The Spacing of Energy Levels in Light Nuclei

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≤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-Z|. Finally, Tables VII and VIII show the dependence of the level spacing on total angular momentum and on |N-Z| in the several isobaric series with A=10, 11, 12, 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=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-Z|=0, Be⁸ has 87 levels, C¹² 192 and O¹⁶ has 60 in the energy range 0-23 Mev. In the series $A=4n$ the level density is considerably greater for |N-Z|=2 than for |N-Z|=0; the reverse is true in the series $A=4n+2$. For odd nuclei the level density is practically independent of |N-Z| up to an excitation energy of 20 Mev, but for higher excitation energies it increases with |N-Z|.