The direct $\gamma$ decays of the giant dipole resonance (GDR) and the giant quadrupole resonance (GQR) of ${}^{208}\mathrm{Pb}$ to low-lying states are investigated by means of a microscopic self-consistent model. The model considers effects beyond the linear response approximation. The experimental $\gamma$-decay widths from GQR to the first $3^{-}$ state and the low-lying dipole states are well reproduced with the Skyrme interaction SkP. The strong sensitivity of $\gamma$ decay to the isospin of the involved states is proven. By comparing the decay widths between GDR to $2_1^{+}$ and GQR to $3_1^{-}$, a much larger weight of the $3_1^{-}$ component in the GQR wave function of ${}^{208}\mathrm{Pb}$ is deduced, with respect to the weight of the $2_1^{+}$ component in the GDR wave function. Thus, we have shown that $\gamma$ decay is a unique probe of the resonance wave functions, and a test ground for nuclear structure models.

• Received 23 July 2020
• Revised 6 May 2021
• Accepted 7 June 2021

DOI:https://doi.org/10.1103/PhysRevC.103.064321