Low excitation corrections to the nuclear density of states by statistical techniques

We study a many fermion system in an equispaced nondegenerate single particle spectrum. Using methods of statistical mechanics, we reproduce Bethe's formula for the nuclear density of states along with low excitation corrections by Rademacher to Bethe's formula. We generalize the result for two species of particles and compare with recent results by Leboeuf.

Figure 1

The density of states for one species of particles in a harmonic well. The top curve is Bethe's approximation and the lower curve is with low excitation energy corrections. Crosses represent the exact number of states.

Figure 2

The density of states for two species of particles in a trapped harmonic well. The top curve is Bethe's approximation. Leboeuf's number-theoretic corrections are higher than the evaluation of the density of states by a saddle-point technique, with the latter represented by a solid line. Crosses represent the exact number of states for two sets of particles.