Disentangling the scattering matrix when there is a dominant reaction mechanism

Our previous strategy for obtaining the $S$ matrix from polarization measurements is applied to a general spin-1/2, two-body reaction at fixed $s$ and $t$. One may test the hypothesis of a dominant reaction mechanism by carrying out a short list of $M$ measurements: $M\le 4$. Subdominant mechanisms may be extracted by a long list of 2$N$-2 measurements: $N$ is the number of independent amplitudes and $N\le 16$. The long list brings in all independent interferences of the dominant amplitude with the remaining amplitudes. The scale of the amplitudes is set by the differential cross section; the amplitudes can be determined only to within an overall phase. The cross section, short list, and long list are the elements of an optimal strategy for amplitude determination; its extension to arbitrary spins is discussed. These formal arguments do pay respect to practical aspects of amplitude determination.