Islands of shape coexistence for Z=38-84 in a non-relativistic mean-field approach using Hartree-Fock-Bogoliubov theory

TL;DR

This work demonstrates that islands of shape coexistence predicted by covariant density functional theory persist when analyzed with a non-relativistic Hartree-Fock-Bogoliubov approach using the Skyrme-SKI3 functional. By tracking proton and neutron single-particle levels relative to the Fermi energy and identifying particle-hole transitions, the authors map neutron- and proton-induced SC across Z=38–84, uncovering both known regions and new adjacent domains. The results reinforce the microscopic p-h excitation mechanism as a robust predictor of SC and reveal nuanced region-by-region behavior across the nuclear chart, with overall good agreement with DDME2 while highlighting areas sensitive to the functional and pairing details. These findings strengthen the theoretical basis for SC and provide a broader, functionally diverse set of predictions to guide future experiments and cross-model validations.

Abstract

Based on the microscopic mechanism of the particle-hole (p-h) excitations in the proton and neutron single-particle energy levels relative to the Fermi energy, a search for islands of shape coexistence (SC) is performed over a wide range of even-even nuclei from Z=38 to 84 using non-relativistic self-consistent mean-field with the Hartree-Fock-Bogoliubov (HFB) theory using the Skyrme-SKI3 functional. The results of the present study show that neutron-induced islands of SC, corresponding to proton p-h excitations, are found around the magic numbers Z=82 and Z=50, centered at the relevant neutron midshells of N=104 and N=66 respectively, while proton-induced islands of SC, corresponding to neutron p-h excitations, are found around the neutron numbers N=90 and N=60, centered at the relevant proton midshells Z=66 and Z=38 respectively. In addition, islands of SC due to both neutron and proton particle-hole excitations are found around N=40, Z=40. The results of the present study are compared with the results of covariant density functional theory using the DDME2 functional, using the same p-h mechanism. The islands of SC that appeared in the CDFT work with the DDME2 functional are corroborated by the present study with the Skyrme-SKI3 functional, thus confirming the robustness of the particle-hole excitations mechanism in searching for islands of SC. In addition, the current study revealed new regions of SC, adjacent to the earlier islands and expanding their shores.

Figures (16)

• Figure 1: (Color online) Left column: single-particle energies of the proton orbitals of $1h_{11/2}$ relative to the Fermi energy as a function of the neutron number $N$ obtained by non-relativistic mean-field HFB theory with Skyrme-SKI3 functional for $Z=78$-84 isotopes. Right column: occupation probability of the same proton orbitals. See Sec. III.A.1 for further discussion.
• Figure 2: (Color online) Same as Fig. 1, but for the proton orbitals $3s_{1/2}$ and $2d_{3/2}$. See Sec. III.A.1 for further discussion.
• Figure 3: (Color online) Same as Fig. 1, but for the proton orbital $1h_{9/2}$. See Sec. III.A.1 for further discussion.
• Figure 4: (Color online) Same as Fig. 1, but for the proton orbital $2d_{5/2}$. See Sec. III.A.1 for further discussion.
• Figure 5: (Color online) Same as Fig. 1, but for the proton orbital $1g_{7/2}$. See Sec. III.A.1 for further discussion.