Recoil corrections for single-nucleon transfer reactions

A formalism is developed for approximately treating the recoil of the projectile in single-nucleon transfer reactions. The “no-recoil” term is evaluated exactly by rotating the nuclear matrix element to a coordinate system where the lighter projectile lies along the z-axis relative to the target nucleus. Recoil terms are constructed by expanding the “recoil phase factor” in terms of spherical harmonic and Bessel functions, and they are again evaluated exactly. Numerical results are then obtained for some representative light-ion reactions of high incident energies. For these reactions, we find that although the first-order recoil term may be very large, higher order terms are correspondingly less important, and convergence is always easily obtained. However, absolute magnitudes of cross sections at forward angles predicted by the present theory and by the local energy approximation differ by up to 50% for the reactions we consider.