Off-shell effects in the three-nucleon system

The triton binding energy and the neutron-deuteron doublet scattering length have been studied with phase-equivalent rank-2 separable potentials in S-waves. The potentials have been constructed from the phase shifts using the solution of the inverse scattering problem. Large off-shell effects are connected with the appearance of additional nodes in the deuteron or the low-energy singlet wave functions.     

Diffraction of a plane electromagnetic wave at a schwarzschild black hole

Using the technique of Debye potentials a rigorous solution of the diffraction problem is given as a superposition of an incident wave, strongly connected with the Coulomb scattering wave function, and a scattered wave, which is purely outgoing for large distances. The solution fulfils the boundary conditions to be the light of a very distant star and to be purely ingoing at the Schwarzschild horizon. The phase shifts of the partial waves are evaluated in the WBK approximation.     

Potential scattering in the generator Coordinate method

The generator coordinate formulation of the quantum-mechanical scattering problem transforms the solution of a problem in Hilbert space into an equivalent problem in Banach space. The structure of this problem is, however, that of an ill-posed problem. In order to shed some light onto the numerical intricacies, we investigate a number of potential scattering systems. One finds that, notwithstanding the numerical uncertainties of the weight function, excellent results for phase shifts (and scattering solutions) can be obtained.     

Scattering from non-overlapping potentials. I. General formulation

The problem of scattering from an assembly of non-overlapping spherical potentials is solved in partial-wave basis for each of the constituent potentials. The resulting scattering operator is a quotient of two infinite matrices and depends on “on-shell” partial wave amplitudes of the individual potentials. It suggests in general a truncation scheme which essentially considers only those partial waves effective for each collision at the given energy. The multiple-scattering series is recovered and limiting cases of low energy and high energy are considered. Applications to high-energy scattering of elementary particles on nuclei are briefly discussed.     

On long-wave sound scattering by a Rankine vortex: Non-resonant and resonant cases

The well-known two-dimensional problem of sound scattering by a Rankine vortex at small Mach number M is considered. Despite its long history, the solutions obtained by many authors still are not free from serious objections. The common approach to the problem consists in the transformation of governing equations to the d’Alembert equation with right-hand part. It was recently shown [I.V. Belyaev, V.F. Kopiev, On the problem formulation of sound scattering by cylindrical vortex, Acoustical Physics 54(5) (2008) 603-614] that due to the slow decay of the mean velocity field at infinity the convective equation with nonuniform coefficients instead of the d’Alembert equation should be considered, and the incident wave should be excited by a point source placed at a large but finite distance from the vortex instead of specifying an incident plane wave (which is not a solution of the governing equations).Here we use the new formulation of Belyaev and Kopiev to obtain the correct solution for the problem of non-resonant sound scattering, to second order in Mach number M. The partial harmonic expansion approach and the method of matched asymptotic expansions are employed. The scattered field in the region far outside the vortex is determined as the solution of the convective wave equation, and van Dyke's matching principle is used to match the fields inside and outside the vortical region. Finally, resonant scattering is also considered; an O(M²) result is found that unifies earlier solutions in the literature. These problems are considered for the first time.     

Distribution characteristic of scattering field for an ellipsoidal target irradiated by an electromagnetic wave from an arbitrary direction

It is of great importance for engineering applications to obtain the expression of scattering field for an ellipsoidal target irradiated by an electromagnetic wave from an arbitrary direction. Literature relevant to this problem is seldom found. In this paper, the scattering field for an ellipsoidal target is presented by utilizing the scale transformation of electromagnetic field and the rotation of coordinate system, with an electromagnetic wave projecting on the target from an arbitrary direction. The obtained result is in good agreement with the solution available from the literature if we consider the scale factors to be unity. Taking a conducting ellipsoidal target for sample, we perform the partial simulations of the ellipsoidal model and a plant leaf model by choosing different scale factors. The obtained results show that the distribution characteristic of scattering field is sensitively affected by the polarization of the incident wave and varies not much with the incident wave angle but changes with the observation point. At some points the scattering energy arrives at its maximum.     

