Nine target nuclei ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{24,26}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28,30}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{40,44}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$ have been studied by the ($\alpha ,2\mathrm{}\alpha$) reaction at an incident beam energy of 90 MeV. Energy resolution of 250-300 keV full width at half-maximum permitted identification of many excited states, although transitions to the ground state consistently dominated the spectra. The ground state angular correlations for equal outgoing energies and angles were similar in shape over this mass region although the magnitude decreased by a factor of 10 from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ to ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$. A phenomenological distorted wave impulse approximation calculation successfully describes most of the angular and energy correlations. A conspicuous failure of the calculation occurs in the energy correlation predictions for recoil momenta greater than 0.6 ${\mathrm{fm}}^{-1\mathrm{}}$. Spectroscopic results are compared with those from $\alpha$ pickup reactions. It is seen that both reactions give nearly the same $\alpha$ clustering mass dependence. Plane wave impulse approximation analysis suggests that the principle parent of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ in an $\alpha$ particle model is the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ground state rather than the first excited state as found in the $\alpha$ pickup reactions.

PACS numbers:

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{24,26}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28,30}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{40,44}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$ ($\alpha ,2\mathrm{}\alpha$), $E_{\alpha }=90\mathrm{}$ MeV, measured energy and angular correlations; DWIA, PWIA analysis, $\alpha$ cluster spectroscopy.

• Received 15 September 1975

DOI:https://doi.org/10.1103/PhysRevC.13.20