite possibly can be observed in practice.Our investigation also suggests that there should exist an infinite number of stable periodic orbits of non-hierarchical triple systems with distinctly unequal masses.Note that our approach has general meaning:in a similar way,every known family of periodic orbits of three-body systems with two or three equal masses can be used as a starting point to generate thousands of new periodic orbits of triple systems with distinctly unequal masses.     

Scattering length scaling laws for ultracold three-body collisions

We present a simple and unifying picture that provides the energy and scattering length dependence for all inelastic three-body collision rates in the ultracold regime for three-body systems with short-range two-body interactions. Here, we present the scaling laws for vibrational relaxation, three-body recombination, and collision-induced dissociation for systems that support s-wave two-body collisions. These systems include three identical bosons, two identical bosons, and two identical fermions. Our approach reproduces all previous results, predicts several others, and gives the general form of the scaling laws in all cases.     

Numerical experiments of the planar equal-mass three-body problem: the effects of rotation

The planar three-body problem with angular momentum is numerically and systematically studied as a generalization of the free-fall problem (i.e., the three-body problem with zero initial velocities). The initial conditions in the configuration space exhaust all possible forms of a triangle, whereas the initial conditions in the momentum space are chosen so that position vectors and momentum vectors are orthogonal. Numerical results are organized according to the value of virial ratio k defined as the ratio of the total kinetic energy to the total potential energy. Final motions are mapped in the initial value space. Several interesting features are found. Among others, binary collision curves seem to spiral into the Lagrange point, and for large k, binary collision curves connect the Lagrange point and the Euler point. The existence of a lunar periodic orbit and a periodic orbit of petal-type is suggested. The number of escape orbits as a function of the escape time is analyzed for different k. The behavior of this number for different time and k shows most remarkably the effects of rotation of triple systems. The number of escape orbits increases exponentially for k相似文献   

Collision Dynamics of Dissipative Matter-Wave Solitons in a Perturbed Optical Lattice

We investigate the stability and collision dynamics of dissipative matter-wave solitons formed in a quasi-onedimensional Bose-Einstein condensate with linear gain and three-body recombination loss perturbed by a weak optical lattice.It is shown that the linear gain can modify the stability of the single dissipative soliton moving in the optical lattice.The collision dynamics of two individual dissipative matter-wave solitons explicitly depend on the linear gain parameter,and they display different dynamical behaviors in both the in-phase and out-of-phase interaction regimes.     

H原子(e,2e)反应中电子角分布的理论研究

使用3C和DS3C模型,计算了不同入射能情形下电子入射离化H原子的三重微分截面,并对截面的结构进行了分析.结果表明:角分布基本上由两个峰组成,即binary峰和recoil峰.两个峰的形状和位置对两个出射电子的能量分配及探测的几何条件十分敏感.更进一步,末态电子与电子的排斥对形成观测到的角分布有显著的贡献,在不同几何条件下,三体相互作用通过不同散射幅的不同权重控制了干涉花样.此外,对直接和交换效应也都进行了研究. 关键词： 角分布 binary峰 recoil峰     

共面不对称条件下Ag+(4p,4d)(e,2e)反应三重微分截面的理论研究

采用扭曲波玻恩近似(DWBA)理论计算了共面不对称几何条件下Ag⁺(4p⁶) 及Ag⁺(4d¹⁰)在不同入射电子能量和散射电子角度下(e,2e)反应的三重微分截面. 散射电子角度为4°, 10°和20°. 计算结果表明, Ag⁺(4p⁶)(e,2e)反应的三重微分截面其binary峰峰位或劈裂峰的谷位与动量转移方向有较大差别, 这可能是由于一种两次两体碰撞造成的. 另外, 还发现Ag⁺(4p⁶)(e,2e)反应三重微分截面的binary峰出现了反常劈裂现象, 这表明离子靶内壳层电离(e,2e)反应过程较外壳层更为复杂.对Ag⁺(4p⁶)及Ag⁺(4d¹⁰), 除binary峰和recoil峰以外, 在其他敲出电子角度出现了新的峰, 本文用几种两次两体碰撞过程对这些新的峰进行了解释.     

The (e, 2e) triple differential cross sections of Cu+ (3p) in coplanar asymmetric geometry

The three-body distorted-wave Born approximation has been used to calculate the (e,2e) triple differential cross sections (TDCSs) of Cu+ (3p) in different kinematical variables in coplanar asymmetric geometry.The angles 4,10 and 20 were selected as the scattering electron angles.Under high incident energy (≥ 500 eV) and high asymmetric detection energy,the binary peaks showed abnormal splits.Such abnormal splits have not been observed in atomic target and outer valence orbitals of ionic target,which indicates that an (e,2e) process for inner valence orbitals of ionic target would be more complicated than outer valence orbitals.Furthermore,some pronounced peaks appeared at certain ejected angles.We considered that these pronounced peaks are probably related to one kind of double-binary collision.     

