Level density within a micro-macroscopic approach

TL;DR

This paper derives a statistical level density for nucleonic systems using a micro-macroscopic approach, bridging the gap between the Fermi gas model and finite systems, and compares theoretical predictions with experimental data.

Contribution

It introduces a micro-macroscopic derivation of level density beyond the standard Fermi gas model, incorporating shell corrections and semiclassical theory.

Findings

The level density transitions between grand-canonical and micro-canonical limits.

The inverse level density parameter K is calculated and matches experimental data.

Shell corrections significantly influence the level density calculations.

Abstract

Statistical level density $\rho(E,A)$ is derived for nucleonic system with a given energy $E$, particle number $A$ and other integrals of motion in the micro-macroscopic approximation beyond the standard saddle-point method of the Fermi gas model. This level density reaches the two limits; the well-known Fermi gas grand-canonical ensemble limit for a large entropy $S$ related to large excitation energies, and the finite micro-canonical limit for a small combinatorical entropy $S$ at low excitation energies. The inverse level density parameter $K$ as function of the particle number $A$ in the semiclassical periodic orbit theory, taking into account the extended Thomas-Fermi and Strutinsky shell corrections, is calculated and compared with experimental data.