Direct fragmentation and hard-scattering processes in relativistic heavy-ion reactions

In a relativistic heavy-ion reaction, there are many processes which contribute to fragmentation phenomenon. Here we examine two: the direct fragmentation process in which the detected subsystem is emitted from a parent nucleus without additional scattering, and the hard-scattering process in which a subsystem from one nucleus makes a collision with a subsystem from the other nucleus. In terms of a combination of these two processes, the proton inclusive data of Anderson et al. for the reaction $\alpha +{}_{}{}^{12}{}_{}{}^{}\mathrm{C}\to p+X$ at different bombarding energies can be successfully analyzed. We find that the direct fragmentation process dominates the cross section at 0° and 180°. On the other hand, the hard-scattering process dominates the cross section at the quasi-elastic peak when the transverse momentum far exceeds 0.1 GeV/c. Our model leads naturally to a new scaling variable which is the generalization of the Feynman scaling variable for situations when the rest masses are not negligible. As the nuclear momentum distribution enters into the model in a very important way, our analysis constitutes in essence a semi-empirical determination of the nuclear momentum distribution. Furthermore, since a single nucleon can carry a large fraction of the momentum of the parent nucleus in a cooperative manner, relativistic heavy-ion reactions may be utilized to provide valuable information on the high momentum tail of the nuclear momentum distribution when the effects of final-state interactions are better understood.