Accurate and perspicuous formulas are derived for the density of states of a degenerate system of any number of types of fermions moving in arbitrary periodic single-particle energy-level schemes. The results are of the standard form with the modification that the excitation energy is to be replaced by an "effective energy." The effective energy contains an additive correction which depends explicitly on the structure and ground-state occupation of the periodic level sequences. The spin-dependent level-density formula for two kinds of particles should be useful in the correlation of observed nuclear level densities with shell-model level sequences. The present work generalizes, unifies, and simplifies earlier treatments of related problems.

• Received 28 April 1969

DOI:https://doi.org/10.1103/PhysRev.187.1193