Scattering Amplitudes from Elastic Cross Sections
The problem of constructing the scattering amplitude from the cross section could theoretically be avoided by performing measurements of intensity correlations on scattered particles at different space-time points. The interest of such measurements has been pointed out by Goldberger et al. (1963, 1964, 1965, 1966), following Hanbury Brown and Twiss (1954, 1956). They proved that, with this technique, it is possible to explicitly measure the phase of a scattering amplitude (with particular relevancy to X-ray scattering). However, obtaining the correlated counting rates of two detectors with the beam intensities nowadays available is hopeless in particle physics. Besides, it is not obvious that overcoming this difficulty will readily yield a solution of the problem. In typical situations, the scattering phase remains deeply involved in the formulas. Therefore, mathematical ways of constructing the scattering amplitude from the cross sections will be of interest for years.
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