Difference in peripherality of the inclusive (p,p′x) and (d,d′x) reactions and its implications for a phenomenological reaction model

Background: Previous studies have revealed the importance of introducing surface correction into a phenomenological model for inclusive (n,n′x) and (p,p′x) reactions. These findings have contributed significantly to the improvement of nuclear data evaluation. However, the necessity for the surface correction in an inclusive (d,d′x) reaction has hardly been investigated. Purpose: The purpose of this study is to investigate the difference in the peripherality of the (p,p′x) and (d,d′x) reactions by a theoretical analysis using a quantum mechanical model, and to obtain a theoretical basis on the surface correction in the (d,d′x) reaction. Methods: The energy spectra and their radial distributions for the (p,p′x) and (d,d′x) reactions are calculated by the one-step semiclassical distorted wave model. Results: The radial distribution of the energy spectra for the (d,d′x) reaction is shifted toward the outer region of the nucleus compared to the (p,p′x) reaction. Based on this finding, we consider a larger surface correction into a phenomenological model for the (d,d′x) reaction than that for the (p,p′x) reaction, and calculated values reproduce the experimental (d,d′x) spectra well. Conclusion: The peripherality of the (d,d′x) reaction is more prominent than that of the (p,p′x) reaction. The stronger surface correction thus should be introduced for the (d,d′x) reaction than for the (p,p′x) reaction.