Description of two-proton radioactivity on the basis of methods of the quantum theory of ternary nuclear fission

The two-proton decay of spherical nuclei is investigated on the basis of the formalism developed in constructing the quantum-mechanical theory of ternary fission. The proposed method for determining the amplitudes of partial widths with respect to two-proton decay and the asymptotic behavior of the wave function for a decaying nucleus makes it possible to solve the problem of describing two-proton radioactivity without recourse to the traditionally used (in R-matrix approaches) cumbersome procedure of matching the internal and the external wave function for the decaying nucleus within the three-body formulation. In the diagonal approximation and with allowance for the properties of the potential describing the interaction of the products of two-proton decay, the structure of the wave function for the Cooper pair of two protons bound in the parent nucleus is analyzed, along with the behavior of the wave function describing the potential scattering of the products of binary decay, the coupling of decay channels being taken into account in this analysis.     

Intensities of resonant brillouin scatterings from multicomponent exciton-polaritons

To reduce the arbitrariness in the current analysis of resonant Brillouin scattering (RBS) from multicomponent polaritons, the intensities of scattering peaks are theoretically studied. The interaction among the multicomponent excitons may contain linear and quadratic terms in translational wave vector, electron-hole exchange interaction, and any other terms that retain translational symmetry. As the scattering mechanisms due to TA and LA phonons, we consider various deformation and piezoelectric potentials. In certain cases, this theory leads to a “selection rule”, which can solve the controversy between the two different dispersion curves for CuBr obtained from RBS and two photon resonant Raman scattering, in favor of the latter. The theory also provides a basis to discuss the problem of additional boundary conditions for multicomponent polaritons in terms of the relative intensities of scattering peaks.     

Equivalent potentials for a nonsymmetric non-local interaction

Scattering formalisms which incorporate antisymmetrization of the projectile with respect to identical particles in the target result in a nonsymmetric non-local interaction. Such an interaction constraints the relative wavefunctions to be orthogonal to redundant states forbidden by the Pauli principle. Concentrating on the nonsymmetric non-local kernel of Saito we try to visualize the mechanisms by which a potential can ensure the required orthogonality. We achieve this by replacing the Saito kernel by an effective symmetric non-local potential. The constructed symmetric potential is found to be phase-equivalent only but not off-shell equivalent to the original kernel. This difference in the off-shell behaviour is attributed to the dynamical origin simulating the redundant states. In close analogy with one of our recent works we also derive an energy-momentum dependent equivalent to the local potential. Our solution of the pseudo inverse problem is exact and provides a basis for writing the phase—and quasiphase—equations. We present numerical results in support of this.     

Der Beugungseffekt bei der elastischen Streuung von Ionenstrahlen an Atomen

For the elastic scattering of ion beams at atoms the diffraction of the matter wave at the atom can be observed in the region of small scattering angles and high energies. The diffraction causes undulations in the differential scattering cross section. In this paper a general solution of the diffraction effect is given. The solution holds for the Yukawa type screened Coulomb potential which is well suited for the small angle scattering of-ions at atoms and which contains two parameters. The computations have been made using the partial wave method and the Jeffreys-Born-approximation for the scattering phase shifts. The solution is presented in a form in which the amplitudes and characteristic constants of the first four undulation maxima and minima are given in dependence of a product which contains one of the potential parameters. The characteristic constants are correlated in a characteristic equation with the second potential parameter and the positions of the diffraction extrema. The conditions for the appearance of the diffraction effect are discussed.     

Time evolution of quasi-stationary states

In this paper we study the time evolution of prepared states in some quantum mechanical models, and discuss the probability of decay and the rate of energy dissipation and their dependence on the form of the interaction. First we consider solvable models with divergent matrix elements for the operatorH ², whereH is the Hamiltonian of the system. We study two specific examples, one with well-defined eigenvalues and the other with renormalizable interaction. The time development of the initial state in the latter case depends on the cut-off parameter. In the second part of the paper, we show the possibility of existence of decaying states with long lifetime, where the amplitude of the initial state decreases like a Bessel function. In the third part, we determine the time development of a prepared state in a simple many-boson problem. Finally we study the problem of penetration of a wave packet through two phase-equivalent potential barriers, and we conclude that from the scattering phase shifts alone, it is not possible to determine the lifetime or the mode of decay of an unstable particle uniquely.     

