Projectile fragmentation reactions are well suited to structure studies of
weakly hound nuclei, hut an accurate reaction theory is necessary to extrac
t quantitative spectroscopic properties. We examine here the accuracy of th
e commonly used eikonal approximation for the nuclear-induced breakup of ha
lo nuclei. Comparing to numerical solutions of the full time-dependent Schr
odinger equation, we find that the eikonal remains fairly accurate for calc
ulating breakup probabilities of halo nuclei even down to 20 MeV/nucleon, r
eproducing relative spectroscopic strengths to within a few percent. Absolu
te reaction probabilities tend to be underpredicted by the eikonal, which w
ould make extracted spectroscopic strengths somewhat too high. We discuss o
ther features that are seen in the full calculation but are missing in the
eikonal approximation such as the "towing" mode.