Elastic Scattering of Alpha-Particles by Carbon

The ${\mathrm{C}}^{12}(\alpha , \alpha ){\mathrm{C}}^{12}$ differential scattering cross sections were measured in a gas scattering chamber at $\theta (\mathrm{c}.\mathrm{m}.\mathrm{})=171.0\mathrm{}°, 147.2°, 125.5°, \mathrm{and} 92.0°$ with alpha-particles accelerated in the Wisconsin electrostatic generator. Cross sections were measured at alpha-particle energies from 0.5 to 4.0 Mev. For zero spin nuclei bombarded by zero spin particles, each partial wave contributing to the cross section vanishes at some angle except that for $l=0\mathrm{}$. The $P$ wave vanishes at 90.0°, the $D$ wave at 125.3°, the $F$ wave at 140.8°, and the $G$ wave at 149.5°. Thus, by observing the cross sections near these angles it was possible to determine the $J$ values and parities of the levels. Analyzing the data by means of the Wigner-Eisenbud one-level approximation to determine the widths and resonant energies confirmed the qualitative characterization of the levels. With the ${\mathrm{O}}^{16}$ ground state as the energy zero, the $J$ values, parities, and excitation energies of the two levels observed are $J=1^{-}$ at 9.58 Mev and $J=2^{+}$ at 9.835 Mev. The uncertainty in these energies is about 10 kev. The reduced width of the $P$ resonance is approximately 100 percent of the single-particle width, and that of the $D$ resonance is 0.15 percent.