Cluster structures in ${}^{12}$C from global energy density functionals

Abstract

Spectroscopic properties of low-lying states and cluster structures in ${}^{12}$C are analyzed in a "beyond mean-field framework" based on global energy density functionals (EDFs). To build symmetry-conserving collective states, axially-symmetric and reflection-asymmetric solutions of the relativistic Hartree-Bogoliubov equations are first projected onto good values of angular momentum, particle number, and parity. Configuration mixing is implemented using the generator coordinate method formalism. It is shown that such a global microscopic approach, based on a relativistic EDF, can account for the main spectroscopic features of ${}^{12}$C, including the ground-state and linear-chain bands as well as, to a certain approximation, the excitation energy of the Hoyle state. The calculated form factors reproduce reasonably well the available experimental values, and display an accuracy comparable to that of dedicated microscopic cluster models.

arXiv comment10 pages, 6 figures

References in corpus (28)

• Alpha cluster condensation in 12C and 16O
• Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond
• Relativistic Nuclear Energy Density Functionals: adjusting parameters to binding energies
• Structure of A=10-13 nuclei with two- plus three-nucleon interactions from chiral effective field theory
• Microscopic Clustering in Light Nuclei
• A finite range pairing force for density functional theory in superfluid nuclei
• Structure of ground and excited states of ${}^{12}$C
• Correlations beyond the mean field in Magnesium isotopes: Angular momentum projection and configuration mixing
• Evidence for Triangular D_3h Symmetry in 12C
• Cluster structures within Fermionic Molecular Dynamics
• Status of Alpha-Particle Condensate Structure of the Hoyle State
• High precision probe of the fully sequential decay width of the Hoyle state in ${}^{12}$C
• Inelastic form factors to alpha particle condensate states in 12C and 16O: what can we learn ?
• Pair decay width of the Hoyle state and carbon production in stars
• Density Functional Theory studies of cluster states in nuclei
• State-of-the-art of beyond mean field theories with nuclear density functionals
• Hoyle band and $\alpha$ condensation in ${}^{12}\mathrm{C}$
• Remarks on the use of projected densities in the density dependent part of Skyrme or Gogny functionals
• Anatomy of molecular structures in ${}^{20}$Ne
• Bare vs effective pairing forces. A microscopic finite-range interaction for HFB calculations in coordinate space
• Cluster-liquid transition in finite saturated fermionic systems
• Quadrupole and octupole collectivity and cluster structures in neon isotopes
• Alpha Cluster Structure and Exotic States in a Self-Consistent Model for Light Nuclei
• Deformation and cluster structures in ${}^{12}$C studied with configuration mixing using Skyrme interactions
• Beyond mean-field study of elastic and inelastic electron scattering off nuclei
• Reorientation-effect measurement of the first 2${}^{+}$ state in ${}^{12}$C: confirmation of oblate deformation
• Single-particle spatial dispersion and clusters in nuclei
• Clusters and halos in light nuclei

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• Low-energy cluster vibrations in N = Z nuclei
• Shape of 13C studied by the real-time evolution method
• Optimized nuclear energy density functionals including long-range pion contributions
• Covariant energy density functionals with and without tensor couplings at the Hartree-Bogoliubov level
• Symmetry-projected variational calculations with the numerical suite TAURUS II. Configuration mixing of symmetry-projected reference states
• Low-energy monopole strength in spherical and deformed nuclei : cluster and soft modes
• Generator coordinate method for nuclear octupole excitations: status and perspectives
• Signatures of $\alpha$-clustering in ${}^{12}$C and ${}^{13}$C
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• Mean-field approximation on steroids: exact description of the deuteron