A coupled-channel study of the five-nucleon system is performed with the resonating-group method. The channels which are explicitly considered are the $d+{}_{}{}^3{}_{}{}^{}\mathrm{He}$ (or $d+{}_{}{}^3{}_{}{}^{}\mathrm{H}$) and the $p+\alpha$ (or ($n+\alpha$) channels. Three- and more-body breakup channels are not included in the calculation, but their effects are crudely taken into account by the introduction of phenomenological imaginary potentials into the formulation. The nucleon-nucleon potential used is purely central, but does yield correct values for the two-nucleon effective-range parameters. Differential scattering and reaction cross sections are calculated at various energies. The result shows that for the $d+{}_{}{}^3{}_{}{}^{}\mathrm{He}$ and $p+\alpha$ differential scattering cross sections, the calculated values in general agree quite well with the experimental data. For the $d+{}_{}{}^3{}_{}{}^{}\mathrm{He}\rightleftarrows p+\alpha$ differential reaction cross sections, the comparison between theory and experiment is somewhat less satisfactory. Although the general features of the experimental angular distributions are well reproduced, the magnitude of the calculated cross section is somewhat too low.

[NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}\mathrm{}(d,d)\mathrm{}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}\mathrm{}(d,p)\mathrm{}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}\mathrm{}(p,d)\mathrm{}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}\mathrm{}(p,p)\mathrm{}$, $E=0-50\mathrm{}$ MeV; calculated $\sigma \left(\theta \right)$. Resonating-group method; coupled-channel calculation.]

• Received 10 September 1973

DOI:https://doi.org/10.1103/PhysRevC.9.56