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 $R_2\equiv \alpha \left[\frac{{A_2}^{\frac{1}{3}}}{({A_1}^{\frac{1}{3}}+{A_2}^{\frac{1}{3}})}\right]$, $\alpha$ being the distance of closest approach in a head-on collision averaged between incident and final channels. If specific assumptions are made for the geometrical parameters of the bound states, values can be extracted for the product of spectroscopic factors, $S^{\mathrm{}\left(1\right)\mathrm{}} S^{\mathrm{}\left(2\right)\mathrm{}}$; reasonable geometries lead to values of $S^{\mathrm{}\left(2\right)\mathrm{}}$ very close to those previously obtained from light-ion reactions. Above the barrier, the fits to calculations which use nuclear distorted waves are less satisfactory; for optical potentials which give nearly equivalent elastic scattering, the calculations show moderate ambiguity. We believe the leading uncertainty in our analysis is due to the approximate treatment of recoil.

• Received 10 May 1973

DOI:https://doi.org/10.1103/PhysRevC.8.1129