Possible neutron and proton halo structure in the isobaric analog states of A=12 nuclei

Abstract

The differential cross sections of the $^{11}\mathrm{B}(^{3}\mathrm{He},d)^{12}\mathrm{C}$ reaction leading to formation of the ${0}^{+}$ ground state and the 15.11-MeV 1 ${}^{+}$, 16.57-MeV ${2}^{\ensuremath{-}}$, and 17.23-MeV ${1}^{\ensuremath{-}}$ excited states of $^{12}\mathrm{C}$ are measured at ${E}_{\text{lab}}=25$ MeV. The analysis of the data is carried out within the coupled-reaction-channels method for the direct proton transfer to the bound and unbound states. The rms radii of the last proton in all states studied are determined. A comparison of the rms radii of the $^{12}\mathrm{B}, ^{12}\mathrm{C}$, and $^{12}\mathrm{N}$ nuclei in the isobaric analog states (IASs) with isospin $T=1$ determined by different methods allows us to arrive at a conclusion that these nuclei in the ${1}^{\ensuremath{-}}$ excited states at ${E}_{x}=2.62, 17.23,$ and $1.80$ MeV, respectively, possess one-nucleon (neutron or proton) halo structure. The enlarged radii and a large probability of the last neutron to be outside of the range of the interaction potential are also found for the ${2}^{\ensuremath{-}}$ states of $^{12}\mathrm{B}, ^{12}\mathrm{C}$, and $^{12}\mathrm{N}$ at ${E}_{x}=1.67, 16.57,$ and $1.19$ MeV, respectively. These IASs also can be regarded as candidates for states with one-nucleon (neutron or proton) halo.