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

A search for self-consistent solutions for the chiral rotational bands in the $N=75$ isotones ${}^{130}\mathrm{Cs}$, ${}^{132}\mathrm{La}$, ${}^{134}\mathrm{Pr}$, and ${}^{136}\mathrm{Pm}$ is performed within the Skyrme-Hartree-Fock cranking approach using ${\mathrm{SKM}}^{*}$ 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 ${}^{132}\mathrm{La}$. The microscopic calculations are compared with the ${}^{132}\mathrm{La}$ 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.