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The root mean square matter radii of halo nuclei provide a basic measure in constructing, constraining, and assessing theoretical models of halo structures. We consider corrections to static density ͑optical limit͒ Glauber model calculations of reaction cross sections of such nuclei at high energy giving careful consideration to their intrinsic few-body structure and the adiabatic nature of the halo nucleus-target interaction. We take as important examples the loosely bound two-and three-body systems 11 Be, 6 He, 11 Li, and 14 Be. The contribution of the valence particles to the calculated reaction cross sections are shown to be significantly reduced, requiring increased halo radii to reproduce experimental data. The implications of these changes for structure models of extended two-and three-body systems are discussed. ͓S0556-2813͑96͒04810-8͔

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