Vanishing radiation amplitudes: Physical null zones

We examine and parametrize a region of the phase space for relativistic $n$-particle collisions in which radiation tree amplitudes vanish. The physical-null-zone theorem, which gives conditions for this null radiation zone to intersect the physical region, is proven. A set of invariant parameters and their ranges are found, and constraints on energies are discussed. A geometrical picture is developed for the phase space and null zone in the massless limit.