Subsidiary Regge Trajectories with Singular Residues. Nucleon-Nucleon Scattering

It is pointed out that the existence of secondary Regge trajectories with intercepts $\alpha \mathrm{}\left(0\right)\mathrm{}$ which differ by integers from that of the leading trajectory at $t=0\mathrm{}$, and residues which are singular at that point, is a very general phenomenon which should occur both in the scattering of particles with spin, and in the scattering of particles of unequal mass. Rules are given for determining if such trajectories exist, and for determining their properties. The case of nucleon-nucleon scattering is discussed as an example.