The Inherent Geometry of the Nuclear Hamiltonian

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.