Ambiguities of complex phase-shift analysis

It is well known that there exist ambiguities of phase-shift analysis for real potential scattering. For complex potential scattering (complex phase shifts) additional ambiguities arise. We deal with the ambiguities of complex phase-shift analysis made for a definite number of partial waves and given energy. For a given set of complex phase shifts describing elastic scattering of spinless particles we give all other sets of complex phase shifts which correspond to the same total cross section and differential elastic cross section. For a given set of complex phase shifts describing the elastic scattering of spin one-half particles on spinless particles, we give all other sets of phase shifts which correspond to the same total cross section, differential elastic cross section and polarization. Not all ambiguous sets of phase shifts are physically acceptable. Checking with the unitary condition allows one to sift out the unacceptable sets.