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A search for the self-consistent solutions for the chiral rotational bands in the $ N=75$ isotones, $ ^{130}$Cs, $ ^{132}$La, $ ^{134}$Pr and $ ^{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 considered four isotones, self-consistent chiral solutions are obtained only in $ ^{132}$La. The microscopic calculations are compared with the $ ^{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 HF 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 the 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.

Search for the Skyrme-Hartree-Fock Solutions for Chiral Rotation in N=75 Isotones

P. Olbratowski, J. Dobaczewski, J. Dudek

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Jacek Dobaczewski 2005-12-28