Angular distributions and ranges of heavy products from quasi-elastic transfer reactions induced by heavy ions inBi209

The projected ranges, angular distributions and range distributions at each laboratory angle have been measured for one-, two-, and three-proton transfer reactions induced in ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ by various heavy ions from ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ to ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$. The products observed were ${}_{}{}^{210}{}_{}{}^{}\mathrm{Po}$, ${}_{}{}^{211}{}_{}{}^{}\mathrm{At}$, and ${}_{}{}^{211}{}_{}{}^{}\mathrm{Rn}$. They were identified by their radioactive decay characteristics. Some complementary experiments have been performed using T1 and Au targets. The angular and energy distributions have been used to identify the most probable reaction paths leading to the observed isotopes. At low incident energy, these reaction paths appear to be those which correspond to the most favorable energetics, for all incident ions. At higher energies, more complex reaction channels have a significant contribution to the production of the observed isotopes. For all incident ions, the position of the angular distribution maximum ${\theta }_{max}$ is governed by the value of the ratio $\frac{E}{B}$ of the incident energy to the interaction barrier. The variation of ${\theta }_{max}$ versus $\frac{E}{B}$ is very similar to that of the rainbow angle corresponding to elastic scattering. This might indicate that quasi-elastic transfer and rainbow scattering occur for similar distances of closest approach between colliding nuclei.