Complete and incomplete fusion inC12+V51atE(C12)=36−100MeV from analysis of recoil range and light particle measurements

Excitation functions and detailed differential recoil range distributions for radioisotope products of the reactions of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ on ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$, together with inclusive proton and $\alpha$ particle spectra, have been measured at energies up to 157 MeV. The range distributions clearly show three separable components, which are attributed to complete fusion of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, incomplete fusion of ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$, and incomplete fusion of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, respectively, with the target. Detailed Monte Carlo modeling of the shapes of the recoil range distributions for these processes, using information on the breakup process derived from the measured $\alpha$ particle spectra, has enabled the separate contribution of each fusion process to the formation of each product studied to be deduced as a function of energy up to 100 MeV. The partitioning amongst the observed products is consistent with statistical model predictions for the subsequent evaporation; this allows the total cross section for each process to be estimated as a function of energy. For projectile energies up to 100 MeV, the observed yield of "breakup" $\alpha$ particles is exhausted by incomplete fusion. The results suggest that incomplete fusion is occurring principally for partial waves near or even outside the hard grazing value, and that the total cross section for the various fusion processes exceeds the hard-grazing cross section.