The isospin properties and the collectivity of the pygmy dipole resonance (PDR) are longstanding open questions in nuclear structure studies. To answer these questions, the $\gamma$ decay of PDR states in ${}^{208}\mathrm{Pb}$ to the low-lying $2_1^{+}$ state is investigated using the Skyrme particle-vibration coupling model. It is found that the $E1 \gamma$ decay from the PDR states to the low-lying $2_1^{+}$ state is strongly suppressed compared to that from the isovector giant dipole resonance (IVGDR), which reveals the predominantly isoscalar character of PDR. A detailed decomposition of the decay diagrams of the amplitudes of the processes contributing to the decay demonstrates the non-negligible presence of the one-particl–one-hole configurations coupled to the $2_1^{+}$ phonon in the PDR wave function. Furthermore, we give a quantitative way to identify the components of complex-configurations in the wave function, and it is found that such component in PDR is smaller than that in IVGDR and much smaller than that in isoscalar giant quadrupole resonance (ISGQR). However, by analyzing the $E2 \gamma$ decay of the PDR and IVGDR to the $3_1^{-}$ state, we find that the $3_1^{-}$ phonon component is larger in the PDR wave function than in the IVGDR.

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• Electromagnetic transitions
• Giant resonances
• Nuclear decay
• Nuclear density functional theory
• Nuclear many-body theory