Fine structure has been shown to be a general phenomenon of nuclear giant resonances of different multipolarities over a wide mass range. In this article we assess various techniques that have been proposed to extract quantitative information from the fine structure in terms of characteristic scales. These include the so-called local scaling dimension, the entropy index method, Fourier analysis, and continuous and discrete wavelet transforms. As an example, results on the isoscalar giant quadrupole resonance in ${}^{208}\mathrm{Pb}$ from high-energy-resolution inelastic proton scattering and calculations with the quasiparticle-phonon model are analyzed. Wavelet analysis, both continuous and discrete, of the spectra is shown to be a powerful tool to extract the magnitude and localization of characteristic scales.

• Received 10 September 2007

DOI:https://doi.org/10.1103/PhysRevC.77.024302