Resonant structures in theO16(O16,C12)Ne20reaction

Formulation is made of an exact finite-range distorted-wave Born approximation for the case in which the distorting potentials depend on the total angular momentum $J$. The general formula thus derived is then simplified for the cases in which the spins of the projectile, target, and ejectile are zero. This simplified form of the new exact finite-range distorted-wave Born approximation formula is applied to the analyses of the resonant structures seen in the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$,${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$($4_1^{+}$) reaction, and it is found that good fits to data are obtained. It is also shown that the mechanism embodied in the band crossing model plays an essential role in achieving these good fits. A detailed discussion concerning the absolute magnitude of the distorted-wave Born approximation cross sections is also presented, based on recent calculations which use the cluster model.