Coupled-channels analyses for large-angle quasi-elastic scattering in massive systems

We discuss in detail the coupled-channels approach for the large-angle quasi-elastic scattering in massive systems, where many degrees of freedom may be involved in the reaction. We especially investigate the effects of single, double and triple phonon excitations on the quasi-elastic scattering for $^{48}$Ti,$^{54}$Cr,$^{56}$Fe,$^{64}$Ni and $^{70}$Zn$+^{208}$Pb systems, for which the experimental cross sections have been measured recently. We show that the present coupled-channels calculations well account for the overall width of the experimental barrier distribution for these systems. In particular, it is shown that the calculations taking into account single quadrupole phonon excitations in $^{48}$Ti and triple octupole phonon excitations in $^{208}$Pb reasonably well reproduce the experimental quasi-elastic cross section and barrier distribution for the $^{48}$Ti$+^{208}$Pb reaction. On the other hand, $^{54}$Cr,$^{56}$Fe,$^{64}$Ni and $^{70}$Zn$+^{208}$Pb systems seem to require the double quadrupole phonon excitations in the projectiles in order to reproduce the experimental data.