Inadequacy of the Simple Distorted-Wave Born-Approximation Treatment of Comparative (p,t) and (p,He3) Transitions

Current theories of direct two-nucleon transfer reactions are tested, by comparing ($p,t$) and ($p,{}_{}{}^3{}_{}{}^{}\mathrm{He}$) transitions on odd-mass nuclei leading to mirror final states. Proton-induced reactions on ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ at 43.7 MeV and on ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ at 49.6 MeV are discussed in detail. Many mirror transitions are analyzed with DWBA calculations in an attempt to fit both angular distributions and cross-section ratios; good results for the shapes of the angular distributions are obtained. The agreement between theory and experiment for the cross-section ratios of mirror ($p,t$) to ($p,{}_{}{}^3{}_{}{}^{}\mathrm{He}$) transitions improves in every case with the inclusion of a strongly spin-dependent force in the nucleon-nucleon interaction, but over-all satisfactory agreement is not obtained. The ($p,t$) transitions are found to be generally stronger than expected, relative to their mirror ($p,{}_{}{}^3{}_{}{}^{}\mathrm{He}$) transitions, and three cases are discussed where the experimental ratios of these cross sections exceed the theoretical upper limit. Two possibilities, both of which introduce coherent effects, are discussed to account for this result: (1) interference terms arising through a spin-orbit interaction in the optical potential or (2) interference terms between a direct-reaction contribution and a core-excitation contribution to the cross section.