Thomas-Fermi approximation to pairing in finite Fermi systems. The weak coupling regime

TL;DR

This paper introduces a semiclassical Thomas-Fermi approach to model pairing in finite Fermi systems, capturing position and size effects, and explaining the behavior of nuclear gaps, especially near drip lines and in neutron star crusts.

Contribution

It develops a new semiclassical Thomas-Fermi theory for pairing in finite Fermi systems that includes size dependence and shell fluctuations, improving upon previous models.

Findings

Thomas-Fermi gaps average quantal arch structures.

Shell fluctuations can nearly recover quantal gap patterns.

Pairing is significantly reduced at the nuclear drip line.

Abstract

We present a new semiclassical theory for describing pairing in finite Fermi systems. It is based on taking the $\hbar \to 0$, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition to the position dependence of the Fermi momentum, the size dependence of the pairing force is also taken into account in this theory. Along isotopic chains the Thomas-Fermi gaps average the well known arch structure shown by the quantal gaps. This structure can be almost recovered in our formalism if some shell fluctuations are included in the level density. We point out that at the drip line nuclear pairing is strongly reduced. This fact is illustrated with the behavior of the gap in the inner crust of neutron stars.