Matter distribution of ${}_{12-20,22}C$ isotopes

The matter distribution is systematically studied for neutron-rich carbon isotopes with $N=6–16$ from the available measured reaction cross sections with ${}_{12}C$ reaction target, using the finite-range Glauber model with Coulomb correction. We have first studied the energy dependence of the ${}_{12}C\text{−}{}_{12}C$ reaction cross sections in a wide range of incident energies from 30–950 MeV/nucleon. A good agreement with the experimental data measured at low and high incident energy is obtained by considering the nuclear density distribution of two Fermi (2pF) parameters, where the two optimized parameters are the size parameter $r_{2pF}$ and the diffusivity parameter $a_{2pF}$. We have therefore extracted the necessary parameters of the proton, neutron, and matter distributions for the whole range of ${}_{12-20,22}C$ isotopes. With a set of calculations of four freely adjustable parameters (proton: $r_{2pF,p}, a_{2pF,p}$) and (neutron: $r_{2pF,n}, a_{2pF,n}$), we present for the first time an accurate determination of the neutron radii together with the proton radii, which are in excellent agreement with the charge radii directly extracted from the measured charge-changing cross sections. The evolution of the central density and diffuseness is studied as a function of the number of neutrons and shows the persistence of the $N=8$ shell closure for ${}_{14}C$. However, an anomalous halo structure is studied for the ${}_{16,19,22}C$ isotopes, where the effect of proton-neutron nuclear interaction could be manifested by the decrease of the central density with large expansion at large distance, leading to a sharp increase of the radii with respect to the neighboring nuclei.