Background: The electric isovector giant dipole resonance (IVGDR) in ${}^{208}\mathrm{Pb}$ has been measured with high energy resolution with the $(p,p^{\prime })$ reaction under extreme forward angles [A. Tamii et al., Phys. Rev. Lett. 107, 062502 (2011)] and shows considerable fine structure.

Purpose: The aim of the present work is to extract scales characterizing the observed fine structure and to relate them to dominant decay mechanisms of giant resonances. Furthermore, the level density of $J^{\pi }=1^{-}$ states is determined in the energy region of the IVGDR.

Methods: Characteristic scales are extracted from the spectra with a wavelet analysis based on continuous wavelet transforms. Comparison with corresponding analyses of $B\left(E1\right)$ strength distributions from microscopic model calculations in the framework of the quasiparticle phonon model and the relativistic random phase approximation allows one to identify giant resonance decay mechanisms responsible for the fine structure. The level density of $1^{-}$ states is related to local fluctuations of the cross sections in the energy region of the IVGDR, where contributions from states with other spin parities can be neglected. The magnitude of the fluctuations is determined by the autocorrelation function.

Results: Scales in the fine structure of the IVGDR in ${}^{208}\mathrm{Pb}$ are found at 80, 130, 220, 430, 640, and 960 keV, and at 1.75 MeV. The values of the most prominent scales can be reasonably well reproduced by the microscopic calculations although they generally yield a smaller number of scales. The inclusion of complex configurations in the calculations changes the $E1$ strength distributions but the impact on the wavelet power spectra and characteristic scales is limited. The level density of $1^{-}$ states is extracted in the excitation energy range $9–12.5$ MeV and compared to a variety of phenomenological and microscopic models.

Conclusions: In both models the major scales are already present at the one-particle one-hole level indicating Landau damping as a dominant mechanism responsible for the fine structure of the IVGDR in contrast to the isoscalar giant quadrupole resonance, where fine structure arises from the coupling to low-lying surface vibrations. The back-shifted Fermi gas model parametrization of Rauscher et al., Phys. Rev. C 56, 1613 (1997) describes the level-density data well, while other phenomenological and microscopic approaches fail to reproduce absolute values or the energy dependence or both.

• Received 29 March 2014

DOI:https://doi.org/10.1103/PhysRevC.89.054322