Folding model analysis of the inelastic $\alpha {+}^{12}$C scattering at medium energies, and the isoscalar transition strengths of the cluster states of ${}^{12}$C

Abstract

The complex optical potential and inelastic form factor given by the folding model for the $\alpha {+}^{12}$C scattering are used to calculate the ($\alpha ,{\alpha }^{\prime }$) cross sections for the known isoscalar states of ${}^{12}$C in an elaborate coupled channel approach. The strengths of the form factors for these states are then fine tuned against the ($\alpha ,{\alpha }^{\prime }$) data to deduce the corresponding $E\lambda$ transition strengths. A significant $E2$ transition strength has been obtained for the $2_2^{+}$ state from the present analysis of the ($\alpha ,{\alpha }^{\prime }$) data measured at $E_{\alpha }=240$ and 386 MeV. The $E\lambda$ transition strengths of the $0_2^{+},3_1^{-},0_3^{+},$ and $1_1^{-}$ states were also carefully deduced, and some difference from the results of earlier analyses has been found and qualitatively understood.

Comments: Accepted for publication in Physical Review C