Noncollective excitations in low-energy heavy-ion reactions: Applicability of the random-matrix model

We investigate the applicability of a random-matrix model to the description of noncollective excitations in heavy-ion reactions around the Coulomb barrier. To this end, we study fusion in the reaction ${}^{16}$O + ${}^{208}$Pb, taking account of the known noncollective excitations in the ${}^{208}$Pb nucleus. We show that the random-matrix model for the corresponding couplings reproduces reasonably well the exact calculations, obtained using empirical deformation parameters. This implies that the model may provide a powerful method for systems in which the noncollective couplings are not so well known.

Figure 1

The number of levels of the ${}^{208}$Pb nucleus up to the excitation energy $\epsilon$ as a function of $\epsilon$. The histogram represents the experimental data [26], while the dashed line shows its fit with a polynomial function up to the sixth order.

Figure 2

The continuous level density for ${}^{208}$Pb obtained as a first derivative of the fitting function $f\left(\epsilon \right)$ shown in Fig. 1.

Figure 3

The strength distributions for ${}^{208}$Pb as a function of excitation energy $\epsilon$. The dashed line shows the distribution of the experimental deformation parameters, while the solid line is obtained based on the random-matrix model using Eq. (9). Both distributions are smeared with a Gaussian function with a width of 0.15 MeV. An overall scaling factor is introduced to the dashed line as the dimension is different between the two curves (see text).

Figure 4

(a), (b) Fusion cross sections ${\sigma }_{\mathrm{fus}}$ and (c) fusion barrier distributions $D_{\mathrm{fus}}\left(E\right)=d^{2}E{\sigma }_{\mathrm{fus}}\left(E\right)d{E}^2$ for the ${}^{16}$O + ${}^{208}$Pb system obtained from three different calculations. Dashed lines show results obtained with the experimental, noncollective deformation parameters, whereas the solid lines are obtained from the random-matrix model. Dotted lines result from calculations that include only the ${}^{208}$Pb collective excitations.