Hindrance of the excitation of the Hoyle state and the ghost of the $2_2^{+}$ state in ${}^{12}$C

Abstract

While the Hoyle state (the isoscalar $0_2^{+}$ excitation at 7.65 MeV in ${}^{12}$C) has been observed in almost all the electron and $\alpha$ inelastic scattering experiments, the second $2^{+}$ excited state of ${}^{12}$C at $E_{\mathrm{x}}\approx 10$ MeV, believed to be an excitation of the Hoyle state, has not been clearly observed in these measurements excepting the high-precision \aap experiments at $E_{\alpha }=240$ and 386 MeV. Given the (spin and isospin zero) $\alpha$-particle as a good probe for the nuclear isoscalar excitations, it remains a puzzle why the peak of the $2_2^{+}$ state could not be clearly identified in the measured \aap spectra. To investigate this effect, we have performed a microscopic folding model analysis of the \ac scattering data at 240 and 386 MeV in both the Distorted Wave Born Approximation (DWBA) and coupled-channel (CC) formalism, using the nuclear transition densities given by the antisymmetrized molecular dynamics (AMD) approach and a complex CDM3Y6 density dependent interaction. Although AMD predicts a very weak transition strength for the direct $(0_1^{+}\to 2_2^{+})$ excitation, our detailed analysis has shown evidence that a weak \emph{ghost} of the $2_2^{+}$ state could be identified in the 240 MeV \aap data for the $0_3^{+}$ state at 10.3 MeV, when the CC effects by the indirect excitation of the $2_2^{+}$ state are taken into account. Based on the same AMD structure input and preliminary \aap data at 386 MeV, we have estimated relative contributions from the $2_2^{+}$ and $0_3^{+}$ states to the excitation of ${}^{12}$C at $E_{\mathrm{x}}\approx 10$ MeV as well as possible contamination by $3_1^{-}$ state.

Comments: Accepted for publication in Phys. Lett. B