Study of theα+O16system with the resonating-group method

Abstract

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.