Microscopic study of intrinsic vorticity in atomic nuclei

The description of collective motion in nuclei is usually performed within a quantal fluid dynamical framework. In such an approach the concept of velocity field plays a central role. In this thesis the intrinsic vortical part of such a field is studied. After a survey of some results obtained within a classical mechanics approach, a microscopic semi-quantal formalism generalizing the so-called Routhian approximation, is developed to describe the coupling of such a field with a global rotation of the nuclear density. This formalism is illustrated for a simple example of vortical field due to Chandrasekhar in three cases: semi-classical approximation a la Wigner, harmonic approximation for the mean field, Hartree-Fock approximation using a Skyrme nucleon-nucleon effective interaction. The core of the physical discussion is concerned here with the harmonic mean field approximation, in particular as far as a potential fingerprint for the quantization of such intrinsic vortical modes is concerned in terms of the existence of a staggering of gamma transition energies within some superdeformed bands. In this thesis the study within the Hartree-Fock approximation consisted in building a numerical code and validating it by comparison with the results obtained within the harmonic approximation. (author)