Binomial level densities

Abstract

It is shown that nuclear level densities in a finite space are described by a continuous binomial function, determined by the first three moments of the Hamiltonian, and the dimensionality of the underlying vector space. Experimental values for ${}^{55}$Mn, ${}^{56}$Fe, and ${}^{60}$Ni are very well reproduced by the binomial form, which turns out to be almost perfectly approximated by Bethe's formula with backshift. A proof is given that binomial densities reproduce the low moments of Hamiltonians of any rank: A strong form of the famous central limit result of Mon and French. Conditions under which the proof may be extended to the full spectrum are examined.

4 pages 2 figures Second version (previous not totally superseeded)

References in corpus (2)

• Particle-Number Reprojection in the Shell Model Monte Carlo Method: Application to Nuclear Level Densities
• Canonical form of Hamiltonian matrices

Cited by in corpus (8)

• The Shell Model as Unified View of Nuclear Structure
• Large-scale prediction of the parity distribution in the nuclear level density and application to astrophysical reaction rates
• Microscopic calculations of nuclear level densities with the Lanczos method
• Behavior of shell-model configuration moments
• Canonical form of Hamiltonian matrices
• Simple models for shell-model configuration densities
• Combinatorial Level Densities from a Microscopic Relativistic Structure Model
• Complexity of Nuclear States for 48Ca