Fermi gas description of nuclear level densities

Journal Article · Mon Apr 01 00:00:00 EST 1991 · Annals of Physics (New York); (United States)

DOI:https://doi.org/10.1016/0003-4916(91)90176-9· OSTI ID:5658562

Engelbrecht, C A; Engelbrecht, J R ^[1]

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1. Univ. of Stellenbosch (South Africa)

In this paper the derivation of nuclear level densities from a Fermi gas treatment of the nucleons is surveyed. In fact, there are three classes of Fermi gas models: the infinite, in which an unlimited number of fermions are available for excitation, the finite, in which this number is finite but the single-particle spectrum is unbounded, and the truncated Fermi gas (TFG), where this spectrum consists of a finite number of levels. Exact calculations within the TFG are possible by means of combinatorial methods, while the finite model may be analyzed by assuming that the assumptions of statistical mechanics apply to the numbers of nucleons in a nucleus and then using a saddle point approximation. The standard Bethe formulae actually correspond to the infinite model and apply to the other models only in the low-energy limit. Furthermore, at very low energies they do not approximate any of the models with high accuracy and should there be corrected, as indicated in the text. For high-energy or high-temperature applications, it is essential to take into account the effects of truncation. The TFG is constructed here in a way which accommodates to two main features in which the results for real interacting nucleons should differ from the Fermi gas picture. In order to make the TFG results accessible for practical applications without having to perform the cumbersome combinatorial calculations for each case of interest, simple approximations are presented for the nuclear level densities, as well as the closely related canonical partition functions, as obtained by means of calculations using the truncated Fermi gas model.

• OSTI ID: 5658562
• Journal Information: Annals of Physics (New York); (United States), Vol. 207:1; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
FERMI GAS MODEL
NUCLEI
ENERGY-LEVEL DENSITY
CALCULATION METHODS
CORRECTIONS
EXCITATION
NUCLEONS
PARTITION FUNCTIONS
SADDLE-POINT METHOD
STATISTICAL MECHANICS
BARYONS
ELEMENTARY PARTICLES
ENERGY-LEVEL TRANSITIONS
FERMIONS
FUNCTIONS
HADRONS
MATHEMATICAL MODELS
MECHANICS
NUCLEAR MODELS
663120* - Nuclear Structure Models & Methods- (1992-)