On energy-dependent scaling factor for the charge-changing cross sections of light elements

Abstract

In this study, the scaling factor for ${}^{28}$\rm Si + ${}^{12}$\rm C charge-changing cross sections (CCCSs) at 90-1296 MeV/nucleon has been used as a basis to introduce the energy dependence in the scaling factor for the light elements. To test the extracted scaling factor, we predict the charge-changing cross sections for ${}^{7,9-12,14}$\rm Be, ${}^{10-15,17}$\rm B, ${}^{11-19}$\rm C, ${}^{13-22}$\rm N, ${}^{15-24}$\rm O, and ${}^{18-21,23-26}$\rm F isotopes at 200-991 MeV/nucleon in the framework of the Glauber model. The calculations use descriptions of nuclei in terms of the Slater determinant involving harmonic oscillator single-particle wave functions, which reproduce the charge radii obtained earlier [Phys. Rev. C {\bf 110} (2024) 014623; {\bf 111} (2025) 064601]. It is found that the theoretical results provide quite a satisfactory explanation of the experimental data in all the cases, and the extracted scaling factor shows systematic energy dependence for the isotopes of a given element. In conclusion, we expect that the present way of finding the scaling factor could be successfully used in the analysis of CCCSs for the elements Z $\le$ 9 at any desired energy in the range 90-1296 MeV/nucleon. This result may further add that the present work provides a practical scheme for predicting the charge-changing cross sections (and inferring proton radii) of \rm Be-\rm F isotopes, where measurements are scarce.