Heavy-Ion Transfer Reactions at Low Energies

Simple asymptotic expressions are obtained for the optimum $Q$ value and for the total heavy-ion transfer cross section with optimum $Q$ value at energies well below the barrier. For such reactions transfer processes are predicted to be more important than compound reactions in agreement with measurements performed on the ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ + ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ system. Calculations on transfer reactions between ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, of current interest in nucleo-synthesis, indicate direct reactions to be of no significance.