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Mapped $spdf$ interacting boson model for quadrupole-octupole collective states in nuclei

K. Nomura

TL;DR

This work develops a mapped $spdf$-IBM framework that incorporates dipole ($p$) bosons to describe quadrupole-octupole collectivity in heavy nuclei. By constraining Gogny-D1M HFB energy surfaces in the $(\beta_1,\beta_2,\beta_3)$ space and mapping them onto the IBM energy surface in the coherent-state basis, the authors determine the $spdf$-IBM Hamiltonian parameters and transition operators, enabling predictions of spectra and transition rates for $^{218-230}$Ra and $^{220-232}$Th. The inclusion of $p$ bosons lowers the negative-parity yrast levels, improves the $1^-_1$ energy ordering, and enhances the description of $B(E1)$, $D_0$, and $B(E3)$ systematics, especially near the transitional region around $N\approx 132$. However, challenges remain for certain nuclei (notably $^{224}$Ra) in reproducing $E1$ strengths, indicating that further refinement of the $E1$ operator and broader applicability to other mass regions are needed.

Abstract

Dipole bosons are introduced in the interacting boson model (IBM) by means of the self-consistent mean-field method. The constrained mean-field calculations employing a given nuclear energy density functional yield the potential energy surfaces in terms of the axially-symmetric quadrupole-octupole, dipole-quadrupole, and dipole-octupole deformations. By mapping these energy surfaces onto the expectation values of the IBM Hamiltonian in the coherent state of the interacting $s$, $p$, $d$, and $f$ bosons, strength parameters of the $spdf$-IBM Hamiltonian are determined. In an illustrative application to octupole-deformed actinides $^{218-230}$Ra and $^{220-232}$Th, it is shown that effects of including $p$ bosons in the IBM mapping are to lower significantly negative-parity yrast levels, and to improve descriptions of observed energy-level systematic in nearly spherical and transitional nuclei, and of the behaviors of the reduced electric dipole transitions and intrinsic dipole moments with neutron number.

Mapped $spdf$ interacting boson model for quadrupole-octupole collective states in nuclei

TL;DR

This work develops a mapped -IBM framework that incorporates dipole () bosons to describe quadrupole-octupole collectivity in heavy nuclei. By constraining Gogny-D1M HFB energy surfaces in the space and mapping them onto the IBM energy surface in the coherent-state basis, the authors determine the -IBM Hamiltonian parameters and transition operators, enabling predictions of spectra and transition rates for Ra and Th. The inclusion of bosons lowers the negative-parity yrast levels, improves the energy ordering, and enhances the description of , , and systematics, especially near the transitional region around . However, challenges remain for certain nuclei (notably Ra) in reproducing strengths, indicating that further refinement of the operator and broader applicability to other mass regions are needed.

Abstract

Dipole bosons are introduced in the interacting boson model (IBM) by means of the self-consistent mean-field method. The constrained mean-field calculations employing a given nuclear energy density functional yield the potential energy surfaces in terms of the axially-symmetric quadrupole-octupole, dipole-quadrupole, and dipole-octupole deformations. By mapping these energy surfaces onto the expectation values of the IBM Hamiltonian in the coherent state of the interacting , , , and bosons, strength parameters of the -IBM Hamiltonian are determined. In an illustrative application to octupole-deformed actinides Ra and Th, it is shown that effects of including bosons in the IBM mapping are to lower significantly negative-parity yrast levels, and to improve descriptions of observed energy-level systematic in nearly spherical and transitional nuclei, and of the behaviors of the reduced electric dipole transitions and intrinsic dipole moments with neutron number.

Paper Structure

This paper contains 9 sections, 17 equations, 11 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Theoretical procedure
  3. Results
  4. Potential energy surfaces
  5. IBM parameters
  6. Low-energy spectra
  7. Transition properties
  8. Detailed energy spectra
  9. Conclusions

Figures (11)

  • Figure 1: Potential energy surfaces for $^{218-230}$Ra in terms of the axial quadrupole $\beta_2$ and octupole $\beta_3$ deformations obtained from the HFB method using the Gogny-D1M EDF with the dipole deformation set to $\beta_1=0$, and the corresponding energy surfaces in the $spdf$-IBM. The minimum is indicated by the solid circle, and energy difference between neighboring contours is 0.4 MeV.
  • Figure 2: Same as the caption to Fig. \ref{['fig:b23']}, but for the dipole $\beta_1$ and quadrupole $\beta_2$ deformations with the octupole deformation $\beta_3$ fixed to be the value corresponding to the minimum in the $(\beta_2,\beta_3)$ space with $\beta_1=0$.
  • Figure 3: Same as the caption to Fig. \ref{['fig:b23']}, but for the dipole $\beta_1$ and octupole $\beta_3$ deformations with the quadrupole deformation $\beta_2$ fixed to be the value corresponding to the minimum in the $(\beta_2,\beta_3)$ space with $\beta_1=0$.
  • Figure 4: Mapped $spdf$-IBM $(\beta_2,\beta_3)$-PESs for $^{222}$Ra with the $\beta_1$ deformation being fixed at several different values.
  • Figure 5: Calculated excitation energies for even-spin positive-parity yrast states for $^{218-230}$Ra and $^{220-232}$Th within the mapped $sdf$-IBM and $spdf$-IBM (solid symbols connected by lines). The corresponding experimental values, represented by open symbols, are taken from NNDC data.
  • ...and 6 more figures