Recent global analyses of ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ have incorporated both elastic-scattering and $\beta$-decay data in addition to direct measurements. In that context, it has been shown that an improvement in the available elastic-scattering data could help determine the contribution of the two subthreshold states, $6.92(2^{+})$ and $7.12(1^{-})$ MeV, and with excellent statistics could restrict resonance parameters above the threshold. To this end angular distributions of ${}^{12}\mathrm{C}(\alpha ,\alpha ){}^{12}\mathrm{C}$ in the $\alpha$-energy range of 2.6–8.2 MeV, at angles from 24${}^{\circ }$ to 166${}^{\circ }$ have been measured at the University of Notre Dame using an array of 32 silicon detectors. Details of the experiment are reported. In the present analysis, the phase shifts have been determined from our previously reported $R$-matrix fit to these data. The uncertainties in the $R$-matrix phase shifts ($\ell =0\dots 6)$ are derived by a new Monte Carlo analysis technique as described in the article. We provide these phase shifts here for general use, in particular for the improved analysis and extrapolation of the $\alpha$ radiative capture to low energies.

• Received 23 September 2008

DOI:https://doi.org/10.1103/PhysRevC.79.055803