KN Scattering in 3D Formulation

KN scattering is formulated in three-dimensional (3D) momentum space. A direct product of the relative-momentum state and the spin state is used as the basis state. The spin quantization axis is chosen along the z-axis. The interaction for the KN system is assumed to take the Yukawa-type. It consists of two terms, the central and the spin-orbit one. Calculations for the cross section based on this technique are shown, as well as comparison with the standard partial-wave calculations.     

Single Impurity Scattering in One-Channel Spinless Luttinger Liquid

Using bosonization and phase shift representation, we rigorously treat backward scattering of electrons on an impurity in a one-dimensional interacting electronic system, and demonstrate that correlation exponents of the system depend on a phase shift induced by the backward scattering, and usual exponent duality of the correlation functions between ultraviolet and infrared fixed points comes from the phase shift dependence of the correlation exponents. Finally, we study the tunnelling conductance of the system at zero temperature and obtain a modified Landauer-Bütiker formula.     

Scattering of Two Spin-Half Particles in a Three-Dimensional Approach

Scattering of two spin- ${\frac{1}{2}}$ particles is formulated in a three-dimensional approach based on a simple three-dimensional momentum-spin basis. Both cases of identical and nonidentical particles are considered. The azimuthal behaviour of the potential and of the T-matrix elements leads to a set of integral equations for the T-matrix elements in two variables, i.e. the momentum magnitude and the scattering angle. Observables can be directly calculated from these T-matrix elements. Some symmetry relations for the T-matrix elements reduce the number of equations to be solved.     

Semi-Relativistic Two-Body States of Spinless Particles with a Scalar-Type Interaction Potential

A semi-relativistic quantum approximation for mutual scalar interaction potentials is outlined and discussed.Equations are consistent with two-body Dirac equations for bound states of zero total angular momentum. Two-body effects near the non-relativistic limit for a linear scalar potential is studied in some detail.     

Semi-Relativistic Reflection and Transmission Coefficients for Two Spinless Particles Separated by a Rectangular-Shaped Potential Barrier

A generalized Schrödinger approximation, due to Ikhdair & Sever, of the semi-relativistic two-body problem with a rectangular barrier in (1+1) dimensions is compared with exact computations. Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers. The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |ε-V₀|<2μ c², where μ is the reduced mass, ε the scattering energy, and V₀ the barrier top energy. The approximate wave numbers are less accurate.     

Relativistic Treatment of Spinless Particles Subject to a Tietz-Wei Oscillator

The bound state solutions of the relativistic Klein-Gordon equation with the Tietz-Wei diatomic molecular potential are presented for the s wave. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived.     

Relativistic Treatment of Spinless Particles Subject to a Tietz-Wei Oscillator

The bound state solutions of the relativistic Klein-Gordon equation with the Tietz-Wei diatomic molecular potential are presented for the s wave. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived.     

Low Energy D(p, p)D Elastic Scattering Including Coulomb Force

The motivation of this paper is to obtain the three-body amplitudes for the Coulomb potential plus a nuclear force in momentum space. Not only the two-body off-shell nuclear amplitude but also the two-body off-shell Coulomb amplitude is important in the three-body calculation. For calculating the Coulomb amplitude, the modified Coulomb potential whose Fourier transformation is analytically equivalent to the pure configuration space Coulomb potential, is introduced. In addition, the decisive screening range parameter is also utilized instead of the screening range. The modified Coulomb potential plus the parameter is called decisive modified Coulomb potential. The three-body proton-deuteron elastic scattering is calculated by using the proper two-body off-shell amplitude for the decisive modified Coulomb potential.     

Relativistic Treatment of Spinless Particles Subject to a Rotating Deng-Fan Oscillator

The bound state solutions of the Klein-Gordon equation with the rotating Deng-Fan molecular potential are presented by using a proper approximation to the centrifugal term within the framework of equal scalar and vector Deng-Fan potentials. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived.     

