Best Reaction Target to Determine Proton Distribution Radii of Atomic Nuclei

We found that a heavy target such as Pb is most suitable for determining the proton distribution radii of unstable nuclei through charge-changing cross-section (σ_{cc}) measurements. Experimentally, low-Z targets are routinely used to determine nucleon distribution radii of unstable isotopes. This approach has recently been extended to study proton distribution radii from σ_{cc} measurements. However, empirical scaling factors have to be introduced to apply the Glauber models. In the present Letter, we systematically investigated the scaling factor using 39 new σ_{cc} data of 18  p-shell nuclei on hydrogen, carbon, silver, and lead targets at around 240  MeV/nucleon. Together with the existing data, we reveal a universal dependence of the scaling factor on both the masses of target nuclei and the separation energies of projectile nuclei. The scaling factors decrease with increasing target-nucleus mass and converge to 1 for the highest-Z target, making the scaling unnecessary. We conclude that instead of a low-Z target, employing a heavy target such as Pb in σ_{cc} measurements is the best option to determine the proton distribution radii of unstable nuclei.