THE PROBLEM OF AMBIGUITY IN THE PHASE SHIFT ANALYSIS OF SCATTERING PROCESSES,
EMMANUEL COLL BOSTON MASS RESEARCH LANGUAGE CENTER
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Starting from the conditions which should be satisfied by the existence of different choices in phase shift analysis, this paper discusses the general ambiguity in the analysis of elastic scattering of particles with arbitrary spins. The transformation matrices among the different sets of phase shifts are given and the real para-meters involved are determined by the system of second order algebraic equations. The problem of ambiguity in the phase shift analysis therefore is reduced to finding the real roots of these equations. The number of different sets of real roots is twice that of the different choices in the phase shift. Therefore, generally kinematic ambiguity in phase shift analysis is solved. The ambiguity in the phase shift analysis corresponds to the spin motion which conserves the components of spin-tensors in the direction of momentum, and the parameters which characterize this type of general spin motion take fixed values. From the properties of the algebraic equations, it is proposed that the ambiguity in cases of whole integral spin is much less than in cases of half integral spin.