Energy-density functionals inspired by effective-field theories: Applications to neutron drops

TL;DR

This paper extends energy-density functionals inspired by effective-field theories to finite neutron systems, benchmarking their predictions against ab initio results and analyzing their effectiveness compared to traditional Skyrme functionals.

Contribution

It introduces a generalization of EFT-inspired energy-density functionals for finite neutron systems, including adjustments based on ab initio data and analysis of their predictive accuracy.

Findings

Two functionals closely match ab initio results for total energies and densities.

The generalized functionals outperform some traditional Skyrme functionals.

Effective masses and other properties are accurately predicted by the new functionals.

Abstract

New energy-density functionals (EDFs) inspired by effective-field theories (EFTs) have been recently proposed. The present work focuses on three of such functionals which were developed to produce satisfactory equations of state for nuclear matter. We aim to extend these functionals to treat finite systems including a spin-orbit contribution and pairing correlations. We illustrate here a first step towards this direction, namely a generalization of such functionals tailored to perform applications to neutron gases confined in harmonic traps. Sets of available \textit{ab initio} results are used as benchmark pseudo-data for adjusting the additional parameters (with respect to the nuclear matter case) that have to be introduced for finite-size systems. Several quantities are predicted and compared to \textit{ab initio} and other EDF results such as, for instance, total energies, potentials, and density profiles. The associated effective masses are also analyzed. In cases where \textit{ab initio} results are available, two of these functionals globally provide predictions which are close one to the other as well as to \textit{ab initio} values. It is shown that, in general, this is not the case for several currently used Skyrme functionals. Directions for improving the third functional are discussed.