Distribution functions of a degenerate Fermi gas with allowance for pairing correlations

With the aim of generalizing the Thomas–Fermi statistical method to systems with pairing correlations of superconducting type in the framework of Hartree–Fock–Bogolyubov theory, the quasiclassical method to terms of order $\hbar^3$ inclusively is used to calculate the single-particle distribution function and the distribution function of the pairing correlations of a degenerate Fermi gas. In connection with the solution of this problem, a method of obtaining quasiclassical estimates of operator functions is developed; it is of independent interest and more general than the method of Kirzhnits.