Forward and Backward "Selection Rule" in a Class of Inelastic Collisions

A rigorous rule which forbids forward and backward scattering is established for a certain class of inelastic collisions. The rule depends only on conservation of angular momentum and parity, and is therefore true, independent of the interaction and of the mechanism of the reaction. The class of collisions (called, in what follows, parity unfavored) consists of two particles $A$, $B$ of spin zero colliding to produce a particle $C$ of spin zero and $D$ of spin $S$ with the intrinsic parities $P_A$, $P_B$, $P_C$, and $P_D$ satisfying the condition $P_A{P}_B{P}_C{P}_D={\mathrm{}(-1\mathrm{})\mathrm{}}^{S+1\mathrm{}}$. It is also remarked that in a parity-unfavored reaction the particle with spin $S$ which is produced is always aligned with respect to the direction of the incident beam. Some applications in elementary-particle interactions and low-energy nuclear reactions are briefly discussed.