Novel and simple description for a smooth transition from $\alpha$-cluster wave functions to $jj$-coupling shell model wave functions

Abstract

We propose an improved version of Antisymmetrized Quasi-Cluster Model (AQCM) to describe a smooth transition from the $\alpha$-cluster wave function to the $jj$-coupling shell model wave function and apply it to the ground state of ${}^{12}$C. The cluster-shell transition in ${}^{12}$C is characterized in AQCM by only two parameters: $R$ representing the distance between $\alpha$ clusters and the center of mass, and $\Lambda$ describing the break of $\alpha$ clusters. The optimal AQCM wave function for the ground state of ${}^{12}$C is an intermediate state between the three-$\alpha$ cluster state and the shell model state with the $p_{3/2}$ subshell closure configuration. The result is consistent with that of the Antisymmetrized Molecular Dynamics (AMD), and the optimal AQCM wave function quantitatively agrees with the AMD one, although the number of degrees of freedom in AQCM is significantly fewer.

11 pages, 6 figures

References in corpus (6)

• Chiral effective field theory and nuclear forces
• Recent developments in no-core shell-model calculations
• Shell Model in the Complex Energy Plane
• Shell Structure of Exotic Nuclei
• Toward understanding the microscopic origin of nuclear clustering
• Simplified modeling of cluster-shell competition in ${}^{20}$Ne and ${}^{24}$Mg

Cited by in corpus (22)

• Microscopic Clustering in Light Nuclei
• Effects of $\alpha$-cluster breaking on 3$\alpha$ cluster structures in ${}^{12}$C
• Consistent description of 12C and 16O using finite range three-body interaction
• Improved version of simplified method for including tensor effect in cluster models
• The possibility of ${}^{14}$C cluster as a building block of medium mass nuclei
• Non-trivial effect for the large radius at the dripline of Oxygen isotopes
• Examination of the stability of a rod-shaped structure in ${}^{24}$Mg
• Explicit inclusion of spin-orbit contribution in THSR wave function
• Density profiles near nuclear surface of ${}^{44,52}$Ti: An indication of $\alpha$ clustering
• Imprints of $\alpha$ clustering in the density profiles of ${}^{12}$C and ${}^{16}$O
• Evidence of bicluster structure in the ground state of ${}^{20}$Ne
• ${}^{12}\mathbf{C}+{}^{16}\mathbf{O}$ molecular resonances at deep sub-barrier energy
• Role of Tensor Interaction as Salvation of Cluster Structure in ${}^{44}$Ti
• ${}^8$He and ${}^9$Li cluster structures in light nuclei
• Consistent description for cluster dynamics and single-particle correlation
• Tensor correlations in ${}^4$He and ${}^8$Be with antisymmetrized quasi cluster model
• Nuclear clustering and the electron screening puzzle
• Cluster-shell competition and effect of adding hyperons
• Persistence of cluster structure in the ground state of ${}^{11}$B
• $\alpha$-cluster excited states in ${}^{32}$S
• 4$\alpha$ linear-chain state produced by ${}^9$Be+${}^9$Be collision
• 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