Extraction of Nuclear Radii from Interaction Cross Section Data

The nuclear density distribution of light radioactive nuclei can be extracted from the experiments when radioactive isotopes are scattered from the stable nuclear target. To obtains distribution parameters or root-mean-square (r.m.s.) radii, the interaction cross-section $\sigma^{(I)}$, measured in these experiments, is usually compared with calculated reaction cross-section, $\sigma^{(r)}$. This difference has been estimated in some nuclei to be less than a few percent. However, that still can significantly affect extracted value for the r.m.s In the presented paper we calculate values of r.m.s. radii for nuclei with atomic weights A$<$40 in various theoretical approaches: the optical approximation, rigid target approximation and the exact expression of Glauber Theory. R.m.s. radii were extracted from comparison of experimentally measured and calculated interaction cross-section $\sigma^{(I)}$.