Theory of Nuclear Level Density

We have compared the level density of a nuclear model deduced from a statistical analysis with the results of the exact counting of the levels of the same model. The tables of levels of ${\mathrm{Ne}}^{20}$ given by Critchfield and Oleksa have been used as a test of the statistical theory. A new derivation of the level density is presented. It starts, as usual, from the independent-particle model. However, it differs from the previous treatments in two respects: (a) the exact states of the nucleons in the central potential are kept throughout the calculations instead of being replaced by a continuous distribution; (b) the effect of mutual interactions of the nucleons of the Majorana, Bartlett, or Heisenberg type is taken into account in the long-range approximation. With these modifications, the statistical theory agrees very well with the exact counting of the levels, both for the total density and for the density of the levels having a given angular momentum. It is shown that the replacement of the nucleon states by a continuous distribution introduced in most previous derivations, and the neglect of the Majorana forces can produce very large errors. An interpretation is presented of the distribution of angular momentum among nuclear levels in terms of rotations of the whole nucleus as a rigid body.