Method for solving the problems of multiple scattering by several bodies in a homogeneous unbounded medium

A method is developed for solving problems of multiple scattering by an aggregate of bodies in a homogeneous unbounded medium. For this purpose, the problem on the multiple scattering produced by two bodies in the field of a plane wave is first considered under the assumption that the initial unperturbed scattering amplitudes of both scatterers are known. The solution is constructed by considering plane waves multiply rescattered by the scatterers. Integral equations are obtained that allow one to calculate the resulting scattering amplitude of each scatterer and the combined scattering amplitude of the system of two scatterers. It is shown that knowledge of the solution to this problem is sufficient to solve the problem on the scattering field of a system consisting of an arbitrary number of scatterers. Expressions for the scattering amplitude in the case of an arbitrary primary field are presented. The relationship between the integral equations describing the multiple scattering in a homogeneous space and the multiple scattering by a single scatterer located near an interface is demonstrated. Approximate expressions are given for calculating the scattering amplitude in the case of multiple scattering.     

Modeling a waveguide with a nonlinear insert with a quadratic nonlinearity

The scalar problem of the scattering of a wave from a nonlinear insertion lying in the interior of a waveguide is reduced by the incomplete Galerkin method to the boundary value problem for a Hamiltonian system. The cases in which this problem admits a solution in finite terms are indicated. Examples are given to illustrate specific phenomena due to the nonlinearity of the problem.     

Weighted-Residual Methods for the Solution of Two-Particle Lippmann–Schwinger Equation Without Partial-Wave Decomposition

Recently there has been a growing interest in computational methods for quantum scattering equations that avoid the traditional decomposition of wave functions and scattering amplitudes into partial waves. The aim of the present work is to show that the weighted-residual approach in combination with local basis functions give rise to convenient computational schemes for the solution of the multi-variable integral equations without the partial wave expansion. The weighted-residual approach provides a unifying framework for various variational and degenerate-kernel methods for integral equations of scattering theory. Using a direct-product basis of localized quadratic interpolation polynomials, Galerkin, collocation and Schwinger variational realizations of the weighted-residual approach have been implemented for a model potential. It is demonstrated that, for a given expansion basis, Schwinger variational method exhibits better convergence with basis size than Galerkin and collocation methods. A novel hybrid-collocation method is implemented with promising results as well.     

Inverse problem of dyon and magnetic monopole dynamics

The problem of finding an electromagnetic field allowing the movement of dual-charged particles on the background of an arbitrary static space-time to have a priori given properties, is considered. A solution of this problem is given, and the degree of arbitrariness of the obtained solution is found. Two particular examples of application of the general results are considered.     

Radar backscattering from Gerstner's sea surface wave

In the framework of a two-scale scattering model, radar backscattering from the rough sea surface was considered. The sea surface was modelled as a superposition of a nonlinear, large-scale Gerstner's wave and small-scale resonant Bragg scattering ripples. The zero-order diffracted field was found by a geometrical optics approach, with shadowing taken into account, and by an 'exact' solution of the diffraction problem obtained numerically. For vertical and horizontal polarizations, the spatial distribution of specific scattering cross sections along the large-scale wave was obtained. The spatially averaged specific backscattering cross sections, as well as the mean Doppler frequency shifts at both polarizations, obtained by the geometrical optics approach are compared with those obtained by using the 'exact' solution of the large-scale diffraction problem. The roles of shadowing and multiple wave scattering processes are discussed, and qualitative explanations of the difference between these two approaches are given.     

Semiclassical real-time tunneling by multiple spawning of classical trajectories

We systematically extend semiclassical real-time propagation methods based on Gaussian wave packets by using the composition property of the time-dependent quantum-mechanical Green function. For the first time, in an application to the problem of barrier tunneling, a semiclassical time-domain calculation of the transmission probability exhibits good agreement with exact quantum mechanical values at energies below the barrier top. Only two insertions of unity are needed for these results in a benchmark model of reactive scattering.