Systematics of momentum distributions from reactions with relativistic ions

The momentum distributions of projectile and target residues from spallation reactions induced by relativistic projectiles already in the literature are transformed into consistent quantities and compared. The momentum imparted to the residual nucleus is presented in terms of a longitudinal velocity, 〈${\beta }_{?}$〉, and a root-mean-squared momentum, $P_{\mathrm{rms}}$. These parameters from all spallation products from many disparate systems display the same systematic dependence on observed mass loss. The rms momentum is shown to depend on the square root of the observed mass loss due to momentum conservation in either of three competing processes with no dependence on the initial reaction. The longitudinal momentum is shown to depend on the observed mass loss and therefore on the excitation energy with only a kinematical factor from the entrance channel. Thus, the longitudinal momenta depend on the velocity but not the mass of the reaction partner.