We present the results of a high-precision quasi-elastic excitation function measurement for the 48Ca + 120Sn system at θLAB = 160° at near-barrier energies in steps of 1.0 MeV. The corresponding quasi-elastic barrier distribution is derived. A large-scale coupled-channel calculation was performed to investigate the role of several reaction channels in the reaction mechanism. An excellent agreement between theory and data was obtained for the barrier distribution. The first quadrupole vibrations of the 48Ca and 120Sn, the 2n, and the 4He transfers have a strong influence on the reaction mechanism and are responsible for the good agreement achieved. The 1n transfer has a minor importance in the result when compared with the 2n transfer, which suggests that the pairing correlation might play an important role in the 2n-neutron transfer process. However, if the octupole vibration of the projectile is included in the coupling scheme, the agreement with the data gets worse. The comparison of the coupled-channel calculations with experimental data leads to the conclusion that the nuclear matter diffuseness of the 48Ca nucleus is 0.56 fm in agreement with most of the double-magic nuclei.