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

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.

💡 Research Summary

The manuscript investigates the phenomenon of shape coexistence (SC) across a broad swath of even‑even nuclei with proton numbers Z = 38–84, employing a non‑relativistic self‑consistent mean‑field framework. The authors use the Hartree‑Fock‑Bogoliubov (HFB) theory as implemented in the HFBTHO code, together with the Skyrme‑SKI3 energy density functional and a mixed volume‑surface pairing interaction (V₀ = ‑300 MeV·fm³, α = 0.5). A large configuration space (N_max = 20, 500 quasiparticle states, β₂ = 0.3) and a quasiparticle cut‑off of 60 MeV ensure numerical convergence.

The central hypothesis is that shape coexistence originates from particle‑hole (p‑h) excitations: as the neutron or proton number varies, specific single‑particle orbitals move relative to the Fermi surface, turning from occupied (hole) to unoccupied (particle) or vice‑versa. When a group of orbitals undergoes such a transition, multi‑particle‑multi‑hole (np‑nh) configurations are generated, leading to two (or more) low‑lying collective bands with distinct deformation but comparable energies.

The authors systematically scan isotopic and isotonic chains, plotting the single‑particle energies of relevant proton and neutron orbitals together with their occupation probabilities. Several distinct “islands” of SC emerge:

1. Neutron‑induced SC (proton p‑h excitations) appear around the major proton shell closures Z = 82 and Z = 50. In the Z = 78–82 region (Pt, Hg, Pb, Po isotopes) the 1h₁₁/₂ (11/2