Abstract
A model is proposed for a description of the octupole vibrational states based on the nuclear shell model. In this model, a one-octupole-phonon representing the collective octupole vibration across the magic core is introduced onto the shell-model states that are microscopically calculated within the valence nucleon space. With this model, a unified description is now possible for the pure shell-model states made by valence nucleons, and the octupole-phonon states excited on the shell-model states. The model is applied to various nuclei around the $^{208}\mathrm{Pb}$ nucleus. Energy levels and electric octupole transition probabilities are well reproduced for both the pure shell-model states and the octupole vibrational states.
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