  Background: Breakup reactions are often used to probe the nuclear structure
of halo nuclei. The eikonal model diverges for Coulomb breakup since it relies
on the adiabatic approximation. To correct this weakness, a Coulomb-corrected
eikonal method (CCE) using the Coulomb first-order-perturbation approximation
was developed.
  Purpose: Since the CCE mixes two reaction models and treats the Coulomb and
nuclear interactions on different footings, we study here an alternative
approach. We develop a simplification to the dynamical eikonal approximation
(S-DEA) which has a similar numerical cost as the usual eikonal model, and
study its efficiency for both nuclear- and Coulomb-dominated breakup reactions.
  Methods: We compare the energy and parallel-momentum cross sections obtained
with the dynamical eikonal approximation, the usual eikonal approximation, the
CCE and the S-DEA.
  Results: The S-DEA leads to precise energy distributions for both breakup
reactions. The corresponding parallel-momentum distributions obtained with the
S-DEA are improved compared to the ones computed with the eikonal model. It is
more efficient for nuclear-dominated breakup than the CCE since it reproduces
better the shape and magnitude of the distribution. However, for the Coulomb
breakup, the distribution lacks asymmetry.
  Conclusions: The simplification of the DEA developed in this work improves
significantly the eikonal descriptions of breakup energy distribution for both
Coulomb- and nuclear-dominated reactions. The asymmetry of the
parallel-momentum distribution is enhanced for nuclear-dominated breakup. This
study confirms that the asymmetry is due to dynamical effects. A direct
prospect of this work would be to extend this model to two-neutron halo-nucleus
projectiles.
