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

We discuss in detail the coupled-channels approach for 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 ⁴⁸Ti, ⁵⁴Cr, ⁵⁶Fe, ⁶⁴Ni, and ⁷⁰Zn+²⁰⁸Pb 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 excitation in ⁴⁸Ti and triple-octupole phonon excitations in ²⁰⁸Pb reasonably well reproduce the experimental quasi-elastic cross section and barrier distribution for the ⁴⁸Ti+²⁰⁸Pb reaction. However, ⁵⁴Cr, ⁵⁶Fe, ⁶⁴Ni, and ⁷⁰Zn+²⁰⁸Pb systems seem to require the double-quadrupole phonon excitations in the projectiles to reproduce the experimental data.