Statistical nuclear properties (level densities, spin distributions)

Abstract

A general overview is given on the phenomenological methods used to describe the level densities in nuclei. Two well-known two-parameter formulas of level densities, the Back-Shifted Fermi Gas (BSFG) model and the Constant Temperature (CT) model, were used. A common ingredient of both is the spin distribution function, which contains in Ericsons's parametrization the spin-cutoff parameter σ. A realistic description of the parameters of both spin distribution function and the two level density models has been obtained by fitting the experimental data of 310 nuclei between 18F and 251Cf, consisting of the complete level schemes at low excitation energies and the s-wave neutron resonance spacings at the neutron binding energy. We determine a simple formula for the spin-cutoff parameter as a function of mass number and excitation energy. Also, an even-odd spin staggering in the spin distribution of the even-even nuclei was observed, and described with a simple formula. Using this newly defined spin distribution function, an empirical set of parameters of the BSFG and CT models was determined by fitting both the low-energy levels and the neutron resonance spacings. For these parameters, simple formulas were proposed that involve only quantities available from the mass tables, and allow reasonable estimations of the level density parameters for nuclei far from stability. Both the BSFG and CT models describe equally well the level densities at energies up to at least the neutron binding energy. Finally, we discuss recent experimental evidence that the CT model is the more correct description of the nuclei in the low-excitation energy (pairing) regime.