  The $^{10}$B+$^{120}$Sn reaction has been systematically studied at
laboratory energies around the Coulomb barrier: E$_{\rm LAB}=$31.5, 33.5, 35.0,
and 37.5 MeV. Cross sections for the elastic scattering and some reaction
processes have been measured: excitation to the $1^+$ state of $^{10}$B;
excitation to the $2^+$ and $3^-$ states of $^{120}$Sn; and the one-neutron
pick-up transfer $^{120}$Sn($^{10}$B,$^{11}$B)$^{119}$Sn. Coupled reaction
channel (CRC) calculations have been performed in the context of the
double-folding S\~ao Paulo potential. The theoretical calculations result in a
good overall description of the experimental angular distributions. The effect
on the theoretical elastic-scattering angular distributions of couplings to the
inelastic and transfer states (through the CRC calculations) and to the
continuum states (through continuum-discretized coupled-channels calculations)
has been investigated.
