The low-energy octupole $3^{-}$ state of ${}^{208}\mathrm{Pb}$ is investigated within the framework of the nuclear shell model with realistic nucleon-nucleon interactions. It is shown that the large correlation energy of this state is essentially due to the scattering of fully-aligned nucleon pairs, with the dominant role played by the scattering of high angular momentum fully-aligned neutron-proton pairs. A large fragmentation of the one-particle one-hole wave function, together with the coherence of the wave function, leads to the collective character of the octupole state. This coherence is shown to be a generic property of yrast natural-parity eigenstates of the nuclear many-body Hamiltonian. It induces a constructive accumulation of interaction strength, which may lead to a significant fragmentation of the wave function and a large correlation energy. Electric transitions from the octupole state to the ground state also benefit from this coherence property, resulting in a large enhancement of the transition probability.

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• Collective levels
• Nuclear physics of explosive environments
• Nuclear structure & decays
• 190 ≤ A ≤ 219
• Shell model