Spreading widths of giant resonances in spherical nuclei: Damped transient response

We propose a general approach to describe spreading widths of monopole, dipole, and quadrupole giant resonances in heavy and superheavy spherical nuclei. Our approach is based on the ideas of the random matrix distribution of the coupling between one-phonon and two-phonon states generated in the random-phase approximation. We use the Skyrme interaction SLy4 as our model Hamiltonian to create a single-particle spectrum and to analyze excited states of the doubly magic nuclei ${}^{132}\mathrm{Sn}, {}^{208}\mathrm{Pb}$, and ${}^{310}126$. Our results demonstrate that the approach enables to us to describe a gross structure of the spreading widths of the giant resonances considered.

Figure 1

${}^{208}\mathrm{Pb}$: (a) experimental $B\left(E1\right)$ strength distribution. (b) Comparison of the results obtained by means of the microscopic (dotted line) and the random (solid line) coupling matrix elements between the one- and two-phonon configurations. (c) $B\left(E1\right)$ strength distribution for one-phonon states (dashed line) and for the PPC case. The smoothing parameter 1 MeV is used for the strength distribution described by the Lorentzian function. The experimental data are taken from Ref. [28].

Figure 2

The same as Fig. 1, in the case of ISGMR in ${}^{208}\mathrm{Pb}$. The experimental data are taken from Ref. [31].

Figure 3

$B\left(E1\right)$ strength distribution of ${}^{208}\mathrm{Pb}$: comparison of the results obtained by means of the random coupling matrix elements between the one- and two-phonon configurations. Results are shown of the calculations [see Eqs. (1) and (2)] with the energies ${\omega }_{{\lambda }_1{i}_1}+{\omega }_{{\lambda }_2{i}_2}$ (solid line) and with random GOE-generated two-phonon energies (dashed line). The smoothing parameter 1 MeV is used for the strength distribution described by the Lorentzian function.