Symmetry Effects in the Spacing of Nuclear Energy Levels

The results of Wigner on mass defects and stability relations make possible a calculation of level density for intermediate nuclei ($A<\mathrm{}60\mathrm{}$) which takes properly into account the dependence of nuclear energies on symmetry character. In general, a configuration of neutrons and protons in single-particle orbits contains many different types of symmetry compatible with the exclusion principle. The various symmetry types arising from one configuration all have the same kinetic energy, but differ in potential energy; decreasing symmetry (increasing number of nodes) is associated with decreasing potential energy. Level densities for the different nuclear types are tabulated. The results indicate a marked increase of density for increasing isotopic number in an isobaric series. Transmutation experiments on isobars should make possible a test of the theory.