Thomas-Fermi studies of pairing in inhomogeneous systems: nuclear and cold atom systems at overflow

TL;DR

This paper introduces a novel Thomas-Fermi approach for inhomogeneous superfluid Fermi-systems, effectively addressing cases where the Local Density Approximation fails, with applications to neutron stars and cold atom traps.

Contribution

A new semiclassical Thomas-Fermi method for superfluid systems that remains accurate where LDA breaks down, demonstrated through relevant physical examples.

Findings

Pairing is reduced at overflow points in superfluid fermionic systems.

The TF approach aligns well with quantal results and outperforms LDA.

Applications to neutron star crusts and cold atom traps validate the method.

Abstract

A novel Thomas-Fermi (TF) approach to inhomogeneous superfluid Fermi-systems is presented and shown that it works well also in cases where the Local Density Approximation (LDA) breaks down. The novelty lies in the fact that the semiclassical approximation is applied to the pairing matrix elements not implying a local version of the chemical potential as with LDA. Applications will be given to the generic fact that if a fermionic superfluid in the BCS regime overflows from a narrow container into a much wider one, pairing is substantially reduced at the overflow point. Two examples pertinent to the physics of the outer crust of neutron stars and superfluid fermionic atoms in traps will be presented. The TF results will be compared to quantal and LDA ones.