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.

Accepted for publication in Phys. Lett. B

References in corpus (5)

• Nuclear rainbow scattering and nucleus-nucleus potential
• Concepts of alpha-particle condensation
• Missing monopole strength of the Hoyle state in the inelastic $\alpha$+${}^{12}$C scattering
• Microscopic study of the isoscalar giant resonances in 208Pb induced by inelastic alpha scattering
• Probing the isoscalar excitations of 12C with inelastic alpha scattering

Cited by in corpus (8)

• Symmetry-guided large-scale shell-model theory
• Hoyle state and rotational features in Carbon-12 within a no-core shell model framework
• Nuclear Alpha-Particle Condensates
• Understanding emergent collectivity and clustering in nuclei from a symmetry-based no-core shell-model perspective
• 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
• Relation between transition density and proton inelastic scattering by ${}^{12}$C target at $E_p=$ 65 and 200 MeV
• Systematic study for relation between nuclear structure and reaction in ${}^{10}$Be nucleus
• Low-energy ${}^{12}$C continuum states in three-$\alpha$ model