We analyze thoroughly the statistical properties of the $1^{-}$ spectrum in energy interval 9.5–18.5 MeV for ${}^{206}\mathrm{Hg}, {}^{204,206,208}\mathrm{Pb}$, and ${}^{210}\mathrm{Po}$ nuclei. To this aim we use the Skyrme interaction SLy4 and the volume pairing interaction, treated in the BCS approximation, as our model Hamiltonian to create a single-particle spectrum and to analyze excited states. The excited states are obtained in the quasiparticle random phase approximation taking into account the coupling between one- and two-phonon states. The obtained spectra (studied by means of the nearest-neighbour spacing distribution, ${\mathrm{\Delta }}_3$–statistics and the Porter-Thomas distribution) indicate on the onset of statistical properties close to those of the Gaussian Orthogonal Ensembles. The comparison of the results, obtained with the aid of the coupling calculated microscopically and by means of the Gaussian random distribution, demonstrates a close similarity in the description of the spreading widths of the Isovector Dipole Giant Resonanse of the considered nuclei. Furthermore, we show that employing the random distribution for the coupling between microscopic one-phonon states and two-phonon states, generated by the Gaussian Orthogonal Ensembles distribution, a good agreement is also obtained with the microscopic description of the decay widths.

• Received 21 August 2018

DOI:https://doi.org/10.1103/PhysRevC.98.044319