Three-body treatment of Coulomb effects in the problem of long-range effective interactions

The problem of Coulomb scattering of a charged particle by a two-particle bound system, consisting of a charged and a neutral particle, is investigated in the integral-equation approach of rigorous three-body theory. The bound state of the two particles is provided by a short-range interaction chosen in the simplest form using anS-wave separable potential. The integral equation defining the effective potential of the interaction of the charged particle with the two-particle bound system is formulated. It is shown that the multiple Coulomb scattering of the involved charged particles generates a sequence of long-range terms in the effective potential. It turns out that the long-range effects of Coulomb scattering are partly cancelled. As a result the polarization potential does not contain the longest-ranged terms which decrease at large distances as ^–2 and ^–3.     

自旋梯可积模型的研究

通过对自旋梯可积模型的研究,求出该模型的能量本征值和两体散射矩阵.用可积模型中的坐标Bethe Ansatz方法,首先由薛定谔方程求得能量的本征方程.设定波函数的具体形式,求出本征能量,然后利用能量本征方程和波函数的连续性求出两体散射矩阵.求出单粒子、双粒子和N₀个粒子的本征能量,同时求得粒子的两体散射矩阵.自旋梯可积模型的本征能量和两体散射矩阵可通过Bethe Ansatz的方法求得.     

Two-particle scattering matrix of two interacting mesoscopic conductors

We consider two quantum coherent conductors interacting weakly via long range Coulomb forces. We describe the interaction in terms of two-particle collisions described by a two-particle scattering matrix. As an example we determine the transmission probability and correlations in a two-particle scattering experiment and find that the results can be expressed in terms of the density-of-states matrices of the noninteracting scatterers.     

Two-body T-matrix continued off the energy shell

A generalized parametrization scheme, which treats both half-shell and off-shell scattering on equal footing, is derived for the two-particle transition operator. The appropriate theory in respect of this is developed by using a wave function approach to off-shell scattering and the computational procedure to be followed is demonstrated by means of a model calculation.     

The three-boson stimulated scattering behaviour

We show the resonance behaviour of three-boson “stimulated scattering” (TBSS) which was observed recently. In a sufficiently cold boson gas the zero momentum particles accumulation should take place as a result of TBSS alone without any collective effects and for any non-bonding two-particle interaction potential.     

A temperature-dependent upper bound on partial wave contributions to the second virial coefficient in the weak coupling limit

A modified form of the Uhlenbeck-Beth representation for the second virial coefficient is used, together with the Fredholm theory of two-particle scattering, to obtain an upper bound on the partial wave contribution to the coefficient which holds if the intermolecular potential is sufficiently weak.     

Scattering of electrons from an interacting region

We address the problem of transmission of electrons between two noninteracting leads through a region where they interact (quantum dot). We use a model of spinless electrons hopping on a one-dimensional lattice and with an interaction on a single bond. We show that all two-particle scattering states can be found exactly. Comparisons are made with numerical results on the time evolution of a two-particle wave packet, and several interesting features are found. For N particles, the scattering state is obtained within a two-particle scattering approximation. For a dot connected to Fermi seas at different chemical potentials, we find an expression for the change in the Landauer current resulting from the interactions on the dot. We end with some comments on the case of spin-1/2 electrons.     

Rearrangement Collisions between Four Identical Particles as a Four-Body Problem

Nuclear reactions between composite particles with rearrangement processes are considered. The cluster model is used in describing the structure of the nuclei. With this structure we have in the initial channel as well as in the final channel, four interacting particles. These reactions are studied as a four-body problem. The scattering amplitudes are approximated by using a separable expansion for the separable potential model. The four-body equations are reduced to integral equations in the form of exact effective two-particle Lippmann-Schwinger equations. These equations are solved by standard methods in a form suitable for numerical calculations. The present four-body treatment is applied calculating the differential cross-sections for different scattering and transfer nuclear reactions. Distorted wave Born approximation calculations are used in calculating the angular distributions. The present theoretical calculations are in good agreement with the experimental angular distributions.     

Two-particle scattering on the lattice: Phase shifts,spin-orbit coupling,and mixing angles

We determine two-particle scattering phase shifts and mixing angles for quantum theories defined with lattice regularization. The method is suitable for any non-relativistic effective theory of point particles on the lattice. In the center-of-mass frame of the two-particle system we impose a hard spherical wall at some fixed large radius. For channels without partial-wave mixing the partial-wave phase shifts are determined from the energies of the nearly spherical standing waves. For channels with partial-wave mixing further information is extracted by decomposing the standing wave at the wall boundary into spherical harmonics, and we solve coupled-channels equations to extract the phase shifts and mixing angles. The method is illustrated and tested by computing phase shifts and mixing angles on the lattice for spin-1/2 particles with an attractive Gaussian potential containing both central and tensor force parts.     

