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Description
The point-proton radius ($r_{\mathrm{p}}$) is a key quantity used to study nuclear structures. Point-proton radius or charge radius ($r_{\mathrm{ch}}$) has been measured using the electron elastic scattering, muonic X-ray, and optical isotope shift methods. However, for nuclei far from the stability line and for certain elements, these methods are not applicable.
An alternative approach is the measurement of charge-changing cross sections ($\sigma_{\mathrm{CC}}$). The $\sigma_{\mathrm{CC}}$ can be measured even with low-intensity heavy-ion beams on the order of a few particles per second. Therefore, this method is a potential tool to study the $r_{\mathrm{p}}$ of a very neutron-rich nucleus.
To date, $\sigma_{\mathrm{CC}}$ measurement has been utilized to derive the $r_{\mathrm{p}}$ of nuclei up to $Z\approx20$. In Ca isotopes, the experimental data were successfully described by combining a Glauber model with a charged-particle evaporation model. This indicates that the evaporation effect plays a crucial role in relating the measured σCC to point-proton distribution.
We investigated $^{114\text{--}137}$Sn isotopes whose $r_{\mathrm{ch}}$ are known from isotope-shift measurements. The experiment was conducted at RIKEN RIBF. The $\sigma_{\mathrm{CC}}$ measurements were performed on a carbon target at approximately 250 MeV/nucleon.
Using the known $r_{\mathrm{ch}}$ as input, we calculated $\sigma_{\mathrm{CC}}$ within the framework that combines the Glauber model and a charged-particle evaporation model, and compared the results with the experimental data. We find that, also for the Sn isotopes, a simple Glauber calculation fails to reproduce the measured $\sigma_{\mathrm{CC}}$, and the inclusion of the charged-particle evaporation effect is essential. Furthermore, the evaporation model parameter for Sn isotopes significantly differs from that for Ca isotopes.