Assessment of Two-Step Processes in (p,t) Reactions

Multiple-step processes (core excitation) are evaluated for the ($p,t$) reaction at a typical energy (30 MeV) and for a typical moderately collective spherical nucleus (nickel). Our model nucleus has three kinds of states; the ground and collective $2^{+}$, which have a strong direct transition, other typical noncollective states which also can be produced in a single step, and a two-phonon triplet, which can be produced only through multiple-step processes. We find that these latter are produced as strongly as the other noncollective states and that the angular distributions and polarizations are characterized by the multipolarity of the over-all transition and not by the multiplicity of the reaction mechanism. Comparison is made with the distorted-wave Born approximation. We find that it underestimates the ($p,t$) cross sections to all three types of states, and that even relative cross sections are in error by up to a factor 2, and absolute cross sections by as much as a factor 5.