Breaking of the z-signature symmetry in the Hartree-Fock-Bogoliubov formalism. Applications to the dynamics of deformed nuclei

This work concerns the extension of the application domain of microscopic calculations in nuclear structure to phenomena breaking the z-signature symmetry. The approach followed consists in solving the many-body problem by means of the mean-field approximation using the Hartree-Fock-Bogoliubov method. By employing the Gogny nucleon-nucleon interaction, mean-field effects as well as pairing correlations are calculated in a self-consistent way. In order to simplify the iterative resolution of the associated system of non-linear equations, the remaining symmetries of the system are explicitly taken into account. In all studies made up to now, the z-signature symmetry was imposed. The solutions of the HFB problem were eigenstates of the z-signature symmetry, a symmetry related to a rotation of π around the z axis. However, many physical phenomena, as rotational bands based on individual excitations and magnetic dipole collective excitations, break this symmetry. In this work the formalism needed to take into account this symmetry breaking is developed and results are given for the two above phenomena. Theoretical rotational bands are in good agreement with experimental data. Band-heads excitation energies as well as moment of inertia are well reproduced. Concerning magnetic dipole excitations, we show that the low-lying l+ states experimentally observed, are not collective scissor excitations, the latter being found at high excitation energy. An interpretation in terms of rather non-collective hexadecapole excitations coupled to individual excitations is proposed. (author)