Tuning p-wave interactions in an ultracold Fermi gas of atoms

We have measured a p-wave Feshbach resonance in a single-component, ultracold Fermi gas of 40K atoms. We have used this resonance to enhance the normally suppressed p-wave collision cross section to values larger than the background s-wave cross section between 40K atoms in different spin states. In addition to the modification of two-body elastic processes, the resonance dramatically enhances three-body inelastic collisional loss.     

A first estimate of triply heavy baryon masses from the pNRQCD perturbative static potential

Within pNRQCD we compute the masses of spin-averaged triply heavy baryons using the now-available NNLO pNRQCD potentials and three-body variational approach. We focus in particular on the role of the purely three-body interaction in perturbation theory. This we find to be reasonably small and of the order 25 MeV. Our prediction for the Ω _ccc baryon mass is 4900(250) MeV in keeping with other approaches. We propose to search for this hitherto unobserved state at B factories by examining the end point of the recoil spectrum against triple charm.     

One-dimensional Boltzmann equation with a three-body collision term

It is shown that a linearized one-dimensional Boltzmann equation with a certain simple three-body collision term is trivially soluable.     

Lambdac enhancement from strongly coupled quark-gluon plasma

We propose the enhancement of Lambdac as a novel quark-gluon plasma signal in heavy ion collisions at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider. Assuming a stable bound diquark state in the strongly coupled quark-gluon plasma near the critical temperature, we argue that the direct two-body collision between a c quark and a [ud] diquark would lead to an enhanced Lambdac production in comparison with the normal three-body collision among independent c, u, and d quarks. In the coalescence model, we find that the Lambdac/D yield ratio is enhanced substantially due to the diquark correlation.     

Few-body Decay and Recombination in Nuclear Astrophysics

Three-body continuum problems are investigated for light nuclei of astrophysical relevance. We focus on three-body decays of resonances or recombination via resonances or the continuum background. The concepts of widths, decay mechanisms and dynamic evolution are discussed. We also discuss results for the triple ?? decay in connection with 2⁺ resonances and density and temperature dependence rates of recombination into light nuclei from ??-particles and neutrons.     

低能电子碰撞He+(e,2e)反应绝对三重微分截面的理论研究

利用Berakdar和Briggs对BBK波函数Sommerfeld参数的修正结果，即考虑第三个粒子存在对两个粒子间相互作用的影响，考虑了入射道的库仑相互作用及出射粒子的交换对称性，计算了在共面等能分配几何情况下低能电子碰撞He⁺(e,2e)反应绝对三重微分截面.结果表明，入射道库仑场对较低的入射能量及小的碰撞参数的三重微分截面影响较大. 关键词：     

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     

Dynamic evolution of triple hierarchical stellar systems

Dynamic evolution of triple hierarchical stellar systems using higher-order perturbations in the framework of a restricted three-body problem was performed. Hierarchical triple systems consist of a relatively close pair and a satellite on a distant orbit. These systems are thought to be stable on cosmological timescales, in contrast to systems where all the distances are comparable. We obtain a solution for intermediate motion, where the mean motions of both components have secular evolutionary terms. Perturbations from the distant component slow down the rotation of the close pair, while its own mean motion secularly increases due to interaction with the binary component. Perturbations are small but may change the configuration of the system of cosmological timescales. The probability that such systems become unstable is high.     

Generalizations of the Fock and Kato expansions to systems of three quantum particles

The Schrödinger and Faddeev approaches to the solution of the problem of three quantum particles in the configuration space are used and developed in this review. Various methods for construction of generalizations of the Fock and Kato expansions to central or noncentral pair interactions of a more general type than Coulomb potentials are described and compared within the approaches in question. Emphasis is placed on the use of these generalizations for quantum-mechanical and numerical analysis of the structure of three-body wave functions and their Faddeev components near the two-body and three-body collision points and in the limit of the linear three-body configuration.     

Electron—impact ionization of Li^＋（ls^2） in the coplanar equal energy—sharing geometry

In this paper, the triple differential cross section for the low-energy electron impact ionization of the Li⁺ ion is considered in the coplanar equal energy-sharing kinematics at an incident energy of 114.083 eV. The emergence of structures in the calculated cross sections is explained in terms of isolated two-body final-state interactions and three-body coupling. The cross section shows two peaks originating from ′classical′ is determined by two-body final-state interactions. In addition, it is demonstrated that the signature of three-body interactions is carried by the magnitude and ratio of these two peaks. The direct and exchange amplitudes are also considered.     

A unitary model for three-body collisions

A connected 3 → 3 formalism for three-body collision processes is reduced to a hierarchy of three on-energy-shell integral equations and one off-energy-shell integral equation. Only the on-energy-shell equations, which involve only on-energy-shell three-body and two-body amplitudes, need be solved exactly in order to obtain elastic and break-up amplitudes satisfying the unitarity constraints exactly. Applied to n-d break-up, the on-energy-shell equations ensure that the n-d initial-state interaction, the nucleon-nucleon final-state interactions, and more complicated 3 → 3 processes are correctly described. After angular momentum analysis the on-energy-shell equations are one-dimensional integral equations, even in the case of local two-body potentials. This unitary model provides a practical scheme for calculating approximate three-body elastic and break-up amplitudes when two-body local potentials are used to describe the two-body subsystems.