Low energy shape oscillations of negative parity in the main and shape-isomeric minima in actinides

We study low energy shape oscillations of negative parity in the first and second (isomeric) minima in actinides. As a main tool we use the phenomenological Woods-Saxon potential with a variety of shape deformations. This allows to include a mixing of various multipolarities when considering oscillations with a fixed $K$ quantum number. The phonon energies are determined either from the collective Hamiltonian with the microscopic-macrocopic energy and cranking mass parameters, or from its simplified version with the constant mass parameters. The results for $K^{\pi}=0^-$,$1^-$ in the first minima are in a reasonable agreement with experimental data, including predicted E1 transitions; the $K^{\pi}=2^-$ energies are systematically overestimated. In the second minimum, as compared to the data for $^{240}$Pu and $^{236}$U, our calculated $K=$1,2 energies are overestimated while the $K=0$ energies are three or more times too large. This signals either a non-collective character of the experimentally assigned $K=0$ states or a serious flaw of the model in the second minimum. More data on the $K=0$, $I^{\pi}=1^-$ collective states in the second minima of other nuclei are necessary to resolve this issue.