Immersing method for the multichannel scattering problem

We propose a method for solution of the multichannel scattering problem. In particular, the scattering problem is considered when a particle makes a finite motion in the transverse direction of the scattering. In this case the scattering becomes multichannel, which is connected with the presence of discrete energy levels of the transverse movement of the particle. For the case of two-channel scattering, the problem is formulated up to the end. A method for determination of scattering amplitudes for the potential V=V(x,y) is proposed.     

Multichannel scattering of a particle in a quantum wire of cylindrical symmetry

The Schrödinger equation for a scattering particle in a quantum wire is considered. We discuss two geometrical forms of cross-section of the wire: the rectangular section and the cylindrical one. It is shown that scattering of the particle on an arbitrary potential V = V (x, y, z,), given in the wire, can be considered as a multichannel scattering, where the index of the channel coincides with the index which determines energy levels of the confined transverse motion of the particle. A method for determination of the amplitudes of transmission T _i and reflection R _i in the case of multichannel scattering is proposed. The case of two-channel scattering is considered in detail and a method for determination of the scattering amplitudes T ₁, T ₂ and R ₁, R ₂ is proposed.     

Practical relativistic three-particle theory with arbitrary particle interactions

Relativistic three-particle equations are established by the rules of Blankenbecler and Sugar, which put the intermediate particles on the mass shell. By use of the Wightman-Gåding momenta we preserve the correct cluster properties, time-reversal invariance and avoid a spurious s = 0 singularity. A reduction to effective multichannel two-particle equations which is not restricted to separble potentials is discussed. Our approach admits the systematical application of perturbation theory to relativistic composite particle scattering problems.     

Eigenvectors of the multichannel scattering matrix at resonance energy values

Explicit representations for the T matrix and the scattering matrix analytically continued to unphysical energy sheets in a multichannel problem featuring binary channels are discussed. From these representations, it follows that a resonance on a given unphysical sheet arises at the (complex) energy value for which the appropriately truncated scattering matrix considered on the physical sheet has zero eigenvalue. It is shown that the channel components of that eigenvector of the truncated scattering matrix which corresponds to zero eigenvalue at a resonance energy value have the meaning of breakup amplitudes for the respective resonance state of the multichannel system being considered.     

Pomeron structure function and diffraction dissociation of virtual photons in perturbative QCD

We study scaling properties of the diffraction dissociation of virtual photons in a deep inelastic scattering. We concentrate on the total diffraction dissociation rate, diffraction excitation mass spectrum and the pomeron structure function to the lowest order in perturbative QCD. We calculate the valence structure function and the strangeness and charm content of the pomeron and estimate the ocean structure function using the pomeron factorization property. We find that quarks carry ≈ 10% of pomeron's momentum. Differential cross section of the (virtual) photon-pomeron scattering is found to exhibit features typical of the hadronic two-body reactions, supporting a treatment of the Pomeron as a particle, whereas the flavor dependence of structure functions does not support the particle treatment of the pomeron. Diffraction dissociation of photons is predicted to make ≈ 15% of the total deep inelastic scattering rate at smallx and largeQ ². Detailed predictions for the mass spectrum and angular distribution of jets produced on the valence component of the pomeron are presented.     

Microscopic R-matrix theory in a generator coordinate basis: (III). Multi-channel scattering

The microscopic R-matrix theory presented in two previous papers is extended to the multichannel scattering case. An antisymmetrized wave function is built in the two-centre harmonic oscillator model. This wave function is proved to be equivalent to the resonating group one even if the nuclei have non-zero spin. The method only requires the calculation of numerical values of matrix elements between Slater determinants. The microscopic R-matrix theory may be applied to study both reactions and inelastic scattering.     