Relativistic Treatment of Spinless Particles Subject to a q-Deformed Morse Potential

The approximate analytical solutions of the Klein-Gordon equation with equal scalar and vector q-deformed Morse potential are presented for arbitrary e-states by using Laplace integral transform. The energy eigenvalues and corresponding wave functions are obtained for n and e values. In this study, in the non-relativistic limit c→∞, it has been also provided that the energy eigenfunctions for Klein-Gordon system turn into those for Schrdinger one.     

Classical Scattering in the Covariant Two-Body Coulomb Potential

The problem of two relativistically-moving pointlike particles of constant mass is undertaken in an arbitrary Lorentz frame using the classical Lagrangian mechanics of Stückelberg, Horwitz, and Piron. The particles are assumed to interact at events along their world lines at a common world time, an invariant dynamical parameter which is not in general synchronous with the particle proper time. The Lorentz-scalar interaction is assumed to be the Coulomb potential (i.e., the inverse square spacetime potential) of the spacetime event separation. The classical orbit equations are found in 1 + 1 spacetime dimensions in the hyperbolic angle coordinates for the reduced problem. The solutions to the reduced motion in these coordinates are the spacetime generalizations of the nonrelativistic Kepler solutions. and they introduce an invariant eccentricity which is a function of other known constants of the motion for the reduced problem. Solutions compatible with physical scattering are obtained by the assumption that the eccentricity is a given function of the ratio of the particle masses.     

Scattering of electrons by a Coulomb center

New results are obtained from which it follows that systematic use of the one-to-one correspondence between a physical quantity and an operator, which permits the existence of a non-negative quantum distribution function, leads to an effective smearing of the potential and to the appearance of a form factor, i.e., to the existence of structure in the scattering center.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 16–19, April, 1980.     

Coulomb Scattering in the Massless Nelson Model I. Foundations of Two-Electron Scattering

We construct two-electron scattering states and verify their tensor product structure in the infrared-regular massless Nelson model. The proof follows the lines of Haag-Ruelle scattering theory: Scattering state approximants are defined with the help of two time-dependent renormalized creation operators of the electrons acting on the vacuum. They depend on the ground state wave functions of the (single-electron) fiber Hamiltonians with infrared cut-off. The convergence of these approximants as t→∞ is shown with the help of Cook’s method combined with a non-stationary phase argument. The removal of the infrared cut-off in the limit t→∞ requires sharp estimates on the derivatives of these ground state wave functions w.r.t. electron and photon momenta, with mild dependence on the infrared cut-off. These key estimates, which carry information about the localization of the electrons in space, are obtained in a companion paper with the help of iterative analytic perturbation theory. Our results hold in the weak coupling regime.     

激光熔覆中球形粒子对激光散射强度的研究

为了研究同轴激光熔覆过程中球形粉末粒子和激光的相互作用,为激光熔覆中激光器和粒子的选择提供一定的理论依据,在进行了一定假设的前提下,应用米氏(Mie)散射理论建立了激光被球形粉末粒子散射的物理模型,应用Mathematica数学软件绘制出了在不同粒子半径和不同激光波长情况下,激光被球形粉末粒子散射后的强度分布图,并对模拟结果进行了分析.研究结果显示:金属粉末粒子的半径和激光的波长是影响激光散射强度分布的重要因素.结果表明:当光学常数q≤30的时候,散射光强在偏离传播方向20.以外还有一个次极大值,且次极大值占总散射光强比例较大,不利于熔池的形成;当光学常数q≥30的时候,散射后的光强主要集中在偏离传播方向5.～6.的小范围内,且在此范围内的散射强度很高,有利于提高激光熔覆效率.     

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.     

Scattering of a low-energy electron in a strong Coulomb field

The low-energy electron scattering cross section in a strong Coulomb field is analyzed theoretically. It is shown that the exact cross section in a wide energy range significantly differs from the results obtained in the first Born approximation and in the nonrelativistic approximation.     

Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities

We study the physics of Dirac fermions in a gapped graphene monolayer containing two Coulomb impurities. For the case of equal impurity charges, we discuss the ground-state energy using the linear combination of atomic orbitals (LCAO) approach. For opposite charges of the Coulomb centers, an electric dipole potential results at large distances. We provide a nonperturbative analysis of the corresponding low-energy scattering problem.