  Background: The eikonal approximation is a high-energy reaction model which
is very computationally efficient and provides a simple interpretation of the
collision. Unfortunately, it is not valid at energies around 10 MeV/nucleon,
the range of energy of HIE-ISOLDE at CERN and the future ReA12 at MSU. Fukui
etal. [Phys. Rev. C 90, 034617 (2014)] have shown that a simple semiclassical
correction of the projectile-target deflection could improve the description of
breakup of halo nuclei on heavy targets down to 20 MeV/nucleon.
  Purpose: We study two similar corrections, which aim at improving the
projectile-target relative motion within the eikonal approximation, with the
goal to extend its range of validity down to 10 MeV/nucleon in
nuclear-dominated collisions, viz. on light targets. The semiclassical
correction substitutes the impact parameter by the distance of closest approach
of the corresponding classical trajectory. The exact continued $S$-matrix
correction replaces the eikonal phase by the exact phase shift. Both
corrections successfully describe the elastic scattering of one-neutron halo
nuclei.
  Method: We extend these corrections and study their efficiency in describing
the breakup channel. We evaluate them in the case of $^{11}\mathrm{Be}$
impinging on $^{12}\mathrm{C}$ at 20 and 10 MeV/nucleon.
  Results: Albeit efficient to reproduce the elastic channel, these corrections
do not improve the description of the breakup of halo nuclei within the eikonal
approximation down to 20 MeV/nucleon.
  Conclusions: Our analysis of these corrections shows that improving the
projectile-target relative motion is not the ultimate answer to extend the
eikonal approximation down to low energies. We suggest another avenue to reach
this goal.
