Discrete non-orthogonal shell model for nuclear structure: Towards heavy elements

TL;DR

This work develops the Discrete Non-Orthogonal Shell Model (DNO-SM), a variational framework that uses a discrete set of non-orthogonal Slater determinants to tackle large shell-model spaces while restoring broken symmetries. It systematically compares projection-after-variation and variation-after-projection approaches, demonstrating that variation-after-projection with Thouless parametrization efficiently captures ground-state correlations, including pairing effects. Benchmarks on light nuclei (e.g., 24Mg and 48Cr) show near-exact energies and correct backbending, while applications to proton-rich Mo isotopes reveal a structural transition linked to multiparticle-multihole configurations and three-body forces. The method is further validated by a complete description of the low-lying spectroscopy of the superheavy nucleus 254No, illustrating rotor-like behavior and the viability of DNO-SM in the heavy regime, with broad implications for unified nuclear-structure studies.

Abstract

We present recent developments of the Discrete Non-Orthogonal Shell Model (DNO-SM) for nuclear structure studies far from stability. Exact shell-model solutions are obtained for typical open-shell light sd and pf nuclei using non-orthogonal Slater determinants consistently derived from the variation after projection approach. The latter represents a powerful method to include correlations from particle-hole excitations. Applications to proton-rich nuclei at the N$\sim$Z line show the important role of these correlations to probe the structure transition in the $^{84,86}$Mo isotopes. We finally present a first complete description of low-lying spectroscopy in the superheavy 254 No, reproducing excellently various band structures and isomers in this challenging nucleus.

Figures (4)

• Figure 1: Comparison of the SM and DNO-SM calculations in the backbending pattern up to the angular momentum $J=16$. E$_\gamma$ is the energy of the corresponding gamma.
• Figure 2: Potential energy surfaces for $^{84,86}$Mo. The surfaces are obtained with the DNP-ZBM3 effective interaction. The area of the black circles represents the probability of the $(\beta,\gamma)$ configurations in the ground state wave function.
• Figure 3: $^{254}$No spectrum from the DNO-SM(VAP) calculations compared to the experimental data (EXP). Energies are in keV. For each band, $K$ denotes the total angular momentum projection quantum number.
• Figure 4: $\gamma$-excitation energies ($E_\gamma$) versus angular momentum ($J$) comparison with the experimental data for the yrast rotational band. The left panel corresponds to the full DNO-SM(VAP) calculation reported in Figure \ref{['SM_254No']}. The right panel shows the yrast band with the angular momentum projection of the Hartree-Fock minimum (AMP-HF).