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Semidassicd expansions for Green functions, sell-energy, phasespace density and density are given and discussed. The many-body problem was treated in tbe relativistic HartrtcFock approximation with a Lagrangian with a standard OBE potential structure including the possibility of space-dependent couplings. The expansions are obtainedby formulating themany-body problemin the mixed poaitionmomentum ( W i p e r ) reprerentstion and application of the h-WignerKirkwood expansion scheme. The resulting self-consistency problems for the zeroth and second order are formulated in three versions.

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The Wigner-Kirkwood semiclassical expansion of the relativistic nuclear Hartree-Fock theory is generalized for finite temperatures by utilizing the spectral representation of the Green function for non-zero temperatures. The expansion is described in greater detail up to second order and the thermostatic properties of nuclear systems are discussed in the same order. For finite nuclear systems static Hartree-Fock calculations at finite temperature describe a hot nucleus in equilibrium with an external vapour. A subtraction scheme is needed to extract the properties of the hot nucleus from those of the system 'gas+hot nucleus'. In the spectral representation method we achieve this goal by subtracting the parts of the occupation probabilities which are related solely to the external gas (vapour phase).

The central-depression parameter is determined by fitting the charge density distributions in lead isotopes to a three-parameter Fermi distribution. The central-depression parameter increases with the number of neutrons due to the isovector coupling channel of the nuclear interaction and its dependency on density.