Determination of neutron halo radii in the first excited states ofC13andBe11with the asymptotic normalization coefficients method

Abstract

An analysis of the differential cross sections of the $^{12}\mathrm{C}(d,p)^{13}\mathrm{C}$ (ground state, or g.s., $1/{2}_{1}^{+}$) and $^{10}\mathrm{Be}(d,p)^{11}\mathrm{Be}$ (g.s., $1/{2}_{1}^{\ensuremath{-}}$) reactions at the incident deuteron energies of 11.8, 25.9, and 30 MeV for the first system, and 12.0 and 25.0 MeV for the second system has been performed by applying the coupled-reaction-channels method. The spectroscopic factors ${S}_{\text{expt}}$, asymptotic normalization coefficients (ANCs), and rms radii of the last neutron in the ground states and the first excited states of the stable $^{13}\mathrm{C}$ and the radioactive $^{11}\mathrm{Be}$ nuclei were extracted. The existence of neutron halos in the first excited state of $^{13}\mathrm{C}$ and the ground state of $^{11}\mathrm{Be}$ is confirmed. The rms radii of halos in these states were found to be $5.72\ifmmode\pm\else\textpm\fi{}0.16$ and $8.0\ifmmode\pm\else\textpm\fi{}0.2$ fm, respectively, in agreement with experimental results. We showed that a halo is also formed in the 0.32 MeV $1/{2}_{1}^{\ensuremath{-}}$ excited state of $^{11}\mathrm{Be}$. The halo radius in this state was determined for the first time and was found to be ${R}_{h}=4.65\ifmmode\pm\else\textpm\fi{}0.20$ fm.