Abstract
Assuming a certain continuity property, we prove, using the old results of Itzykson and Martin, that, except for an obvious ambiguity, there are only at most two amplitudes reproducing an elastic differential cross section at a given energy.
Highlights
Assuming a certain continuity property, we prove, using the old results of Itzykson and Martin, that, except for an obvious ambiguity, there are only at most two amplitudes reproducing an elastic differential cross section at a given energy
We consider only the situation where the scattering amplitude is an entire function of order 1
We do not believe this because the differential cross section remains continuous at the limit
Summary
Given a differential cross section at one energy in the elastic region, can one find the scattering amplitudes? We restrict ourselves to the spinless case. Martin [6] assuming that there is a finite number of partial waves and showing that if the cross section is less than 1.38, the solution is unique. Martin [6] undertook a different approach, assuming that the scattering amplitude is a genuine entire function, i.e., not a polynomial, and succeeded to prove that in most cases there are not more than 2 solutions. We modify a polynomial amplitude, to make it an entire function and succeed to prove that for polynomial amplitudes of arbitrarily large degree there are only 2 solutions. We move to amplitudes with infinite number of partial waves and succeed, we believe, in proving that there are only 2 solutions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
