The Thomas-Fermi method with applications to the nucleus is revisited. Incorporation of new developments like the treatment of fluctuations and correlations and nuclear pairing will be described. Level densities, response functions and density-density correlations are presented explicitly.

The variational content of the Wigner–Kirkwood ℏ expansion of the density matrix is analyzed in mean field approximation. A new variational method based on a strict expansion of the energy density in powers of ℏ is established. It is applied to the case of fermions moving in an external potential, as well as to the self-consistent problem in semi-infinite matter. The standard density functional theory is reviewed and contrasted with the new method.

The curvature energy coefficient of the nuclear mass formula a(c) is first calculated for the model case of a Fermi gas bounded by an external Woods-Saxon potential. The semiclassical theory of Wigner and Kirkwood is used and a(c) is found to be close to zero. It is, however, shown that this low value is due to the lack of self-consistency of the potential. When available, the results of the model compare very well with quantal values and the extrapolation to the spherical cavity (billiard) checks with the value for a(c) known from the Balian-Bloch theory. Second, the selfconsistent case is generalised to finite range forces. No indication is found that this modifies the fact that all theoretical values for a(c) are larger than about 7 MeV which is an order of magnitude above the empirical value.

Constraints on the photon production calculated by kinetic approaches are studied by means of sum rules at finite temperature for simple quantum systems. For the square-well potential the exact production rate is compared with its semi-classical limit in order to introduce the principle problem. For the scattering of hard spheres the photon-production cross section is derived exactly by a partial-wave expansion. This serves to study the more realistic example of a gas of hard spheres. The corresponding kinetic-photon production rates are found to violate the sum rules, due to a singular behaviour at small gamma energies. Thus the hypothesis of incoherent free scattering is not valid in that range because of destructive interferences which quench the production rates significantly. For the application to nuclear collisions at intermediate energies these quenching effects are found to be important for gamma energies even up to a few hundred MeV.

On the basis of an approximate O(4) invariance of the nonperturbative QCD vacuum we investigate in a phenomenological bag percolation model when hadrons become deconfined. Our estimates show that the necessary temperatures and hadronic densities should be higher than commonly assumed.

The phase-space distribution of semi-infinite nuclear matter is expanded in an \ensuremath{\Elzxh} series analogous to the low-temperature expansion of the Fermi function. Besides the usual Wigner-Kirkwood expansion, oscillatory terms are derived. In the case of a Woods-Saxon potential, a smallness parameter is defined, which determines the convergence of the series and explains the very rapid convergence of the Wigner-Kirkwood expansion for average (nuclear) binding energies.

The Wigner function of half infinite nuclear matter using the infinite wall and the Woods Saxon potentials is calculated. The oscillatory structure is investigated in detail. The accuracy of several semiclassical approximations to the Wigner function is discussed.

The nuclear phase-space distribution is calculated in a semi-classical approximation using the inverse Laplace transformation of the Bloch density. For a local Woods-Saxon potential, both the phase-space and the momentum distributions are shown as functions of the temperature.

First the technique of partial ħ-resummation is used to obtain semiclassical current distributions of slowly-rotating normal fluid nuclei. We find that the average intrinsic current flows mainly in the nuclear surface. The analogy with the Bohr-van Leeuven theorem of diamagnetism is pointed out. Strutinsky- and temperature-averaged calculations are in good agreement with the semiclassical results. Secondly we study rotating superfluid nuclei and find in semiclassical approximation analytic closed expressions for the currents using a deformed harmonic-oscillator potential. The currents pass with increasing gap continuously from rigid-rotation flow to irrotational flow patterns. Analogous results hold true for the moment of inertia. For a fixed value of the gap our formulas for the moment of inertia interpolate smoothly between irrotational flow and rigid-body values as a function of deformation.

The pairing effects are included in the calculation of the currents in a rotating nucleus by means of the single particle density. The correction to the density due to the rotating field may be shared into two parts : the first one depends only on the constant pairing field Ɗ but leads to no current in the laboratory frame for high Ɗ values. The second part depends on the reaction of the pairing field to the rotationnal field and leads to the expected irrotationnal current flow.

Nous montrons cornent la partie moyenne de la transEormée de Wigner de p correspondant à un potentiel Woods-Saxon peut être calculée semi-classiquement.Nous trouvons une diffusivité dans l'espace de phase appréciable mais toujours bien plus petite que l'énergie de Fermi, ce qui justifie le développement en -5 à la Wigner-Kirkwood.En utilisant ce fait, nous proposons et réalisons une nouvelle méthode semi-classique pour le problème Hartree-Fock qui est directement basée sur le développement en 5 de Wigner-Kirkwood.En conséquence, nous n'avons pas besoin d'une fonctionnelle 7 I p 1 .Abstract -It is shown how the smooth part of the Wigner transform of p corresponding to a Woods-Saxon potential can be calculated semiclassically.We find that its surface thickness in phase space is appreciable but always much smaller than the Fermi energy thus justifying the Wigner-Kirkwood 5 expansion.Using this fact we propose and perform a new semiclassical Hartree-Fock method directly based on the Wigner-Kirkwood expansion.No functional ~[ p ] is therefore needed.

Semiclassical fission barrier calculations are presented. Monopole vibrating nuclei ‘see’ effectively a reduced fission barrier. Mass parameters for superfluid nuclei are given in the semiclassical approximation. It is shown that intrinsic currents of rotating nuclei flow in the surface only. The gap equation is solved in the local density approximation and it is found that nuclear superfluidity is located in the nuclear surface. Momentum distributions of nucleons in nuclei are calculated and found to be strongly diffuse and distorted Fermi spheres in the nuclear surface.

The phase-space distribution of nucleons in a nucleus is calculated semi-classically. The Fermi distribution is found to become strongly diffuse, approaching the nuclear surface. Furthermore, the distribution turns out to be very anisotropic in the surface, being more diffuse for momenta perpendicular to the surface than for those lying in the tangential plane to the surface.

The Wigner-Kirkwoodℏ-expansion of the Wigner transform of the Bloch density can be resummed in the case of non local potentials if we keep only up to second order derivatives of the Wigner transform of the non-local potential with respect to the phase space variables. We also investigate a second approximation to the Bloch density where care has been taken with respect to a consistentℏ expansion. For a one dimensional example we calculate the smooth part of the density and the corresponding energy demonstrating that both approximations to the Bloch-density yield well defined average densitiesand energies.

We study semiclassical approximations to the density matrix of a system of Fermions in a one body potential. We derive an expression for the propagator in terms of first and second derivatives of the potential. Our result is thus exact for a harmonic oscillator potential and is equivalent to a partial resummation of the Wigner-Kirkwoodh-expansion. It leads to densities which are well-defined also in the classically forbidden region.

The Faddeev equations for three nucleons are iterated up to third order using separable interactions: the Tabakin potential for the first order and the Yamaguchi potential for the other orders. This method is applied to the quasi-free scattering 2H(p, 2p)n and 2H(s, np)p. Apparent convergence of the rescattering series is obtained for incident lab energies Elab ⪆ 40 MeV and the shape and magnitude of the experimental results are thus reproduced.