Angular Distributions and Correlations for Alpha-Particle Scattering by ${\mathrm{C}}^{12}$, ${\mathrm{Mg}}^{24}$, and ${\mathrm{Ca}}^{40}$

Angular distributions of alpha particles scattered from ${\mathrm{Mg}}^{24}$ and ${\mathrm{Ca}}^{40}$ are reported and effective interaction radii are obtained, based on the Born approximation for elastic scattering and direct-interaction theory for inelastic scattering. For ${\mathrm{Mg}}^{24}$, levels at 0, 1.37, 4.2, and 6.3 Mev yield interaction radii of 6.4, 6.55, 6.5, and 6.5, respectively (units of ${10}^{-13\mathrm{}}$ cm). Evidence is presented in support of the assignment of the 6.3-Mev level to ${\mathrm{Mg}}^{24}$ rather than to ${\mathrm{Mg}}^{25}$ or ${\mathrm{Mg}}^{26}$, with spin and parity 1 -. For ${\mathrm{Ca}}^{40}$, levels at 0 and 4.48 Mev yield interaction radii of 6.65 and 7.3, respectively. Alpha-gamma angular correlations, which correspond closely to those predicted on the basis of direct-interaction theory, were obtained for ${\mathrm{C}}^{12}$ (4.43-Mev level) and for ${\mathrm{Mg}}^{24}$ (1.37-Mev level). For ${\mathrm{Ca}}^{40}$ (4.48-Mev level) the correlation corresponds qualitatively to that predicted for a 1 - level with cascade decay through an intermediate state to ground level. Further evidence is presented which supports this interpretation. A higher level in ${\mathrm{Ca}}^{40}$ is observed at 8.4 Mev. All alpha bombardments were made at 43 Mev incident energy.