The Spacing of Energy Levels in Light Nuclei

Abstract

The single particle model supplemented by a semiempirical determination of the dependence of potential energy on symmetry character is used to obtain statistical information about the distribution of energy levels in light nuclei ($A\ensuremath{\le}16$). Table II shows the analysis of the lowlying configurations for $A=16$ into states with definite values of the orbital angular momentum and the symmetry character. Similar tables which we have prepared for values of $A<16$ have been omitted because of their length. Tables III to VI give the spin multiplet structure as a function of the symmetry type and the isotopic number $|N\ensuremath{-}Z|$. Finally, Tables VII and VIII show the dependence of the level spacing on total angular momentum and on $|N\ensuremath{-}Z|$ in the several isobaric series with $A=10, 11, 12, \mathrm{and} 13$.The most frequently occurring value of the orbital angular momentum is $L=2$ ($D$ states). Levels with total angular momentum $F=2$ (even nuclei) and $F=\frac{5}{2}$ (odd nuclei) are most closely spaced. The level spacing is not a monotonic decreasing function of $A$; for example, in the series $A=4n$ and $|N\ensuremath{-}Z|=0$, ${\mathrm{Be}}^{8}$ has 87 levels, ${\mathrm{C}}^{12}$ 192 and ${\mathrm{O}}^{16}$ has 60 in the energy range 0-23 Mev. In the series $A=4n$ the level density is considerably greater for $|N\ensuremath{-}Z|=2$ than for $|N\ensuremath{-}Z|=0$; the reverse is true in the series $A=4n+2$. For odd nuclei the level density is practically independent of $|N\ensuremath{-}Z|$ up to an excitation energy of 20 Mev, but for higher excitation energies it increases with $|N\ensuremath{-}Z|$.