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Theoretical Studies of alpha Clustering in Nuclei and Beyond

Takaharu Otsuka, Alexander Volya, Naoyuki Itagaki

Abstract

This article comprises three sections. Section 2 starts with a review of ab initio no-core shell model calculations by Monte Carlo Shell Model. Alpha clustering arises for 8,10,12Be and 12C with Daejeon16 and JISP16 interactions, even in the ground state of 12C. Hoyle state is shown to be dominated by alpha clustering in triangular configurations. As the ground and Hoyle states show strong deformations, they are good cases to investigate rotational excitations. As an original work, the recently proposed fully quantum (mechanical) formulation for deformation and rotation is extended to cluster states. Dual rotational modes are proposed: compact-object and distant-object rotations. The former is found in many heavy nuclei, whereas the latter can be found for clustering states. While 8Be is an example for the latter, 12C is a rare example that both modes appear. Atomic molecules and hadrons can be viewed similarly. Possible relevance to fission is mentioned. Section 3 presents a general framework for an extended no-core shell model with cluster-nucleon configuration interaction, combining traditional shell-model-like configurations with explicit microscopic configurations representing cluster degrees of freedom. The section reviews the microscopic origins of cluster substructures in light nuclei, emphasizing how nucleonic degrees of freedom, nucleon-nucleon interactions, and continuum coupling naturally extend the traditional shell model into configuration-interaction frameworks that incorporate clustering and reaction dynamics. Section 4 presents that although the cluster structure is robust in Be-C nuclei, some jj-coupling shell model components are mixed in the ground state of 12C. Using the antisymmetrized quasi cluster model, we can clearly model this competition between the cluster and shell components. The spin-orbit interaction is key.

Theoretical Studies of alpha Clustering in Nuclei and Beyond

Abstract

This article comprises three sections. Section 2 starts with a review of ab initio no-core shell model calculations by Monte Carlo Shell Model. Alpha clustering arises for 8,10,12Be and 12C with Daejeon16 and JISP16 interactions, even in the ground state of 12C. Hoyle state is shown to be dominated by alpha clustering in triangular configurations. As the ground and Hoyle states show strong deformations, they are good cases to investigate rotational excitations. As an original work, the recently proposed fully quantum (mechanical) formulation for deformation and rotation is extended to cluster states. Dual rotational modes are proposed: compact-object and distant-object rotations. The former is found in many heavy nuclei, whereas the latter can be found for clustering states. While 8Be is an example for the latter, 12C is a rare example that both modes appear. Atomic molecules and hadrons can be viewed similarly. Possible relevance to fission is mentioned. Section 3 presents a general framework for an extended no-core shell model with cluster-nucleon configuration interaction, combining traditional shell-model-like configurations with explicit microscopic configurations representing cluster degrees of freedom. The section reviews the microscopic origins of cluster substructures in light nuclei, emphasizing how nucleonic degrees of freedom, nucleon-nucleon interactions, and continuum coupling naturally extend the traditional shell model into configuration-interaction frameworks that incorporate clustering and reaction dynamics. Section 4 presents that although the cluster structure is robust in Be-C nuclei, some jj-coupling shell model components are mixed in the ground state of 12C. Using the antisymmetrized quasi cluster model, we can clearly model this competition between the cluster and shell components. The spin-orbit interaction is key.
Paper Structure (23 sections, 65 equations, 21 figures, 5 tables)

This paper contains 23 sections, 65 equations, 21 figures, 5 tables.

Table of Contents

  1. Introduction
  2. First-principle realization of $\alpha$ clustering and dual rotational modes in quantum many-body systems
  3. First-principles realization of $\alpha$ clustering in $^{8}$Be and $^{12}$C
  4. General description of rotational excitations within quantum many-body theory
  5. Rotational excitations built on cluster states
  6. Rotational mode in $^{8}$Be
  7. Coexistence of two rotational modes in $^{12}$C
  8. Summary
  9. Prospects 1: Atomic molecules
  10. Prospects 2: Fission
  11. A review on cluster model approaches
  12. Introduction
  13. Cluster configurations
  14. Center of mass and boosting
  15. Cluster channels
  16. ...and 8 more sections

Figures (21)

  • Figure 1: Schematic illustrations of $\alpha$ clustering in atomic nuclei, for a$^{4}$ He=$\alpha$ particle, b$^{8}$Be, and c$^{12}$C (three possible cases, i, ii and iii). The green areas represent atomic nuclei allowing some movements of $\alpha$ clusters. Taken from otsuka_2022 with permission.
  • Figure 2: Level energies of a $^{8}$Be and b $^{12}$C (left) Experimental dataensdf12CBE2, and (right) theoretical results in each panel. Taken from otsuka_2022 with minor changes with permission.
  • Figure 3: Density profiles of $^{12}$C with that of $^{4}$ He=$\alpha$ particle The density profiles for $^{12}$C were obtained from intrinsic states, and in panels ${\bf i} - {\bf i}$, eigenstates are decomposed according to shapes using T-plot analysis. Taken from otsuka_2022 with permission.
  • Figure 4: Overall picture of ground and Hoyle states of $^{12}$C
  • Figure 5: Two-dimensional representation of matter density profile of $^{12}$C compared to $^{4}$He and $^{8}$Be Densities of $^{4}$He and $^{8}$Be are shown in the far left part. Panels c - i correspond, respectively, to Panels c - i of Fig. \ref{['fig:12C_density']}. Two-way arrow indicates the distance between two peaks of $^{8}$Be density with the length $\sim$3.6 fm, and is also shown for some panels for $^{12}$C. Modified from figures in otsuka_2022 with permissions.
  • ...and 16 more figures