Recoil Damping in Heavy-Ion Transfer Reactions

An earlier suggestion by the authors that the unexpected features of angular distributions in heavy-ion transfer reactions at energies above the Coulomb barrier may be explained by including recoil and finite-range effects in a direct-reaction theory, is examined in detail. It is shown that the finite mass of the transferred particle may be taken into account approximately by the inclusion of a recoil phase factor in the transfer function of the usual distorted-wave Born amplitude. The implications of modifying the transfer function are worked out with the help of a sharp-cutoff diffraction model for the scattering of the strongly absorbing nuclear cores. Simple, closed expressions for the transfer differential cross sections are obtained. Unlike the earlier work, these expressions are valid for arbitrary angular momentum transfers, and intrinsic spins are included. When the zero-range limit is used or the mass of the transferred particle is neglected, the model predicts extreme diffraction oscillations in the angular distributions. However, if finite-range and recoil terms are retained, then, at sufficiently high energies and large angular momentum transfers, the theory gives strong damping of the diffraction oscillations. The resulting structureless angular distributions fall off with a $\frac{1}{q^3}$ dependence on the linear momentum transfer $q$, in excellent agreement with experiment. The theory is applied to the recent experimental results of Birnbaum, Overley, and Bromley for the ${\mathrm{C}}^{12}$(${\mathrm{N}}^{14}$, ${\mathrm{N}}^{13}$)${\mathrm{C}}^{13}$ reaction. Substantial damping of the angular distributions is predicted.