Energy Dependence of the Three-Nucleon Transfer Reactions on Light Nuclei

Excitation functions and angular distributions for ($p,\alpha$) reactions on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ have been measured from 19- to 45-MeV incident energy. The mean slope of the integrated cross sections for all the above reactions and for ($p,\alpha$) reactions on ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, and ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ is the same, when plotted as a function of the intermediate-system excitation energy, and is of the type ${[{\left(E_p\right)}_{\mathrm{c}.\mathrm{m}.\mathrm{}}+B_p]}^{-3.75\mathrm{}}$. For the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ targets, the differential and integrated cross sections, which have been measured in energy steps of the order of some hundred keV, show a marked resonant structure with modulations having widths and spacings of the order of 1 MeV. Angular distributions, although presenting a well-developed diffraction pattern especially at forward angles, vary very rapidly with energy, particularly below 30 MeV. The analysis of excitation functions performed with a distorted-wave Born-approximation point triton pickup calculation gives ambiguous results. A statistical Hauser-Feshbach calculation gives too steep a slope which agrees with experimental data only when direct transitions are hindered. The analysis of the excitation functions, performed in the framework of the pre-equilibrium decay model, gives satisfactory results. This could indicate that $\alpha$ emission from light nuclei cannot be treated as a simple direct effect.