The Inherent Geometry of the Nuclear Hamiltonian

TL;DR

This paper reveals that the symmetries of the nuclear Schrödinger equation align with a face-centered cubic lattice, suggesting a high-density model that combines liquid-drop and independent-particle features for nuclear structure predictions.

Contribution

It demonstrates that nuclear symmetries correspond to a face-centered cubic lattice, unifying liquid-drop and independent-particle models within a lattice framework.

Findings

Nuclear symmetries match face-centered cubic lattice symmetries.

High-density IPM retains liquid-drop and IPM predictive properties.

Lattice model explains nuclear properties with geometric symmetry.

Abstract

The symmetries inherent to the nuclear version of the Schr\"odinger wave-equation are identical to the symmetries of a face-centered cubic lattice, as already noted by Wigner in 1937 in the initial development of the independent-particle model (IPM) of nuclear structure. The significance of the identity is that it implies a high-density version of the IPM that has the gross properties of a liquid-drop, rather than a diffuse, chaotic gas of nucleons. As a consequence, all of the predictive strengths of the liquid-drop model (binding energies, radii, nuclear densities, vibrational states, etc.) and the "independent-particle" predictions of the IPM (nuclear spins, parities, magnetic moments, etc.) are retained in the lattice.