[en] This talk describes recent three-dimensional self-consistent Hartree-Fock calculations. After an introduction providing the basic approximations and the different symmetries, we present an application to quadrupole deformation. We pursue with a study of octupole deformation properties of ²²²Ra and ¹⁴⁴Ba nuclei for which states of good (positive and negative) parity are projected out. Finally we discuss an extension to the study of rotation and high-spin states with the cranked self-consistent Hartree-Fock method. As an example, the ²⁴Mg nucleus is studied as a function of angular momentum from ground state up to fission

[en] In heavy ion collisions it has been possible to obtain composite systems at rather high excitation energies corresponding to temperatures of several MeV. The theoretical studies of these systems are based on concepts borrowed from thermodynamics or statistical physics, such as the temperature. In these lectures, we present the concepts of statistical physics which are involved in the physics of heavy ion as they are produced nowadays in the laboratory and also during the final stage of a supernova collapse. We do not attempt to describe the reaction mechanisms which yield such nuclear systems nor their decay by evaporation or fragmentation. We shall only study their static properties. The content of these lectures is organized in four main sections. The first one gives the basic features of statistical physics and thermodynamics necessary to understand quantum mechanics at finite temperature. In the second one, we present a study of the liquid-gas phase transition in nuclear physics. A phenomenological approach of the stability of hot nuclei follows. The microscopic point of view is proposed in the third part. Starting from the basic concepts derived in the first part, it provides a description of excited or hot nuclei which confirms the qualitative results of the second part. Furthermore it gives a full description of most properties of these nuclei as a function of temperature. Finally in the last part, a microscopic derivation of the equation of state of nuclear matter is proposed to study the collapse of a supernova core

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[en] In heavy ion collisions at energies called Ganil or Sara energies, high excitation composite system formation has been evidenced. Excitation temperatures can reach 6 MeV for the lighter systems. This lecture is aimed at presenting the basic concepts of statistical physics which are underlying heavy ion physics. It includes three great chapters. Statistical mechanics and some elements of thermodynamics are recalled to understand quantum mechanics at a non-zero temperature. A study in the nuclear frame of liquid-gas phase transformation is presented. A phenomenologic application of hot nuclei stability is deriving. At least, a microscopic presentation is proposed: from presented statistical physics concepts, it provides a highly excited nuclei description (or hot nuclei). It allows furthermore a complete description of most of nuclei characteristics in relation with the temperature

[en] We present in this paper the general framework of a method which permits to restore the rotational and particle number symmetries of wave functions obtained in Skyrme HF + BCS calculations. This restoration is nothing but a projection of mean-field intrinsic wave functions onto good particle number and good angular momentum. The method allows us also to mix projected wave functions. Such a configuration mixing is discussed for sets of HF + BCS intrinsic states generated in constrained calculations with suitable collective variables. This procedure gives collective states which are eigenstates of the particle number and the angular momentum operators and between which transition probabilities are calculated. An application to ²⁴Mg is presented, with mean-field wave functions generated by axial quadrupole constraints. Theoretical spectra and transition probabilities are compared to the experiment

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[en] We propose and discuss a prescription suitable to include the contribution of continuum states in mean-field calculations at high temperature

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[en] The TDHF method is half a century old. It may seem paradoxical that it now raises such a flurry of activity in nuclear theory. The reason for this, obviously, is the breakthrough which occurred a few years ago in terms of spectacular numerical solutions. In particular, these solutions exhibited an almost universal coverage of nuclear phenomena, ranging from elastic scattering to fusion, including dissipation and collective motion

[en] Study of superdeformed (SD) rotational bands in the Hg-Pb mass region has been undertaken within the microscopic Hartree-Fock (HF) theory. In this approach, the basic ingredient is an effective nucleon nucleon interaction, which is the only input of the model. The large deformation is set in by a quadrupole constraining operator whose strength is increased until the nucleus reaches a superdeformed equilibrium shape. An overview of this open-quotes isthmusclose quotes of shape isomerism os superdeformation at zero angular momentum will be presented. Rotational bands are then constructed by means of the usual cranking operator. Without pairing, the ground SD band of ¹⁹²Hg has been calculated and identical, or twinned bands, have been obtained in both ¹⁹⁴Hg and ¹⁹⁴Pb. The deexcitation γ-ray energies between these bands differ by at most 2 keV over a range of angular momentum similar to the experimental one. In this calculation, the predicted moment of inertia is only slowly varying with the rotation and does not reproduce the much larger variation observed experimentally. To correct for this behaviour, one has to include pairing correlations. However, it is known that in the simple BCS approximation, the decrease of these correlations is much too fast when the angular momentum is cranked up. To include them in a realistic manner, the HF mean field has been corrected by the Lipkin-Nogami prescription. This amounts to an approximate variation after projection onto the correct nucleon number. Preliminary results show that pairing correlations are still present at spins larger than 40ℎ for the SD band of ¹⁹⁴Pb. The full calculation of the identical bands obtained with pairing correlations in this mass region is under progress