Scaling Phenomenon of Isotopic Cross Section in p+⁵⁶Fe Spallation Reactions

An empirical formula is proposed to predict the isotopic cross section in spallation reactions. The measured fragments in the 300, 500, 750, 1 000 and 1 500 MeV/u p+⁵⁶Fe spallation reactions have been adopted to perform the analysis. The cross sections of isotopes predicted by the proposed empirical formula have been compared to the experimental results, which shows that the empirical formula can predict the results well. But with the change of the mass and incident energy, the difference between the calculated results and experimental data is larger. The proposed empirical formula is found to predict the isotopic cross sections better, by incorporating the incident energy and mass dependents of fragments.