Low-energy ${}^{12}$C continuum states in three-$\alpha$ model

Abstract

The electric multipole strength distributions for transitions from the ${}^{12}\mathrm{C}(0_1^{+})$ ground state to $3\alpha$ ($0^{+}$, $1^{-}$, $2^{+}$, and $3^{-}$) continuum states are studied in terms of $3\alpha$ model. Several sets of the $3\alpha$ Hamiltonian are introduced phenomenologically with conventional $\alpha$-$\alpha$ interaction potentials and $3\alpha$ potentials with different range parameters. The transition strength distributions are obtained from wave functions of $3\alpha$ bound- and continuum states calculated by the Faddeev three-body formalism. From these strength distributions, the resonance parameters (energy, $3\alpha$-decay width, and transition strength) of $3\alpha$ resonance states are extracted. Dependencies of these observables on interaction potential models are studied to examine the introduced interaction models. Using the transition strength distributions, excitation-energy spectra in the ${}^{12}\mathrm{C}(\alpha ,{\alpha }^{\prime })3\alpha$ reaction are calculated to compare with experimental data.

arXiv comment23 pages, 7 figures

References in corpus (25)

• Tables of E2 Transition Probabilities from the first $2^{+}$ States in Even-Even Nuclei
• Microscopic Clustering in Light Nuclei
• Structure and rotations of the Hoyle state
• Structure of ground and excited states of ${}^{12}$C
• Unambiguous Identification of the Second 2+ State in 12C and the Structure of the Hoyle State
• Status of Alpha-Particle Condensate Structure of the Hoyle State
• Pair decay width of the Hoyle state and carbon production in stars
• Ab Initio Description of Open-Shell Nuclei: Merging No-Core Shell Model and In-Medium Similarity Renormalization Group
• Hoyle band and $\alpha$ condensation in ${}^{12}\mathrm{C}$
• Decay and structure of the Hoyle state
• Three-body calculations of triple-alpha reaction
• Breathing-like excited state of the Hoyle state in ${}^{12}\mathrm{C}$
• Missing monopole strength of the Hoyle state in the inelastic $\alpha$+${}^{12}$C scattering
• Coordinate space proton-deuteron scattering calculations including Coulomb force effects
• Monopole excitation of the Hoyle state and linear-chain state in 12C
• Reorientation-effect measurement of the first 2${}^{+}$ state in ${}^{12}$C: confirmation of oblate deformation
• No evidence of an 11.16 MeV 2+ state in 12C
• Hindrance of the excitation of the Hoyle state and the ghost of the $2_2^{+}$ state in ${}^{12}$C
• Consistency between the monopole strength of the Hoyle state determined by structural calculation and that extracted from reaction observables
• Investigating the predicted breathing-mode excitation of the Hoyle state
• Low Energy Proton-Deuteron Scattering with a Coulomb-Modified Faddeev Equation
• Precision measurement of the $E2$ transition strength to the 2${}_1^{+}$ state of ${}^{12}$C
• Three-body bremsstrahlung and the rotational character of the 12C-spectrum
• Monopole transition strength function of ${}^{12}$C in three-$\alpha$ model
• Understanding the total width of the $3_1^{-}$ state in ${}^{12}\mathrm{C}$

Cited by in corpus (1)

• Examination of the $\alpha$-cluster breaking in the four $0^{+}$ bands of ${}^{12}$C with the variation of multiple bases of the antisymmetrized molecular dynamics