Analysis of the Independent Particle Model approach to Nuclear Densities

TL;DR

This paper critically examines the use of the Darwin-Fowler approximation within the statistical independent particle model for nuclear densities, highlighting its inconsistencies and advocating for combinatorial approaches for better microscopic accuracy.

Contribution

The study compares traditional and recent approaches to nuclear density modeling, emphasizing the limitations of the Darwin-Fowler approximation and promoting combinatorial methods for improved consistency.

Findings

Darwin-Fowler approximation can be theoretically inconsistent in some IPM applications.

Combinatorial IPM approaches offer better microscopic consistency.

Some results based on Darwin-Fowler are coincidental rather than valid.

Abstract

We present an analysis of the use of the Darwin-Fowler approximation in connection with the statistical IPM, by comparing the results of our recent studies with the occupation number approach (OCN) and some traditional statistical independent particle model (IPM) approaches. The analysis of level density works based on the statistical IPM reveals that the use of the the Darwin-Fowler approximation, in some of them, is theoretically inconsistent and some of their results should rather be considered as theoretical coincidences with other consistent approaches, than proofs of their validity. We conclude that, in general, the use of the Darwin-Fowler approximation with the statistical IPM should be used criteriously or, if possible, avoided altogether and suggest that the combinatorial IPM approaches have important advantages over the other models and formalisms analyzed in this paper, especially regarding the consistency of the microscopic description of the nuclear structure and dynamics of non highly excited systems.