LEVEL DENSITIES IN LIGHTER NUCLEI

Abstract

There has been discussion in the literature as to whether the cumulative number of levels in light nuclei varies more nearly as exp(const. [Formula: see text]) or exp(const. E), where E is the excitation energy. The question is examined in this paper. It is found that if one constructs "step diagrams" by plotting the cumulative number versus the energy, both formulas represent the data almost equally well. However, additional consideration of levels counted above neutron and proton binding energies shows that exp(const. [Formula: see text]) fails badly to represent the data, whereas exp(const. E) continues to give good fits. In either case E may be measured above an arbitrary ground-state energy E₀. If the satisfactory formula is written in the form exp(E–E₀)/T, then it is found that the dependence of the slope on mass number may be expressed in approximately the form T⁻¹ = 0.0165A MeV⁻¹, but there are significant deviations from this relation apparently related to shell structure. The intercepts E₀ are quite variable but are roughly clustered according to the oddness or evenness of the neutron and proton numbers of the nucleus.