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Construction of the scattering amplitude from the differential cross-sections

Alain J. Martin
- 01 Jan 1969 - 
- Vol. 59, Iss: 1, pp 131-152
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TLDR
In this article, the authors established rigorously a sufficient condition for the existence of a scattering amplitude corresponding to a given angular distribution for scalar particles in the elastic region, where the condition is max [(1/4π) · e|F(13)|| F(23)|dΩ3/|F (12)|]=sinµ<1.79.
Abstract
We establish rigorously a sufficient condition for the existence of a scattering amplitude corresponding to a given angular distribution for scalar particles in the elastic region. The condition is max [(1/4π) · e|F(13)||F(23)|dΩ3/|F (12)|]=sinµ<1. We show that if |sinµ|<0.79 the amplitude is unique, except for one obvious ambiguity. Further, by examining the case of a finite, but arbitrarily large number of partial waves, we show that it is very likely that the solution is still unique for 0.79<sinµ<1. We also discuss the number of solutions in other situations.

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Journal ArticleDOI

Inversion of molecular scattering data

TL;DR: In this paper, the authors reviewed the practical applicability of such procedures in molecular physics rather than on the question of existence and uniqueness, and the procedures which had been applied to the determination of spherically symmetric, interatomic potentials by the inversion of actual scattering data are critically surveyed and illustrated by approprite examples.
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A new point of view in the analysis of two-body reactions

TL;DR: In this article, an original method for the analysis of two-body reactions, based on the use of the zeros of the scattering amplitude, is presented. But this method is not suitable for the case of single body reactions.
Journal ArticleDOI

Ambiguities of complex phase-shift analysis

TL;DR: In this paper, the ambiguities of complex phase shift analysis made for a definite number of partial waves and given energy are dealt with, and all ambiguous sets of phase shifts are physically acceptable.
Journal ArticleDOI

Fixed momentum transfer analysis of pion-nucleon scattering

TL;DR: The πN scattering amplitudes have been determined at 38 momentum transfer values for 0 t −1 GeV 2 and expressed in terms of expansions, which are convergent throughout the energy range and have correct fixed-t analyticity and s − u crossing properties.
Journal ArticleDOI

Principles and problems of phase-shift analysis

TL;DR: In this article, it is shown that the inelastic threshold of the unitarity constraint on a scattering amplitude is only an inequality and a continuum of different amplitudes will correspond to exactly the same observables.
References
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Book

Orthogonal polynomials

Gábor Szegő
Journal ArticleDOI

Unitarity and High-Energy Behavior of Scattering Amplitudes

TL;DR: In this paper, upper and lower bounds of the imaginary part of a scattering amplitude are obtained for physical and unphysical values of the scattering angle, respectively, from unitarity alone, and it is shown that the total cross section cannot increase faster than the logarithm squared of the energy under assumptions appreciably more general than Mandelstam representation.
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