Anomalous Backward Alpha-Scattering

The elastic $\ensuremath{\alpha}$ scattering to backward angles has been studied for $^{40,42,44,48}\mathrm{Ca}$ between 40.7 and 72.3 MeV. The cross sections for $^{40}\mathrm{Ca}$ are larger than those for the higher isotopes up to the highest energies. They show backward increases that disappear above 50 MeV. The enhancement factor for $^{40}\mathrm{Ca}$ over $^{42,44}\mathrm{Ca}$ varies smoothly with energy. $^{48}\mathrm{Ca}$ does also show a backward cross-section enhancement over $^{42,44}\mathrm{Ca}$. $\ensuremath{\alpha}$-cluster rotational bands in the $^{44}\mathrm{Ti}$ compound state, four-nucleon correlations in $^{40}\mathrm{Ca}$, and the $l$-dependent optical model are discussed as approaches to understand the anomaly. The rotator model appears to agree qualitatively with the experimental data. It involves rotational bands extending at least up to $J=16$ in $^{44}\mathrm{Ti}$.