The halo nuclei 1 1 Be and 1 1 Li have been studied in core-breakup reactions where the halo neutrons are expected to be released without a major distortion due to the reaction. The widths of the halo-neutron momentum distributions have been extracted in coincidence with He fragments, Γ = 32 +/- 4 MeV/c, and Li fragments, Γ = 42 +/- 4 MeV/c for 1 1 Be and with He fragments, Γ = 42 +/- 6 MeV/c for 1 1 Li. The 1 1 Be breakup gives a very low neutron multiplicity of 0.38+/-0.09 which is a manifestation of the shadowing of the neutron in the core-breakup reaction. This value can be understood from a simple theoretical calculation, which also accounts for the observed transverse momentum widths at small angles.