Properties of the First 1/2⁺ Excitation State of ¹³C by 22 MeV Proton Inelastic Scattering

The differential cross sections of 22 MeV proton inelastic scattering for the first 1/2⁺ excitation state (E_x = 3.09 MeV) of ¹³C have been measured between 9°and 130°. The broad peak located at ～ 120°, which has been systematically observed in the 0⁺ → 0^-, 1/2^- → 1/2⁺, and 1⁺ → 1^- transitions for the ¹⁶O, ¹³C, and ^14,15N (p,n) charge exchange reactions at E_p = 35 MeV, has been observed for the first time in the present proton inelastic scattering. The present experimental data are analysed by using microscopic distorted-wave Born approximation. From the comparison of present experimental data and theoretical results at forward angles, our analysis indicates the existence of neutron halo in the first 1/2⁺ excitation state of the ¹³C nucleus. In addition, by reasonable modification of shell model wavefunction of the first 1/2⁺ excitation state, we can well describe the experimental form factors of (e,e') and the experimental differential cross sections of (p,p') at incident energy of 547 MeV.