Measurements of the ($\alpha$,$2\alpha$) reaction on ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ targets at $E_{\alpha }=140\mathrm{}$ MeV were made at 20 angle pairs. The quasi-free knockout mechanism appears to dominate the reaction. The experimental data were analyzed with distorted-wave impulse approximation calculations. The factorization approximation employed in the calculations was tested explicitly and found to be valid. The shapes of the calculated energy sharing spectra are in satisfactory agreement with the data. The predicted absolute cross sections were found to be very sensitive to the cluster-core bound state radius parameter, and a bound state radius $R=2.52\mathrm{}{A_c}^{\frac{1}{3}}$ fm is necessary to obtain absolute spectroscopic factors consistent with existing theoretical values. Several possible explanations for this excessive value are suggested. Comparisons are made with other alpha knockout and transfer reactions.

NUCLEAR REACTIONS ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ ($\alpha$,$2\alpha$), $E_{\alpha }=140\mathrm{}$ MeV; measured $\sigma (E_{\alpha 1},E_{\alpha 2},{\theta }_{\alpha 1},{\theta }_{\alpha 2})$ DWIA analysis; deduced absolute spectroscopic factors.

• Received 26 November 1979

DOI:https://doi.org/10.1103/PhysRevC.21.1705