Differential cross sections for the $0_2^{+}$ state at $E_x=7.654$ MeV in ${}^{12}\mathrm{C}$ were measured with the ($p,p^{\prime }$) reaction at an incident energy of $E$${}_p=300$ MeV, and in an angular range from ${\theta }_{\mathrm{Lab}}=2.7$${}^{°}$ to ${40}^{°}$. The cross-section data were compared with the distorted-wave Born-approximation calculations employing three types of transition densities obtained in a macroscopic collective model, a microscopic $\alpha$-cluster model, and a microscopic $\alpha$-cluster condensation model. It is concluded that the measured angular distribution of the differential cross sections for the ${}^{12}\mathrm{C}$($p,p^{\prime }$) reaction at 300 MeV is consistently described with the assumption that the $0_2^{+}$ state at $E_x=7.654$ MeV is the dilute $\alpha$-cluster condensed state.

• Received 5 March 2010

DOI:https://doi.org/10.1103/PhysRevC.81.054604