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Static nuclear properties associated with a Skyrme-like force in the SkM parametrisation have been extensively studied for both spherical and deformed nuclei through Hartree-Fock plus BCS calculations. These calculations include in particular the determination of the s°°Pu fission barrier up to the second saddle point. The validity of some currently used approximations to the Hartree-Fock approach (self-consistent Strutinsky approach, expectation value method and twostep iterative method) has also been assessed . The results of the microscopic calculations have been systematically compared to the corresponding self-consistent results obtained within the extended Thomas-Ferrai framework. Such semiclassical calculations also allow a proper characterisation of the SkM force surface properties (in the liquid drop or droplet model sense) . Whereas ground-state radii and multipole moments are found in excellent agreement with experimental data, binding energies are systematically too high and fission barriers are significantly too low. These two defects are shown to be correlated through the too low surface tension of the force. A modified parametrisation is discussed which heals both these defects while keeping intact the good reproduction of other properties . This constitutes a first step in the direction of current efforts to determine a better parametrisation of Skyrme-like forces .

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Introduction 277 4.2. Bulk properties of spherical nuclei 2. Justification of the semiclassical approach based on the 4.3. Deformation energies and fission barriers of heavy microscopical Skyrme-Hartree-Fock formalism 280 nuclei 2.1. The Skyrme-HF energy density 280 4.4. Adjustment of the force SkM* 2.2. Separation of shell effects 284 4.5. Perturbative inclusion of shell effects 2.3. Strutinsky-averaging as a microscopical link to the 5. Liquid drop model type expansion of the ETF binding ETF model 285 energy 2.4. Summary 286 5.1. Leptodermous expansion of the energy for symmetric 3. The extended Thomas-Fermi model 286 nuclei 3.1. The Wigner-Kirkwood expansion 286 5.2. Semi-infinite nuclear matter calculations 3.2. The ETF functionals r[pJ and J[p] 288 5.3. Discussion of the droplet model 3.3. Density variation method and discussion of the ETF 6. Extension to nuclear systems at finite temperature Euler equations 290 6.1. Earlier approaches 4. Semiclassical variational calculations for finite nuclei 295 6.2. The ETF model at finite temperature 4.1. Parametrisation of the nuclear densities 295 6.3. Discussion of the ETF Euler equation at T>0 tWork partially supported by Deutsche Forschungsgemeinschaft (Az Br 733/1, 2-2).

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