The resonating-group method is used to study the $\alpha +{}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ system. The cluster internal functions used are translationally invariant antisymmetrized products of single-particle wave functions of the lowest configuration in harmonic-oscillator wells, with width parameters chosen to yield the correct rms radii of both the $\alpha$ and the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ clusters. A generator-coordinate technique is employed to derive the integrodifferential equation which governs the relative motion between the clusters. The result shows that a fairly satisfactory description of the ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ rotational bands can be obtained. In addition, it is found that, with the introduction of a phenomenological imaginary potential to take reaction effects into account, the calculation also yields differential scattering cross sections which agree rather well with experimental data.

[NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\alpha ,\alpha )$; calculated phase shifts and $\sigma \left(\theta \right)$. Resonating-group method with generator-coordinate technique.]

• Received 31 March 1976

DOI:https://doi.org/10.1103/PhysRevC.14.23