Octupole deformation in quasiparticle states of odd-mass and odd-odd nuclei

As a follow up of [Phys. Scr. 99 055305 (2024)], where we studied axial octupole shapes in two-quasiparticle states of even-even nuclei, we investigate this type of shapes in odd-mass and odd-odd well-deformed nuclei, using the Skyrme-Hartree-Fock-BCS approach with selfconsistent blocking and a constraint on the expectation value Q 30 of the axial octupole moment operator. To interprete the pattern of the resulting deformation energy curve as a function of Q 30 , we extend the perturbative mechanism of Ref. [1]. We deduce selection rules which can predict, from the single-particle spectra at Q 30 = 0, whether in a given multi-quasiparticle state the deformation energy curve has a local minimum at a vanishing or a finite value of Q 30 . The predictions of this perturbative mechanism are compared with actual Skyrme-Hartree-Fock-BCS calculations with a constraint on the expectation value Q 30 . Overall we obtain a qualitative agreement and we show that quantitative predictions are limited by the role of pairing correlations and strong octupole coupling between quasi-degenerate members of a single-particle parity doublet.