Role of noncollective excitations in heavy-ion fusion reactions and quasi-elastic scattering around the Coulomb barrier

Despite the supposed simplicity of double-closed shell nuclei, conventional coupled-channels calculations, that include all of the known collective states of the target and projectile, give a poor fit to the fusion cross section for the ${}^{16}$O + ${}^{208}$Pb system. The discrepancies are highlighted through the experimental barrier distribution and logarithmic derivative, that are both well defined by the precise experimental fusion data available. In order to broaden our search for possible causes for this anomaly, we revisit this system and include in our calculations a large number of noncollective states of the target, whose spin, parity, excitation energy, and deformation parameter are known from high-precision proton inelastic-scattering measurements. Although the new coupled-channels calculations modify the barrier distribution, the disagreement with experiment remains both for fusion and for quasi-elastic (QE) scattering. We find that the $Q$-value distributions for large-angle QE scattering become rapidly more important as the incident energy increases, reflecting the trend of the experimental data. The mass-number dependence of the noncollective excitations is discussed.

Figure 1

The fusion cross sections [Figs. 1a and 1b], the fusion barrier distribution, $D_{\mathrm{fus}}=d^2\left(E{\sigma }_{\mathrm{fus}}\right)/d{E}^2$, [Fig. 1c], and the logarithmic slope, $L\left(E\right)=d\left[\ln \left(E{\sigma }_{\mathrm{fus}}\right)\right]/dE$, [Fig. 1d], for the ${}^{16}$O + ${}^{208}$Pb reaction. The fusion cross sections are plotted both on linear and logarithmic scales in Figs. 1a and 1b, respectively. The dashed lines are obtained by taking into account only the collective excitations of ${}^{16}$O and ${}^{208}$Pb, while the dot-dashed lines take into account the non-collective excitations of ${}^{208}$Pb in addition to the collective excitations. The solid lines are the same as the dot-dashed lines, but shifted in energy. The experimental data are taken from Refs. [25, 26].

Figure 2

Quasi-elastic scattering cross sections [Fig. 2a] and the quasi-elastic barrier distribution [Fig. 2b] for the ${}^{16}$O + ${}^{208}$Pb system. The meaning of each line is the same as in Fig. 1. Data are taken from Ref. [28].

Figure 3

Same as Fig. 1, but with the double octupole phonon excitations.

Figure 4

Same as Fig. 2, but with the double octupole phonon excitations.

Figure 5

The Q-value spectra for the quasi-elastic scattering at ${\theta }_{\mathrm{c}.\mathrm{m}.}$ = 170${}^{\circ }$ for the ${}^{16}$O + ${}^{208}$Pb system for six different incident energies. The dashed peaks correspond to the collective excitations while the solid peaks correspond to the non-collective excitations. The solid line is obtained by smearing the peaks with a gaussian function.

Figure 6

Fusion cross section and fusion barrier distribution for the ${}^{32}$S + ${}^{208}$Pb system. The meaning of each line is the same as in Fig. 1. The experimental data are taken from Ref. [28].

Figure 7

Fusion cross section and fusion barrier distribution for the ${}^{40}$Ca + ${}^{208}$Pb system. The meaning of each line is the same as in Fig. 1.