  Currently, one application of the mean-field methods in nuclear physics is
the investigation of exotic nuclear symmetries. This is related, in particular,
to the study of nuclear rotation about an axis tilted with respect to the
principal axes of the mass distribution in the Tilted-Axis Cranking (TAC)
model. The present work presents one of the first TAC calculations performed
within fully self-consistent methods. The Hartree-Fock method with the Skyrme
effective two-body interaction has been used. A computer code has been
developed that allows for the breaking of all spatial symmetries of the
solution. As a first application, calculations for the magnetic bands in 142Gd
and for the chiral bands in 130Cs, 132La, 134Pr, and 136Pm have been carried
out. The appearance of those bands is due to a new mechanism of breaking the
spherical symmetry and to the spontaneous breaking of the chiral symmetry,
respectively. The self-consistent solutions for 142Gd confirm the important
role of the shears mechanism in generating the total angular momentum. However,
the agreement with experimental data is not satisfactory, probably due to the
lack of the pairing correlations in the calculations or to the possibly
overestimated deformation. The results obtained for 132La constitute the first
fully self-consistent proof that the nuclear rotation can attain a chiral
character. It has been shown that the chiral rotation can only exist above a
certain critical angular frequency. It has also been checked that the terms of
the Skyrme mean field odd under the time reversal have no qualitative influence
on the results.
