  We re-examine the matter radii of diffuse halo nuclei, as deduced from
reaction cross section measurements at high energy. Careful consideration is
given to the intrinsic few-body structure of these projectiles and the
adiabatic nature of the projectile-target interaction. Using $^{11}$Li,
$^{11}$Be and $^{8}$B as examples we show that data require significantly
larger matter radii than previously reported. The revised value for $^{11}$Li
of 3.55 fm is consistent with three-body models with significant $1s$-intruder
state components, which reproduce experimental $^{9}$Li momentum distributions
following $^{11}$Li breakup, but were hitherto thought to be at variance with
cross section data.
