Search for the Skyrme-Hartree-Fock solutions for chiral rotation in N=75 isotones

A search for self-consistent solutions for the chiral rotational bands in the N=75 isotones {sup 130}Cs, {sup 132}La, {sup 134}Pr, and {sup 136}Pm is performed within the Skyrme-Hartree-Fock cranking approach using SKM* and SLy4 parametrizations. The dependence of the solutions on the time-odd contributions in the energy functional is studied. From among the four isotones considered, self-consistent chiral solutions are obtained only in {sup 132}La. The microscopic calculations are compared with the {sup 132}La experimental data and with results of a classical model that contains all the mechanisms underlying the chirality of the collective rotational motion. Strong similarities between the Hartree-Fock and classical model results are found. The suggestion formulated earlier by the authors that the chiral rotation cannot exist below a certain critical frequency is further illustrated and discussed, together with the microscopic origin of a transition from planar to chiral rotation in nuclei. We also formulate the separability rule by which the tilted-axis-cranking solutions can be inferred from three independent principal-axis-cranking solutions corresponding to three different axes of rotation.