Extraction of the RMS Radii of ¹³C from Asymptotic Normalization Coefficients

The asymptotic normalization coefficients (ANCs) for three bound states of ¹³C (¹²C+n) are extracted from the angular distributions of ¹²C(d,p) reactions at E_lab = 11.8MeV. With these ANCs, the calculated root-mean-square (rms) radii of these three states agree with our previous results. The ANCs are 1.93±0.17, 1.84±0.16, and 0.149±0.012fm^-1/2, and the rms radii < r² >^1/2 are 3.39±0.31, 5.04±0.75 and 3.68±0.40 fm for the ground state, the first and third excitation states, respectively. Further analyses show that the first excitation state with D₁ = 50.3% is a true neutron halo state, while the third excitation state with D₁ = 25.2% is a neutron skin state.