P-matrix description of the two-particle interaction

1992 ◽  
Vol 70 (4) ◽  
pp. 252-256 ◽  
Author(s):  
V. A. Babenko ◽  
N. M. Petrov ◽  
A. G. Sitenko
Keyword(s):  
Scattering Amplitude ◽  
Scattering Problem ◽  
Particle Interaction ◽  
Inverse Scattering Problem ◽  
Simple Expression ◽  
Matrix Description ◽  
P Matrix ◽  
Separable Expansion ◽  
Physical Quantities ◽  
Matrix Series

This paper deals with the formalism of the P-matrix description of the two-particle interaction within the framework of which the inverse scattering problem is considered. Separating, explicitly the P-matrix background part, associated with the free motion, yields a simple expression for the off-energy-shell scattering amplitude that immediately provides its separable expansion. Such separation corresponds to the partial summation of the initial P-matrix series and improves the description of physical quantities as functions of energy, provided the residual P matrix is approximated by a finite number of pole terms.

Inverse scattering problem for transparent obstacles

1982 ◽  
Vol 92 (2) ◽  
pp. 361-367 ◽  
Author(s):  
Vesselin Petkov
Keyword(s):  
Inverse Scattering ◽  
Convex Domain ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Normal Derivative ◽  
Index Of Refraction ◽  
Image Position ◽  
Compact Boundary ◽  
Limiting Values

Let K ⊂ ℝ3 be an open bounded strictly convex domain with smooth connected compact boundary ∂K. SetWe wish to study the filtered scattering amplitude, related to the transmission problemHere w± are the limiting values of w on ∂Ω; from the Ω;± side, while ∂w±/∂n are the corresponding limiting values of the normal derivative ∂w?/∂n on ∂Ω;. The function α(x) ∈ C∞(K¯), called the index of refraction, has the property α(x) > 0 for x ∈ K¯.

Inverse scattering for three-dimensional quasi-linear biharmonic operator

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Markus Harju ◽  
Jaakko Kultima ◽  
Valery Serov
Keyword(s):  
Inverse Scattering ◽  
Space Variable ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Regularity Conditions ◽  
Biharmonic Operator ◽  
Essential Information ◽  
Complex Valued

Abstract We consider an inverse scattering problem of recovering the unknown coefficients of a quasi-linearly perturbed biharmonic operator in the three-dimensional case. These unknown complex-valued coefficients are assumed to satisfy some regularity conditions on their nonlinearity, but they can be discontinuous or singular in their space variable. We prove Saito’s formula and uniqueness theorem of recovering some essential information about the unknown coefficients from the knowledge of the high frequency scattering amplitude.

Inverse scattering problem and the Schwinger approximation

1992 ◽  
Vol 70 (4) ◽  
pp. 282-288 ◽  
Author(s):  
M. A. Hooshyar ◽  
T. H. Lam ◽  
M. Razavy
Keyword(s):  
Scattering Amplitudes ◽  
Wave Scattering ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Nucleon Nucleon ◽  
S Wave ◽  
Physical Systems ◽  
Nucleus Scattering ◽  
The Stability

A new method of inversion of the S-wave scattering amplitude based on the Schwinger variational method is presented. This method is accurate and stable and is applicable to a number of interesting physical systems such as nucleon–nucleon or nucleon–nucleus scattering even when the data are known for a finite nonrelativistic range of energies. ⁁Examples of different scattering amplitudes and their corresponding potential functions are given to show the accuracy and the stability of the method.

scholarly journals Holomorphic Extensions Associated with Fourier–Legendre Series and the Inverse Scattering Problem

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1009
Author(s):  
Enrico De Micheli
Keyword(s):  
Spectral Density ◽  
Inverse Scattering ◽  
Scattering Amplitude ◽  
Laguerre Polynomials ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Holomorphic Extension ◽  
Legendre Series ◽  
Partial Waves ◽  
Legendre Expansion

In this paper, we consider the inverse scattering problem and, in particular, the problem of reconstructing the spectral density associated with the Yukawian potentials from the sequence of the partial-waves fℓ of the Fourier–Legendre expansion of the scattering amplitude. We prove that if the partial-waves fℓ satisfy a suitable Hausdorff-type condition, then they can be uniquely interpolated by a function f˜(λ)∈C, analytic in a half-plane. Assuming also the Martin condition to hold, we can prove that the Fourier–Legendre expansion of the scattering amplitude converges uniformly to a function f(θ)∈C (θ being the complexified scattering angle), which is analytic in a strip contained in the θ-plane. This result is obtained mainly through geometrical methods by replacing the analysis on the complex cosθ-plane with the analysis on a suitable complex hyperboloid. The double analytic symmetry of the scattering amplitude is therefore made manifest by its analyticity properties in the λ- and θ-planes. The function f(θ) is shown to have a holomorphic extension to a cut-domain, and from the discontinuity across the cuts we can iteratively reconstruct the spectral density σ(μ) associated with the class of Yukawian potentials. A reconstruction algorithm which makes use of Pollaczeck and Laguerre polynomials is finally given.

scholarly journals Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Trung Truong
Keyword(s):  
Inverse Scattering ◽  
Maxwell Equations ◽  
Field Data ◽  
Periodic Structures ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Unique Determination

AbstractThis paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

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