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Shell and cluster structures in $^{20}$Ne in the variation of multiple bases of the antisymmetrized molecular dynamics

Takayuki Myo, Mengjiao Lyu, Qing Zhao, Masahiro Isaka, Niu Wan, Hiroki Takemoto, Hisashi Horiuchi, Akinobu Doté

TL;DR

The paper introduces a multicool variation of antisymmetrized molecular dynamics (AMD) to variationally optimize multiple AMD bases simultaneously, enabling a unified microscopic description of shell-like and cluster structures in $^{20}$Ne. By combining AMD with angular-momentum projection and a pseudo-potential–based orthogonalization for excited states, the authors describe six bands ($K^\pi=0^+_{1-4},0^-,2^-$) and reveal both deformed mean-field and cluster components, including a shell-like $0^+_2$ state previously hard to obtain. The results reproduce overall trends in $B(E2)$ and $E0$ transitions and illustrate how clustering and deformation compete across bands, with density distributions illustrating $^{16}$O+$\alpha$ and $^{12}$C+$2\alpha$ configurations. Remaining energy discrepancies for some bandheads point to the need for deformed Gaussian nucleon wave packets and improved treatment of $^{12}$C, suggesting clear paths for further refinement of a fully microscopic description of $^{20}$Ne.

Abstract

We investigate the structures of $^{20}$Ne in the variation of the multiple bases of the antisymmetrized molecular dynamics (AMD). In this method, the multiple AMD bases are superposed and optimized simultaneously in the total-energy variation. This scheme is beneficial for describing the various configurations in $^{20}$Ne. In the results, we confirm the shell and cluster structures in the $K^π=0^+_{1-4}$ bands, such as the deformed states in the $K^π=0^+_{1,4}$ bands with the $α$ cluster development, and the spherical shell-like states in the $K^π=0^+_2$ band, the latter of which is difficult to describe in the previous AMD calculations imposing the quadrupole deformation. We evaluate the monopole and quadrupole transitions in these states. The negative parity states of $^{20}$Ne with $K^π=0^-$ and $2^-$ are discussed in relation to the shell and cluster structures. As a result, six kinds of the $K^π$ bands in $^{20}$Ne are described comprehensively in the microscopic framework of nuclei.

Shell and cluster structures in $^{20}$Ne in the variation of multiple bases of the antisymmetrized molecular dynamics

TL;DR

The paper introduces a multicool variation of antisymmetrized molecular dynamics (AMD) to variationally optimize multiple AMD bases simultaneously, enabling a unified microscopic description of shell-like and cluster structures in Ne. By combining AMD with angular-momentum projection and a pseudo-potential–based orthogonalization for excited states, the authors describe six bands () and reveal both deformed mean-field and cluster components, including a shell-like state previously hard to obtain. The results reproduce overall trends in and transitions and illustrate how clustering and deformation compete across bands, with density distributions illustrating O+ and C+ configurations. Remaining energy discrepancies for some bandheads point to the need for deformed Gaussian nucleon wave packets and improved treatment of C, suggesting clear paths for further refinement of a fully microscopic description of Ne.

Abstract

We investigate the structures of Ne in the variation of the multiple bases of the antisymmetrized molecular dynamics (AMD). In this method, the multiple AMD bases are superposed and optimized simultaneously in the total-energy variation. This scheme is beneficial for describing the various configurations in Ne. In the results, we confirm the shell and cluster structures in the bands, such as the deformed states in the bands with the cluster development, and the spherical shell-like states in the band, the latter of which is difficult to describe in the previous AMD calculations imposing the quadrupole deformation. We evaluate the monopole and quadrupole transitions in these states. The negative parity states of Ne with and are discussed in relation to the shell and cluster structures. As a result, six kinds of the bands in Ne are described comprehensively in the microscopic framework of nuclei.
Paper Structure (15 sections, 9 equations, 10 figures, 9 tables)

This paper contains 15 sections, 9 equations, 10 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Theoretical methods
  3. Antisymmetrized molecular dynamics (AMD)
  4. Variation of multiple AMD basis states
  5. Hamiltonian
  6. Results
  7. Energy variation
  8. Energy spectrum
  9. $K^\pi=0^+_1$
  10. $K^\pi=0^+_2$
  11. $K^\pi=0^+_3$
  12. $K^\pi=0^+_4$
  13. $K^\pi=0^-$
  14. $K^\pi=2^-$
  15. Summary

Figures (10)

  • Figure 1: Intrinsic energy (left) and radius (right) of the total wave function of $^{20}$Ne with positive parity state. The strength $\lambda$ of the pseudo potential changes.
  • Figure 2: Intrinsic energy (left) and radius (right) of the total wave function of $^{20}$Ne with negative parity state. The strength $\lambda$ of the pseudo potential changes.
  • Figure 3: Intrinsic density distributions of the representative configurations of $^{20}$Ne for the positive parity state. The upper four panels (lower four panels) show the ground state (the excited state with $\lambda=1000$ MeV). Units of densities and axes are fm$^{-3}$ and fm, respectively. The deformation parameters $\beta$ of the configurations are shown at the bottom of each panel.
  • Figure 4: Excitation energy spectrum of $^{20}$Ne for the experiment (black) tilley98 and the multicool calculation (red) in units of MeV.
  • Figure 5: Intrinsic density distributions of the representative configurations of $^{20}$Ne ($0^+_1$) in the $K^\pi=0^+_1$ band. Units of densities and axes are fm$^{-3}$ and fm, respectively. The deformation parameters $\beta$ and the squared overlaps with the $0^+_1$ state in units of % are also shown at the bottom of each panel.
  • ...and 5 more figures