Entanglement interferometry for precision measurement of atomic scattering properties

We report on a matter wave interferometer realized with entangled pairs of trapped 87Rb atoms. Each pair of atoms is confined at a single site of an optical lattice potential. The interferometer is realized by first creating a coherent spin superposition of the two atoms and then tuning the interstate scattering length via a Feshbach resonance. The selective change of the interstate scattering length leads to an entanglement dynamics of the two-particle state that can be detected in a Ramsey interference experiment. This entanglement dynamics is employed for a precision measurement of atomic interaction parameters. Furthermore, the interferometer allows us to separate lattice sites with one or two atoms in a nondestructive way.     

Elasticity,factorization and S-matrices in (1+1)-dimensions

The hypothesis of vanishing particle-production, non-vanishing backward scattering and a factorisation condition on the S-matrix allow an infinite arbitrariness in the two-particle scattering amplitudes. The general form is explicitly obtained.     

Ladder approximation of the equation of state for degenerate fermi systems

The equation of state is discussed for a system of degenerate fermions. The formation of bound states is allowed for; the latter may exhibit the Bose-Einstein condensation. A complex representation is given which includes bound and scattering two-particle states as well. Different (generalized) representations in terms of scattering quantities are given for the continuum contribution.     

Two-particle correlations and the origin of intermittency in muon-nucleon interactions

The relation between two-particle correlations, in particular the Bose-Einstein effect, and the intermittency signal is investigated in muon-nucleon scattering at 280 GeV using data of the European Muon Collaboration. From a comparison of the second factorial moments for unlike and negative charges with each other and with the predictions of the Lund model it is concluded that the observed intermittent behaviour is due to Bose-Einstein interference.     

Polariton-polariton kinematic interaction modulation and kinematic bipolaritons in organic microcavities

We study polariton-polariton kinematic interactions in organic microcavities. Using the Agranovich-Toshich transformation, to transform the Frenkel excitons from Paulions into Bosons, the exciton-exciton kinematic interaction is derived. In the strong coupling regime, the polariton excitonic part results in the polariton-polariton kinematic interaction. The scattering amplitude is calculated and the effective potential is obtained for a scattering between two free polaritons. The effective potential can be modulated by changing the exciton-cavity photon detuning, and we show the crossover of the effective potential from attractive into repulsive one. A pole in the two-particle Green's function is the signature of the formation of polariton bound state, i.e. bipolariton. Due to the smallness of the polariton effective mass, the obtained bound state is very shallow and appears below the minimum of the lower polariton branch, and falls inside the natural bandwidth of the polariton branch.     

Unitarity relation for deep inelastic scattering

Saturating the multiparticle states in the unitarity relation for virtual Compton scattering by two-particle states consisting of an infinite set of high mass vector mesons and a nucleon leads to a non-linear integral equation the solution of which determines the behaviour in the scaling limit and the non-forward scaling functions for deep inelastic scattering.     

On the anomalous behaviour of the doublet pd phase shift caused by a polarization potential

An estimate of pd scattering polarization effects is given in the framework of a simple two-particle model. The S-wave effective-range function is found to be discontinuous for energies E ∼ 2.3 keV.     

<Emphasis Type="Italic">PT</Emphasis> symmetry and Hermitian Hamiltonian in the local supercritical pomeron model

The local reggeon field theory is studied perturbatively taking advantage of the PT symmetry in the Hamiltonian formulation. In the lowest non-trivial order we show that the pomeron interactions renormalize the slope. In the same order we find a non-local pair potential acting between pomerons, which has a singular structure. However, the analysis of the scattering operator shows that at small coupling constant bound states do not appear so that the two-particle spectrum is not changed.     

Quantum-statistical mechanics of a system of charged particles at high temperatures

If a quantum-mechanical potential is introduced the calculation of the quantummechanical binary distribution function for a system with Coulomb interaction is reduced to the well-known mathematical formalism of classical statistical mechanics in the case ofnλ³?1 (λ being the thermal wavelength). The two-particle quantummechanical potential is determined by the two-particle Slater sum. In this paper we calculated the two-particle Slater sum using an expansion according toe ² and the resolvent formalism. From the binary distribution function the correlation energy and the free energy as well were determined up to ordere ⁶. Symmetry effects were taken into account.     

Separability of a two-particle t-matrix in the case of the three-body problem

A factorization is proposed in this article of a two-particle t-matrix for the problem of three bodies, the scattering phase and the half-mass amplitude being described exactly for any approximation order. The uniform convergence of the approximation process is also proved.