Neutron scattering off neutron halos can provide important information about the internal structure of nuclei close to the neutron drip line. In this work, we use halo effective field theory to study the s-wave scattering of a neutron and the spin-parity JP=12+ one-neutron halo nuclei Be11, C15, and C19 at leading order. In the J=1 channel, the only inputs to the Faddeev equations are their
... [Show full abstract] one-neutron separation energies. In the J=0 channel, the neutron-neutron scattering length and the two-neutron separation energies of Be12, C16, and C20 enter as well. The numerical results show that the total s-wave cross sections in the J=1 channel at threshold are of the order of a few barns. In the J=0 channel, these cross sections are of the order of a few barns for n−Be11 and n−C19 scattering, and about 60 mb for the n−C15 scattering. The appearance of a pole in pcotδ close to zero in all three cases indicates the existence of a virtual Efimov state close to threshold in each of the Be12, C16, and C20 systems. Observation of this pole would confirm the presence of Efimov physics in halo nuclei. The dependence of the results on the neutron-core scattering length is also studied.