Determine the energetically favored nuclear pasta shape

Determine which nuclear pasta shape is energetically favored at each baryon density by comparing the converged energies of all candidate structures, rather than only obtaining optimized configurations for individually prescribed shapes.

Background

The nuclear-pasta calculations use guiding potentials to stabilize prescribed sphere, rod, and slab configurations at fixed baryon density and proton fraction. Consequently, each reported solution is optimal only within the selected shape and is not necessarily the global ground state.

Identifying the equilibrium pasta phase requires energy comparisons among all relevant candidate geometries at each density. The paper explicitly leaves this comparison for future work, so the phase selection and associated phase boundaries remain unresolved within the presented calculations.

References

Because the shape is imposed in this way, the solutions reported below are the optimal configurations for each given shape, not necessarily the global ground state at that density; determining which shape is energetically favored at a given $n_\text{B}$ requires comparing the converged energies of all candidate structures, which we leave to future work.

— Neural-Network-Based Variational Method in Nuclear Density Functional Theory: Application to the Kohn--Sham method  (2609.00836 - Yoshimura et al., 1 Sep 2026) in Section 3.3, Nuclear pasta phases

The continuous advancement of high-precision measurement methods is driven by these unresolved fundamental questions, including the exploration and characterization of such exotic cluster configurations, the potential existence of $\alpha$-cluster Bose-Einstein condensation at the nucleon level, and the critical influence of cluster structures on the nuclear equation of state (EoS) in low-density astrophysical environments.

— Signals for Nuclear Solid-Liquid Phase Transition in Clustering Nuclei  (2609.05145 - Cao et al., 4 Sep 2026) in Introduction