Reaction cross sections of carbon isotopes incident on a proton

We systematically study total reaction cross sections of carbon isotopes with $N=6\text{\ensuremath{-}}16$ on a proton target for wide range of incident energies. An emphasis is put on the difference from the case of a carbon target. The calculations include the reaction cross sections of $^{19,20,22}\mathrm{C}$ at $40A$ MeV, the data of which have recently been measured at RIKEN. The Glauber theory is used to calculate the reaction cross sections. To describe the intrinsic structure of the carbon isotopes, we use a Slater determinant generated from a phenomenological mean-field potential, and construct the density distributions. To go beyond the simple mean-field model, we adopt two types of dynamical models: One is a core$+n$ model for odd-neutron nuclei, and the other is a core$+n+n$ model for $^{16}\mathrm{C}$ and $^{22}\mathrm{C}$. We propose empirical formulas which are useful in predicting unknown cross sections.