Interaction cross sections (sigma(1)) for Me isotopes from the stability line to the vicinity of the neutron drip line have been measured at around 240 MeV/nucleon using BigRIPS at RIBF, RIKEN, The sigma(1) for Ne27-32 in every case exceed the systematic mass-number dependence of sigma(1) for stable nuclei, which can be explained by considering the nuclear deformation. In particular the sigma(1) for Ne-29 and Ne-31 are significantly greater than those of their neighboring nuclides. These enhancements of sigma(1) for Ne-29 and Ne-31 cannot be explained by a single-particle model calculation under the assumption that the valence neutron of Ne-29 (Ne-31) occupies the 0d(3/2) (0f(7/2)) orbital, as expected from the standard spherical shell ordering. The present data suggest an s dominant halo structure of Ne-29 and s- or p-orbital halo in Ne-31. (C) 2011 Elsevier B.V. All rights reserved.