Generalized Second-Order Thomas-Fermi Method for Superfluid Fermi Systems

TL;DR

This paper extends the second-order Thomas-Fermi approximation to superfluid Fermi systems by incorporating effective mass and spin-orbit effects, enabling more accurate modeling of inhomogeneous superfluid Fermi systems.

Contribution

The paper introduces a generalized second-order Thomas-Fermi method for superfluid Fermi systems, including density-dependent effective mass and spin-orbit potential effects.

Findings

Implemented and tested correction terms across different energy intervals.

Demonstrated applicability to finite nuclei calculations.

Enhanced modeling accuracy for inhomogeneous superfluid Fermi systems.

Abstract

Using the $\hbar$-expansion of the Green's function of the Hartree-Fock-Bogoliubov equation, we extend the second-order Thomas-Fermi approximation to generalized superfluid Fermi systems by including the density-dependent effective mass and the spin-orbit potential. We first implement and examine the full correction terms over different energy intervals of the quasiparticle spectra in calculations of finite nuclei. Final applications of this generalized Thomas-Fermi method are intended for various inhomogeneous superfluid Fermi systems.