The root mean square matter radii of halo nuclei provide a basic measu
re in constructing, constraining, and assessing theoretical models of
halo structures. We consider corrections to static density (optical li
mit) Glauber model calculations of reaction cross sections of such nuc
lei at high energy giving careful consideration to their intrinsic few
-body structure and the adiabatic nature of the halo nucleus-target in
teraction. We take as important examples the loosely bound two- and th
ree-body systems Be-11, He-6, Li-11, and Be-14. The contribution of th
e valence particles to the calculated reaction cross sections are show
n to be significantly reduced, requiring increased halo radii to repro
duce experimental data. The implications of these changes for structur
e models of extended two- and three-body systems are discussed.