On the Density of Energy Levels of Heavy Nuclei

Abstract

The present calculation of the density of energy levels of a heavy nucleus is based on the statistical model of Van Vleck. As in Bethe's calculation, the particles are assumed to move in a simple potential hole, but the depth of the hole varies with the velocity of the particle. If exchange forces act, the interaction energy of a given particle with the remainder of the nucleus decreases as the velocity of the particle increases. This results in a lower density of states of the individual particles at the top of the Fermi distribution. Bethe's formula for the density of excited levels of the nucleus as a whole may be applied to the present situation if this change in the density of the individual particle states is taken into account. The spacing between the levels is over a hundred times larger than that found by Bethe, and, if one uses the Gamow value for the radius of a radioactive nucleus (∼9×${10}^{-13\mathrm{}}$ cm), is much too large to be reconciled with the frequent occurrence of resonance levels for the capture of slow neutrons. If one uses the new value for the radius suggested by Bethe (∼13×${10}^{-13\mathrm{}}$ cm), the present theory gives more reasonable values.