REDUCTIONS OF PHASE-SPACE INTEGRAL IN TERMS OF SIMPLER PROCESSES

By using a 2 3-body reaction as a basic process, a recurrence relation is derived for the phase-space integral Rn of the reaction pa+pbp1+ +pn. By iteration, Rn can be written in the variables s^i=(p1++pi)2, ti=(pa-p1-pi)2, and si=(pi+pi+1)2, i=1,n-1. The kinematical boundaries are stated explicitly, and the relation of this form to the form obtained from 1 2- and 2 2-body basic processes is clarified. This expression can also be applied to the Monte Carlo generation of events and to the summing of iterative production models by integral-equation techniques. The transformation of s^i to Toller angles is carried out, but the resulting expression is seen to be impractical at finite energies. Useful geometrical interpretations of Gram determinants of four-momentum vectors are given. © 1969 The American Physical Society.