Generalized second-order Thomas-Fermi method for superfluid Fermi systems

Using the (h) over bar expansion of the Green's function of the Hartree-Fock-Bogoliubov equation, we extend the secondorder Thomas-Fermi approximation to generalized superfluid Fermi systems by including the density-dependent effectivemass 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.