Natural Units For Nuclear Energy Density Functional Theory

TL;DR

This paper applies naive dimensional analysis to nuclear energy density functionals, revealing most parameters are natural and consistent with theoretical expectations, aiding in constraining and improving functional fits.

Contribution

It introduces a method to assess the naturalness of Skyrme functional parameters using chiral effective theory-based units, providing insights into their hierarchy and optimization.

Findings

Most parameters are natural with dimensionless constants near one.

Deviations indicate functional deficiencies or optimization issues.

The scale aligns with other nuclear physics determinations.

Abstract

Naive dimensional analysis based on chiral effective theory, when adapted to nuclear energy density functionals, prescribes natural units and a hierarchy of contributions that could be used to constrain fits of generalized functionals. By applying these units, a large sample of Skyrme parametrizations is examined for naturalness, which is signaled by dimensionless coupling constants of order one. The bulk of the parameters are found to be natural, with an underlying scale consistent with other determinations. Significant deviations from unity are associated with deficiencies in the corresponding terms of particular functionals or with an incomplete optimization procedure.