RESTORATION OF ROTATIONAL SYMMETRY BY USING 3-DIMENSIONAL CRANKING

In the three-dimensional cranking approach the deformed nucleus is rotated about any chosen axis, i.e. contrary to the ordinary cranking this axis does not necessarily coincide with one of the principal axes of the nuclear deformation. The inclusion of the three-dimensional cranking term ω · I = ωxIx + ωyIy + ωzIz into the Hartree-Fock-Bogoliubov theory enables one to bui quasiparticle states with non-standard "spin vectors" 〈I〉, thus denoting for simplicity the corresponding cranking expectation value of the angular momentum vector operator I, that may get also non-parallel to the principal axes of deformation. This freedom in the orientation of the spin vector provides us in fact with two Euler angles necessary for transforming cranking states from the body-fixed into the laboratory system. The generator coordinate (GCM) method is applied in order to quantize the system of cranked quasiparticles. As generator basis, a particular family of cranking states is constructed where all members have a common spin vector 〈I〉, but each belonging to a distinct orientation of the deformed mean field in space. Accordingly, the collective variables characterizing the generator basis are two Euler angles and the phase angle of the rotation about the spin vector. Eigenstates of good angular momentum (a.m.) can be found by solving the Hill-Wheeler equation. The physical meaning of this procedure which is different from the usual a.m. projection, becomes transparent by applying of the so-called horizontal expansion (HEX) of Dönau et al. onto the GCM hamiltonian kernel. This expansion finally leads to a practical scheme for extending the cranked Strutinsky mean field approach aiming to recover the broken rotational symmetry. The resulting method allows us to take into account the collective modes analogous to the classical precessional and wobbling motion and to treat the coupling of configurations in the band crossing region. Furthermore, electromagnetic transition amplitudes can be straightforwardly calculated, which is of great importance for interpreting high-spin experiments. © 1990.