Scalling Phenomenon Of Isotopic Cross Section In Spallation Reactions

Proton therapy and its devices are a hot topic in the current medical physics community.In proton therapy,the reaction initiated by protons is mainly a severe reaction such as a spallation reaction.However,when studying the scaling phenomenon of the cross-section of the fragment produced by the spallation reaction in proton therapy,it is found that the existing experimental data has less data on the small-mass target nuclei and it is more difficult to do experiments.There is no effective model to study the spallation reaction.Therefore,it is necessary to propose a code or empirical formula to predict the cross section of the fragment in the spallation reaction.So,a simple empirical formula is proposed in this paper to predict the cross-section values generated by isotopes in the spallation reaction.An empirical formula is proposed to predict the isotopic cross section in spallation reactions.The measured fragments in the 300,500,750,1000 and 1500 MeV/u ⁵⁶Fe+p spallation reactions have been adopted to perform the analysis.To predict the cross section of framents,the 1500MeV/u56Fe+p reaction is taken as the reference system,and ³⁶Ar is taken as the reference fragment.The cross sections of isotopes predicted by the proposed empirical formula have been compared to the experimental results,which shows that it 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 well by incorporating the incident energy and mass dependents of fragments.The cross sections of fragments predicted by the proposed empirical formula and the spallation residue cross section?SPACS?parameterizations have been compared to the experimental results,showing that both of them can predict the results well.At the same time in order to consider the effects of asymmetry caused by different projectile nucleus reactions,The yield of fragments in the 1000 MeV/u ¹³⁶Xe+p reactions can also be predicted by the proposed formula,while the SPACS parameterizations significantly underestimate the measured results.Therefore,the cross-section values generated by this method for predicting the residual nuclear generation in spallation reactions are of great significance for proton therapy.