Relationship between cross section and matrix normalization of polarized radiation scattering

A simple relationship between the total scattering cross section and the normalizing constant of the scattering matrix for the general case of an arbitrary scattering particle and elliptically polarized incident radiation is obtained. The polarized radiation is described by the Stokes parameters I, Q, U, V. The obtained relationship is a consequence of two forms of energy conservation. The first one is in terms of the total scattering cross section. The other one involves the normalizing constant of the scattering matrix. The obtained relationship contains dimensionless integrals of the radiation scattered over all directions of scattering. The integrals depend on the elements of the first row of the scattering matrix and on the relative values of the Stokes parameters of the incident radiation. In the case of cross section, the incident radiation is assumed to be a plane wave. In the case of normalization constant, the incident radiation is assumed to be a convergent beam. The possible dependence of the scattering integrals on specificities of the particle illumination is taken into account in the obtained relationship. The relationship may be helpful in the various cases. So, the relationship allows one to determine any of the two characteristics of the scattering process under investigation, cross section or normalizing constant, via the other one. The relationship can be used for obtaining the scattering integrals and for analyzing the influence of the incident radiation polarization on cross section and normalizing constant.     

Scattering of a Light Particle by a System of Harmonic Oscillators

We discuss the asymptotic wave function of a quantum system in ?³ composed by heavy and light particles, in the case where the light particles are in scattering states and no interaction is assumed among particles of the same kind. We first review a recent result concerning the case of K heavy and N light particles, where the one-particle potential acting on each heavy particle decays at infinity. Then we consider the case of one light particle interacting with a system of harmonic oscillators and prove the same kind of result following, with some modification, the proof of the previous case. A possible application to the analysis of the scattering of a light particle from condensed matter is also outlined.     

Investigation of scattering processes in quantum few-body systems involving long-range interaction by the complex-rotation method

The complex-rotation method adapted to solving the multichannel scattering problem in the two-body system where the interaction potential contains the long-range Coulomb components is described. The scattering problem is reformulated as the problem of solving a nonhomogeneous Schrödinger equation in which the nonhomogeneous term involves a Coulomb potential cut off at large distances. The incident wave appearing in the nonhomogeneous term is a solution of the Schrödinger equation with longrange Coulomb interaction. This formulation is free from approximations associated with a direct cutoff of Coulomb interaction at large distances. The efficiency of this formalism is demonstrated by considering the example of solving scattering problems in the α-α and p-p systems.     

Scattering of Hawking photons as a barrier to particle absorption by black holes

Electromagnetic scattering interactions between photons emanating from a Schwarzschild black hole and an incident charged particle should generate a repulsive force between the particle and black hole. The net scattering cross-section is calculated here as a function of the mass M of the black hole and the mass m of the particle for scenarios in which the particle is point-like and initially stationary, with proper energy ε=m, at some location far from the black hole. It follows from comparing the repulsive scattering force to the corresponding gravitational force that, in order for the particle to be drawn to the black hole, ε/Tbh must be greater than a certain lower bound that is of the order ¹⁰−3 for spin-1/2 or spin-0 particles with unit-charge. Although the scattering restriction is weaker than the requirement ε/Tbh?1 obtained independently from field-theoretic and thermodynamic treatments, the recurrence of a lower bound on the Boltzmann factor ε/Tbh in limitations on particle absorption suggests a physical unity whose nature is fundamentally thermodynamic.     

Multichannel treatment of the (e,H) collision problem using the quasiparticle method

The (e, H) collision problem is treated using the multichannel quasiparticle method recently introduced by Grassberger and Sandhas. We derive single variable integral equations for the singlet and triplet transition amplitudes valid for scattering energies up toE≈8 eV and especially calculate the scattering lengths which are in good agreement with previous results found by variational methods.     

Boundary condition model for diffractive elastic scattering

Diffractive elastic scattering is studied by a boundary condition model that does not utilize a potential model.S-matrix elements are calculated and compared to those found from an optical potential model calculation. The unitarity of the model is related to the boundary condition imposed. A radially ingoing boundary condition is imposed on the wave function at one angle only, at a scattering angle of 180 °. This condition is required to hold in the vicinity of the nuclear radius, but not for all radii. Elastic scattering peaks at forward and backward angles are reproduced and discussed. The model is applied to composite particle scattering above the Coulomb barrier.     

