Coupled-channel-Born-approximation study of (p,t) reactions leading to two-phonon states of vibrational nuclei

A coupled-channel-Born-approximation (CCBA) study is made of ($p,t$) reactions leading to two-phonon states of vibrational nuclei. A detailed numerical analysis is performed, particularly for the ${}_{}{}^{116}{}_{}{}^{}\mathrm{Cd}\mathrm{}(p,t)\mathrm{} {}_{}{}^{114}{}_{}{}^{}\mathrm{Cd}$ reaction with the incident energy $E_p=28\mathrm{}$ MeV. It is shown that many features observed in the reactions, which cannot be explained by the distorted-wave Born approximation (DWBA), can successfully be accounted for by CCBA. It is also shown that three-step processes play an essential role in the successful explanation of the observed data, particularly the cross sections of the $0^{+}$ and $4^{+}$ two-phonon states.