Cluster-Model Calculation for Phase Shifts ofα−αScattering

In the framework of the binary alpha cluster model, phase shifts for $s$, $d$, $g$, $i$, and $k$ partial waves for $\alpha -\alpha$ scattering are calculated through the excitation energy of 40 MeV. These are compared with recent experments which appear to suggest the existence of the rotational states with $J^{\pi }=6^{+}, 8^{+}$ of the nucleus ${\mathrm{Be}}^8$, beyond the lowest three states with $J^{\pi }=0^{+}, 2^{+}, \mathrm{and} 4^{+}$. A reasonable agreement is obtained between the calculated phase shifts and the real part of the experimental ones. The present result is also compared with the phase shifts obtained by the phenomenological $\alpha -\alpha$ two-body potential models. A detailed analysis shows that the angular-momentum-dependent but energy-independent core radii of the two-body potential models coincide with the outermost nodes of the scattering functions within the contact distance of two $\alpha$ nuclei. The wave functions within the contact distance do not vanish, however, and hence the repulsive core in a literal sense does not exist. This result is examined in reference to the cluster structure of the ${\mathrm{Be}}^8$ compound nucleus.