Phase-shift analysis is the extraction of the scattering amplitude from the scattering cross section and other experimentally observable quantities such as polarizations. When only elastic scattering is energetically allowed, unitarity determines the unobservable angle-dependent complex phase of the scattering amplitude with, at most, only a few discrete alternative solutions. Above the inelastic threshold the unitarity constraint on a scattering amplitude is only an inequality and a continuum of different amplitudes will correspond to exactly the same observables. In practical cases these differences can be important. Extra theoretical input of a dynamical nature can, in principle, remove the continuum ambiguity but, because numerical analytic continuation is always involved, data of absurd accuracy are required. Thus unique answers can, in practice, only be found by introducing further model-dependent assumptions ; it is important to recognize this and ensure that these assumptions are as dynamically plausible as possible. Recent results using the structure of the amplitude in both kinematic variables suggest that fixed-t dispersion relations might form a sound basis for an inelastic phase-shift analysis.

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