[en] The reaction cross sections of ${}^{15,16}$C+${}^{12}$C and ${}^{15,16}$C+${}^{27}$Al are calculated at intermediate energies using microscopic complex optical potential (OP) derived from Brueckner G-matrix. Glauber model (GM) with and without in-medium effects are also used for comparison. Different models for the density distributions such as deformed Fermi density, whose deformation parameters and radii are determined by RMF calculations, a harmonic oscillator (HO), harmonic oscillator plus Gaussian (HOG) and two-parameters Fermi (2pF) are used. It is found that ${}^{16}$C can be described by HO, HOG, and 2pF densities with the same matter radius ∼2.75 fm, while ${}^{15}$C can be described by HOG (${}^{14}$C core and one neutron in the S${}_{1/2}$ state) with matter radius 2.88 fm, when using the OP in the calculation of the reaction cross section, which indicates the halo structure of ${}^{15}$C. Glauber model with in-medium effects predicted matter radius 2.8 fm for both ${}^{15}$C and ${}^{16}$C. A clear halo structure is shown in the extracted density distribution of ${}^{15}$C predicted by both the OP and GM models, while for ${}^{16}$C a neutron skin, in the range 0.3-0.4 fm, which is smaller than of ${}^{15}$C, is predicted without a long extended tail, as that predicted for ${}^{15}$C, which indicates the absence of halo structure for ${}^{16}$C, in contrast with most of the other predictions.