Nucleon Transfer with Oxygen Ions Below and Near the Coulomb Barrier

Excitation functions have been measured at ${\theta }_{\mathrm{lab}}={170}^{\circ }$ for the reactions ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$)${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$ ($E_{\mathrm{lab}}=56.0\mathrm{} \mathrm{to} 63.0$ MeV), ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$)${}_{}{}^{89}{}_{}{}^{}\mathrm{Y}$ (42.5 to 50.0 MeV), and ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$(${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$)${}_{}{}^{141}{}_{}{}^{}\mathrm{Ce}$ (56.0 to 61.0 MeV) proceeding to low excited states. Analysis has been made using the sub-Coulomb distorted-wave Born-approximation theory of Buttle and Goldfarb with inclusion of Coulomb correction terms in the form factor and the Buttle-Goldfarb approximation for recoil corrections. Good fits are obtained to the excitation functions at the lower energies. Normalization at these energies determines an essentially invariant quantity, namely the joint probability for the transferred nucleon being at radius $R_1$ with respect to the first core nucleus and radius $R_2$ with respect to the second, where $R_1\equiv \alpha \left[\frac{{A_1}^{\frac{1}{3}}}{({A_1}^{\frac{1}{3}}+{A_2}^{\frac{1}{3}})}\right]$ and