Measurements and analysis of thePb208(C12,C)13, (C12,B11), and (C12,C14) reactions

Abstract

A ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ target was bombarded with 97.9-MeV ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ions accelerated in the Oak Ridge isochronous cyclotron and the reaction products detected with a 60-cm long position-sensitive proportional counter placed at the focal plane of an Elbek spectrograph. Differential cross sections were measured for the ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$), ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$), and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$) reactions. The single-nucleon transfer data, together with previous measurements taken for the same two reactions at 77.4 and 116.4 MeV, were analyzed using exact finite-range, full-recoil, distorted-wave Born-approximation calculations. Elastic scattering for ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ + ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ at 74.6 MeV and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ at 86.1 MeV was also measured and optical optical potential fits obtained to provide potentials for use in the distorted-wave Born-approximation calculations. Both Woods-Saxon and folded potentials were used in fitting the elastic data. The importance of the various interaction terms in the distorted-wave Born approximation was studied. Good agreement was found between theory and experiment for the (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$) reactions, and the spectroscopic factors deduced were satisfactory. The data for the (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$) reactions, although also yielding satisfactory spectroscopic factors, tend to peak at smaller angles than the predicted...