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A simple analytical formula is given to express the transition probability in a quasi-elastic transfer reaction. This formula is derived from the DWBA amplitude, using assumptions based on the fact that the main contribution to the DWBA integral comes from a narrow domain of distances of approach. Recoil effects are taken into account. This method is applied to calculate the excitation functions for one and two-proton transfer reactions induced in209Bi by heavy ions, below and near the barrier. The curves obtained are compared to the excitation functions measured for the production of residual210Po and211At. The corresponding transfer reactions involve excitation energiesE* of the residue lying in the range 0–8 MeV. This excitation energy is taken as a free parameter in the calculation, and the valuesE opt *  which lead to the best agreement between the calculated and experimental curves are consistent with the classical values for the optimum reactionQ-values.

Simple formulae for heavy ion subcoulomb transfer probabilities. Application to one and two-proton transfers in bismuth