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Pairing correlations and odd-even staggering in reaction cross sections of weakly bound nuclei

We investigate the odd-even staggering (OES) in reaction cross sections of weakly bound nuclei with a Glauber theory, taking into account the pairing correlation with the Hartree-Fock-Bogoliubov (HFB) method. We first discuss the pairing gap in extremely weakly bound nuclei and show that the pairing gap persists in the limit of zero separation energy limit even for single-particle orbits with the orbital angular momenta $l=0$ and $l=1$. We then introduce the OES parameter defined as the second derivative of reaction cross sections with respect to the mass number, and clarify the relation between the magnitude of OES and the neutron separation energy. We find that the OES parameter increases considerably in the zero separation energy limit for $l=0$ and $l=1$ single-particle states, while no increase is found for higher angular momentum orbits with {\it e.g.,} $l=3$. We point out that the increase of OES parameter is also seen in the experimental reaction cross sections for Ne isotopes, which is well accounted for by our calculations.