Analytic eikonal model for intermediate energy stripping and pickup reactions

We have developed an analytic eikonalized amplitude for the intermediate energy ($p$,$d$) reaction based on the distorted wave Born approximation. Eikonalization of the distorted waves naturally separates the important dynamical quantity, the momentum transfer, into longitudinal and transverse components. Upon evaluation of the amplitude using techniques similar to those employed by Amado, Dedonder, and Lenz for elastic scattering, we find the dependence of the transverse momentum transfer to be dominated by distortion effects. Consequently the shapes of the angular distributions are similar to those for elastic scattering. The geometry of the binding well of the picked-up neutron determines most of the dependence of the longitudinal momentum transfer. This fixes the dependence on bombarding energy. Many simple systematic features of these reactions are predicted using the analytic eikonalized amplitude and are observed in full partial wave calculations.