  We examine the validity of surface approximation for breakup reactions using
a fully quantum-mechanical model proposed by Ichimura, Austern, and Vincent
(IAV). Analogous to the semi-classical picture, we introduce radial cut-offs to
scattering waves in the IAV framework, which we refer to as IAV-cut. Systematic
calculations are conducted for nonelastic breakup reactions induced by $^6$Li
and deuterons at various incident energies. A comparison between the results
obtained from IAV and IAV-cut is performed. The excellent agreement observed
between IAV and IAV-cut in $^{6}$Li induced reactions, regardless of incident
energy and target nuclei, signifies their insensitivity to the inner part of
the scattering wave function, thus providing validation for the semi-classical
picture. However, for deuteron induced breakup reactions, the IAV-cut results
exhibit a suppression in the cross section, suggesting a strong dependence on
the interior wave functions. This suppression is further enhanced as the
incident energy increases.

Nuclear Theory