Proton radii of Be, B, and C isotopes

We investigate the neutron number $(N)$ dependence of root mean square radii of point proton distribution (proton radii) of Be, B, and C isotopes with the theoretical method of variation after spin-parity projection in the framework of antisymmetrized molecular dynamics (AMD). The proton radii in Be and B isotopes changes rapidly as $N$ increases, reflecting the cluster structure change along the isotope chains, whereas, those in C isotopes show a weak $N$ dependence because of the stable proton structure in nuclei with $Z=6$. In neutron-rich Be and B isotopes, the proton radii are remarkably increased by the enhancement of the two-center cluster structure in the prolately deformed neutron structure. We compare the $N$ dependence of the calculated proton radii with the experimental ones reduced from the charge radii determined by isotope shift and those deduced from the charge changing interaction cross section. It is found that the $N$ dependence of proton radii can be a probe to clarify enhancement and weakening of cluster structures.