Phenomenological analysis of the excitation functions of proton-induced fragmentation reactions

Proton-induced fragmentation reactions are considered within the framework of a two-step model. In the first step, the incident proton penetrates the target, knocks out few nucleons and leaves the residual nucleus in an excited state. In the second step, the residual nucleus fragments once its excitation energy exceeds a certain threshold, the crack energy. The fragmentation probability is described by a phenomenological. expression inspired by the experimental data on the fragment yield mass distribution and the theoretical calculations using statistical models. An analytical expression is obtained for the fragmentation product cross-sections which is found to agree reasonably with the experimental data. The crack energies extracted from the comparison with experiment have a mean value of E(cr)/A = (4.1 +/- 0.5) MeV.