Starting from the conditions which should be satisfied by the existence of different choice in the phase shift analysis, in this paper the general ambiguity in the analysis of elastic scattering of particles with arbitrary spins has been discussed. The transformation matrices among the different sets of phase shift are given, the real parameters involved are determined by the system of second order algebraic equations. The problem of ambiguity in the phase shift analysis therefore is reduced to the problem of finding the teal roots of those equations. The number of different sets of real roots is twice that of different phase shift choice. Therefore, the kinematical ambiguity in the phase shift analysis in general is solved. When the channel spin is 1/2, it has been shown that only two sets of phase shift exist; when the channel spin is 1, only two sets of phase shift are given also, therefore it has been shown that the Minami's ambiguity is the whole ambiguity in these cases. When the channel spin is 3/2, it has been found that there are four different sets of phase shift. Therefore, in addition to the known transformation there are two new transformation matrices in that case. In general, the ambiguity in the phase shift analysis corresponds to the motion of spin which conserves the components of spin-tensors in the direction of momentum, and the parameters which characterize those general spin motion take the fixed values. In our discussion it has been shown that the systems of algebraic equations which are satisfied by the real parameters in the transformation matrices in the whole integral spin cases are quite different from that in the half integral spin cases. Therefore, the numbers of real roots in those two cases are also different, this means that the numbers of different phase shift sets are quite different. From the properties of those algebraic equation it has been suggested that the ambiguity in the case of integer spin is much smaller than that in the case of half integer spin.
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