Construction of the scattering amplitude from the differential cross-sections
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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.read more
Citations
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Inversion of molecular scattering data
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A new point of view in the analysis of two-body reactions
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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.
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Fixed momentum transfer analysis of pion-nucleon scattering
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Principles and problems of phase-shift analysis
J E Bowcock,H Burkhardt +1 more
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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Unitarity and High-Energy Behavior of Scattering Amplitudes
A. Martin,A. Martin +1 more
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.