Regge-Pole Theory and Spin Independence of the Total Cross Sections

The general conditions under which the total cross sections are independent of spin are discussed. It is shown that the forward elastic scattering matrix is proportional to the unit matrix in the helicity space if and only if the crossed channels either do not flip helicities, or do not flip helicities more than 1 and have the quantum number $P={\mathrm{}(-1\mathrm{})\mathrm{}}^J$. This theorem follows directly from the Trueman-Wick crossing relations. In particular, the theorem implies that the total cross sections are spin-independent at the high-energy limit if the forward elastic-scattering amplitudes are dominated by the Pomeranchuk trajectory.