Determination of the scattering amplitude from the differential cross-section and unitarity |
| |
| Authors: | D. Atkinson P. W. Johnson R. L. Warnock |
| |
| Affiliation: | (1) Theoretical Institute of the University, Groningen, Netherlands;(2) Present address: Illinois Institute of Technology, Chicago, Illinois, USA;(3) Physikalisches Institut der Universität Bonn, Germany;(4) Department of Physics, Imperial College, London, U.K. |
| |
| Abstract: | When the differential cross-section for spin-zero elastic scattering is given, the elastic unitarity condition constitutes a nonlinear integral equation for the phase of the scattering amplitude. Existence and uniquences theorems for solutions of the equation were obtained by Newton and Martin. Some improvements of the Newton-Martin results on uniqueness and iterative construction of solutions are obtained. Certain details of rigour in the applications of Schauder's theorem by Newton and by Martin are supplied. The case of inelastic spin-zero scattering is treated by adding a term to the unitarity condition to account for absorption. It is shown that in the inelastic region one may have infinitely many different scattering amplitudes with a given differential cross-section. This result is potentially important in phase-shift analysis, since it means that there is a  continuum ambiguity in the determination of phases and elasticities from scattering data.Work supported in part by the National Science Foundation and a NATO Research Grant. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