Strong dependence of multichannel ballistic transport on the geometric symmetry

Ballistic electron transport in Aharonov–Bohm-type ring structures is investigated where the single-channel problem is nontrivially extended to the multichannel one in which the important interchannel scattering effect is considered. It is found that theS-matrix of a ring structure should reflect the geometric symmetry if the interchannel scattering effect is properly accounted for and that the symmetry relationships of theS-matrix plays a crucial role in the conductance oscillation behavior in ballistic two-dimensional rings. The magnetostatic as well as the electrostatic Aharonov–Bohm effects are studied for two ring structures of different symmetry.     

Amplitudes of multichannel scattering on the barrier with a constant height in the scattering direction

The immersing method is applied to solve the N-channel scattering problem. In particular, we consider the particle scattering on a multidimensional potential barrier, which is constant in the scattering direction and arbitrary in the lateral direction. For this case the scattering amplitudes t _m and r _m (m = 1, 2, …, N) are determined. Transition from the obtained formulas to the case of thin potential is performed. For this case analytical expressions of transmission amplitudes t _m and reflection amplitudes r _m are obtained. We show that the product of transmission and reflection amplitudes in the channel m does not depend on the scattering channel. It is assumed that the scattering particle falls on the potential with the longitudinal wave vector k _l corresponding to the channel l.     

Transfer-matrix for the multichannel scattering problem

A transfer-matrix for the multichannel scattering problem is obtained. The elements of this matrix are expressed in terms of transmission and reflection amplitudes. On the basis of the matrix for a system of N localized and nonoverlapped scattering centers the recurrent equations for the transfermatrix elements are derived and the initial conditions are defined.     

Equation for spectrum of electron states in a potential well with uneven bottom

A method is proposed to determine the spectrum of bound states of electron making a stationary motion in a three-dimensional quantum well with uneven bottom. It is shown that the problem of finding the energy eigenvalues is reduced to investigation of multichannel scattering of the particle from the internal part of potential. Equation for the energy, depending on the transmission and reflection amplitudes, is obtained. For illustration of application of the method to concrete systems, a three-dimensional asymmetric quantum well with uneven bottom is considered.     

Light scattering in a layer of correlatively arranged optically soft particles

The light scattering by an ensemble of monodisperse spatially correlated optically soft spherical particles is studied in the interference approximation. A model of the interaction of particles is proposed in which the spatial correlation between particles is determined by a radius R _c exceeding the particle radius R _p. The radial distribution function is calculated in the Percus-Yevick approximation for hard spheres of the radius R _c. To simulate the radiation scattering from an individual particle of the radius R _p, the Mie equations are used. It is shown that, in a medium of correlated small nonabsorbing particles of the radius R _c > R _p, an abnormal wavelength dependence of the refractive index is possible at a low volume concentration of particles. The results obtained explain some experimentally observed features of the scattering in sodium borosilicate glasses with a small concentration of scattering centers.     

Effect of instrumental particle sizing resolution on the modelling of aerosol radiative parameters

A more realistic estimation of the scattering and hemispheric backscattering coefficients, σ_sp and σ_bsp, and their respective optical cross section, C_sca and C_bk, of aerosol particles is presented on the basis of the exact resolution of the width of the size bins of the particle counter instruments when size distribution measurements are used, and, with the exact optical detector instruments ability. The scattering and hemispheric backscattering cross sections, C_sca and C_bk, of the particles are averaged over the full size bins of the particle counter instrument, while these quantities are usually estimated only on the value of the mean geometric diameter of each size bin. Six instruments, the APS, ASASP-X, DMPS, FSSP-100, ELPI, and SMPS frequently used in particle size distribution measurements are reviewed, for spherical sea-salt particles at a wavelength λ=0.55 μm. The comparison using the conventional geometric mean diameter versus the use of the full size bin leads to large amount of errors for the optical cross section with non-negligible effects on their respective optical coefficients. The maximal accuracy expected for these optical quantities depend on the particle diameter as well as on the channel width of the instruments, and are also function of the angular detector probe used to measure them.