Pear Shape and Tetrahedral Shape Competition in Actinide Nuclei

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Abstract The shape competition and coexistence between the pear-shape octuple and the tetrahedral octupole deformations in actinide nuclei are investigated by employing the realistic nuclear mean-field theory using the phenomenological, so-called ``universal" Woods-Saxon Hamiltonian with newly adjusted parameters containing no parametric correlations. Both types of octupole deformations exhibit significant octupole effects in N=132, N=134, and N=136 nuclei. Nuclear potential energy calculations within the multi-dimensional deformation spaces reveal that the tetrahedral deformation effects generally lead to deeper energy minima in most nuclei with N=134 and N=136. Interestingly, in the nuclei 218 86Rn132, 222 88Ra134, and 222 86Rn136, selected for the illustration of the studied effects, the influence of pear-shape octupole deformation is comparable to that of tetrahedral octupole deformation. Consequently, the coexistence of both kinds of octupole shapes is predicted by the potential energy calculations. In particular, we have reproduced the experimental results known for pear-shape rotational bands obtaining in this way an estimate of the quality of the modelling parametrisation. With the same Hamiltonian, we have predicted the properties of the tetrahedral symmetry rotational bands. To facilitate the possible experiment-theory collaboration we have derived the exact spin-parity tetrahedral-band structures by applying the standard methods of the group representation theory for the Td point-group.